derivate_prof_fagiano.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "derivate_prof_fagiano.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyO5v6bZ+iAJHD/TwleZY20P",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/giuliovv/trajectory_planning/blob/master/derivate_prof_fagiano.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "rqgokKyhEcZp"
      },
      "outputs": [],
      "source": [
        "import sympy\n",
        "from sympy import Symbol, Sum, IndexedBase, Matrix\n",
        "from sympy.parsing.sympy_parser import parse_expr"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = IndexedBase(\"alpha\", \"i\")\n",
        "xr = IndexedBase(\"x_r\", \"i\")\n",
        "yr = IndexedBase(\"y_r\", \"i\")\n",
        "xl = IndexedBase(\"x_l\", \"i\")\n",
        "yl = IndexedBase(\"y_l\", \"i\")\n",
        "\n",
        "x = IndexedBase(\"x\", \"i\")\n",
        "y = IndexedBase(\"y\", \"i\")\n",
        "\n",
        "kp = Symbol(\"k_p\")\n",
        "kl = Symbol(\"k_l\")\n",
        "\n",
        "i = Symbol(\"i\")\n",
        "N = Symbol(\"N\")\n",
        "\n",
        "g = Symbol(\"gamma\")"
      ],
      "metadata": {
        "id": "hSxBgmoTEuoO"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "Oa8GQ_2sI4VL"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def print_latex(text, title=\"\", fontsize=40):\n",
        "  lat = sympy.latex(text)\n",
        "\n",
        "  #add text                                                                       \n",
        "  plt.text(0, 0.5, r\"$%s = %s$\" % (title, lat), fontsize=fontsize)                                  \n",
        "\n",
        "  # #hide axes                                                                      \n",
        "  fig = plt.gca()\n",
        "  fig.axis('off')\n",
        "  plt.draw()"
      ],
      "metadata": {
        "id": "kBs5YVGtIsZ4"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Formulation"
      ],
      "metadata": {
        "id": "DhltFliTIthO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[x[i-1], y[i-1], 1], [x[i], y[i], 1], [x[i+1], y[i+1], 1]])\n",
        "A"
      ],
      "metadata": {
        "id": "vSYpU9J5FJHf",
        "outputId": "d1ca0327-ded8-4f94-f9d9-cbceba1861b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        }
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}{x}_{i - 1} & {y}_{i - 1} & 1\\\\{x}_{i} & {y}_{i} & 1\\\\{x}_{i + 1} & {y}_{i + 1} & 1\\end{matrix}\\right]$",
            "text/plain": [
              "Matrix([\n",
              "[x[i - 1], y[i - 1], 1],\n",
              "[    x[i],     y[i], 1],\n",
              "[x[i + 1], y[i + 1], 1]])"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = Matrix([x[i-1]**2+y[i-1]**2, x[i]**2+y[i]**2, x[i+1]**2+y[i+1]**2])\n",
        "b"
      ],
      "metadata": {
        "id": "A7x5derwFcVw",
        "outputId": "9e8751e2-bc53-43dc-8c12-65a3cccaea5f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        }
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}{x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\\\{x}_{i}^{2} + {y}_{i}^{2}\\\\{x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\end{matrix}\\right]$",
            "text/plain": [
              "Matrix([\n",
              "[x[i - 1]**2 + y[i - 1]**2],\n",
              "[        x[i]**2 + y[i]**2],\n",
              "[x[i + 1]**2 + y[i + 1]**2]])"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "param = A.inv()*b\n",
        "param"
      ],
      "metadata": {
        "id": "oNw9RwluFuZE",
        "outputId": "ae75af9e-c55d-464e-b884-f19f265c0071",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 110
        }
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left({y}_{i - 1} - {y}_{i}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right) \\left(- {y}_{i + 1} + {y}_{i}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i}^{2} + {y}_{i}^{2}\\right) \\left({y}_{i + 1} - {y}_{i - 1}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}}\\\\\\frac{\\left(- {x}_{i + 1} + {x}_{i - 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i + 1} - {x}_{i}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left(- {x}_{i - 1} + {x}_{i}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}}\\\\\\frac{\\left({x}_{i + 1} {y}_{i - 1} - {x}_{i - 1} {y}_{i + 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left(- {x}_{i + 1} {y}_{i} + {x}_{i} {y}_{i + 1}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i - 1} {y}_{i} - {x}_{i} {y}_{i - 1}\\right) \\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}}\\end{matrix}\\right]$",
            "text/plain": [
              "Matrix([\n",
              "[                                              (x[i + 1]**2 + y[i + 1]**2)*(y[i - 1] - y[i])/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i - 1]**2 + y[i - 1]**2)*(-y[i + 1] + y[i])/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i]**2 + y[i]**2)*(y[i + 1] - y[i - 1])/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])],\n",
              "[                                             (-x[i + 1] + x[i - 1])*(x[i]**2 + y[i]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i + 1] - x[i])*(x[i - 1]**2 + y[i - 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i + 1]**2 + y[i + 1]**2)*(-x[i - 1] + x[i])/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])],\n",
              "[(x[i + 1]*y[i - 1] - x[i - 1]*y[i + 1])*(x[i]**2 + y[i]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (-x[i + 1]*y[i] + x[i]*y[i + 1])*(x[i - 1]**2 + y[i - 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i - 1]*y[i] - x[i]*y[i - 1])*(x[i + 1]**2 + y[i + 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])]])"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "center = Matrix([param[0]/2, param[1]/2])\n",
        "center"
      ],
      "metadata": {
        "id": "l1sYXdc9Fx28",
        "outputId": "6398dab4-01d6-421e-972b-abbb67f4099b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left({y}_{i - 1} - {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right) \\left(- {y}_{i + 1} + {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i}^{2} + {y}_{i}^{2}\\right) \\left({y}_{i + 1} - {y}_{i - 1}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\\\\\frac{\\left(- {x}_{i + 1} + {x}_{i - 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1} - {x}_{i}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left(- {x}_{i - 1} + {x}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\end{matrix}\\right]$",
            "text/plain": [
              "Matrix([\n",
              "[ (x[i + 1]**2 + y[i + 1]**2)*(y[i - 1] - y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i - 1]**2 + y[i - 1]**2)*(-y[i + 1] + y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i]**2 + y[i]**2)*(y[i + 1] - y[i - 1])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]))],\n",
              "[(-x[i + 1] + x[i - 1])*(x[i]**2 + y[i]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1] - x[i])*(x[i - 1]**2 + y[i - 1]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1]**2 + y[i + 1]**2)*(-x[i - 1] + x[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]))]])"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "radius = sympy.sqrt(center[0]**2+center[1]**2+param[2])\n",
        "radius"
      ],
      "metadata": {
        "id": "cMuQ02KjIKZy",
        "outputId": "37c2e0d2-3fbc-4612-aa19-2941e5c784d9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 95
        }
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\sqrt{\\frac{\\left({x}_{i + 1} {y}_{i - 1} - {x}_{i - 1} {y}_{i + 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left(- {x}_{i + 1} {y}_{i} + {x}_{i} {y}_{i + 1}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i - 1} {y}_{i} - {x}_{i} {y}_{i - 1}\\right) \\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\left(\\frac{\\left(- {x}_{i + 1} + {x}_{i - 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1} - {x}_{i}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left(- {x}_{i - 1} + {x}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\right)^{2} + \\left(\\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left({y}_{i - 1} - {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right) \\left(- {y}_{i + 1} + {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i}^{2} + {y}_{i}^{2}\\right) \\left({y}_{i + 1} - {y}_{i - 1}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\right)^{2}}$",
            "text/plain": [
              "sqrt((x[i + 1]*y[i - 1] - x[i - 1]*y[i + 1])*(x[i]**2 + y[i]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (-x[i + 1]*y[i] + x[i]*y[i + 1])*(x[i - 1]**2 + y[i - 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i - 1]*y[i] - x[i]*y[i - 1])*(x[i + 1]**2 + y[i + 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + ((-x[i + 1] + x[i - 1])*(x[i]**2 + y[i]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1] - x[i])*(x[i - 1]**2 + y[i - 1]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1]**2 + y[i + 1]**2)*(-x[i - 1] + x[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])))**2 + ((x[i + 1]**2 + y[i + 1]**2)*(y[i - 1] - y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i - 1]**2 + y[i - 1]**2)*(-y[i + 1] + y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i]**2 + y[i]**2)*(y[i + 1] - y[i - 1])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])))**2)"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rho = 1/radius\n",
        "rho"
      ],
      "metadata": {
        "id": "JyZw_riLIW73",
        "outputId": "d92e20bb-f8aa-404b-a357-102d1286d72a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 109
        }
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{1}{\\sqrt{\\frac{\\left({x}_{i + 1} {y}_{i - 1} - {x}_{i - 1} {y}_{i + 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left(- {x}_{i + 1} {y}_{i} + {x}_{i} {y}_{i + 1}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\frac{\\left({x}_{i - 1} {y}_{i} - {x}_{i} {y}_{i - 1}\\right) \\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right)}{{x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}} + \\left(\\frac{\\left(- {x}_{i + 1} + {x}_{i - 1}\\right) \\left({x}_{i}^{2} + {y}_{i}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1} - {x}_{i}\\right) \\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left(- {x}_{i - 1} + {x}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\right)^{2} + \\left(\\frac{\\left({x}_{i + 1}^{2} + {y}_{i + 1}^{2}\\right) \\left({y}_{i - 1} - {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i - 1}^{2} + {y}_{i - 1}^{2}\\right) \\left(- {y}_{i + 1} + {y}_{i}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)} + \\frac{\\left({x}_{i}^{2} + {y}_{i}^{2}\\right) \\left({y}_{i + 1} - {y}_{i - 1}\\right)}{2 \\left({x}_{i + 1} {y}_{i - 1} - {x}_{i + 1} {y}_{i} - {x}_{i - 1} {y}_{i + 1} + {x}_{i - 1} {y}_{i} + {x}_{i} {y}_{i + 1} - {x}_{i} {y}_{i - 1}\\right)}\\right)^{2}}}$",
            "text/plain": [
              "1/sqrt((x[i + 1]*y[i - 1] - x[i - 1]*y[i + 1])*(x[i]**2 + y[i]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (-x[i + 1]*y[i] + x[i]*y[i + 1])*(x[i - 1]**2 + y[i - 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + (x[i - 1]*y[i] - x[i]*y[i - 1])*(x[i + 1]**2 + y[i + 1]**2)/(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1]) + ((-x[i + 1] + x[i - 1])*(x[i]**2 + y[i]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1] - x[i])*(x[i - 1]**2 + y[i - 1]**2)/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i + 1]**2 + y[i + 1]**2)*(-x[i - 1] + x[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])))**2 + ((x[i + 1]**2 + y[i + 1]**2)*(y[i - 1] - y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i - 1]**2 + y[i - 1]**2)*(-y[i + 1] + y[i])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])) + (x[i]**2 + y[i]**2)*(y[i + 1] - y[i - 1])/(2*(x[i + 1]*y[i - 1] - x[i + 1]*y[i] - x[i - 1]*y[i + 1] + x[i - 1]*y[i] + x[i]*y[i + 1] - x[i]*y[i - 1])))**2)"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "rho = rho \\\n",
        "    .subs(x[i+1], xr[i+1]+a[i+1]*(xl[i+1]-xr[i+1])) \\\n",
        "    .subs(x[i], xr[i]+a[i]*(xl[i]-xr[i])) \\\n",
        "    .subs(x[i-1], xr[i-1]+a[i-1]*(xl[i-1]-xr[i-1])) \\\n",
        "    .subs(y[i], yr[i]+a[i]*(yl[i]-yr[i])) \\\n",
        "    .subs(y[i+1], yr[i+1]+a[i+1]*(yl[i+1]-yr[i+1])) \\\n",
        "    .subs(y[i-1], yr[i-1]+a[i-1]*(yl[i-1]-yr[i-1])) \\\n",
        "    # + g*sympy.Max(0, a[i]-1) + g*sympy.Min(0, a[i]) # Constraint\n",
        "\n",
        "\n",
        "print_latex(rho, title=\"rho\")"
      ],
      "metadata": {
        "id": "xv7lT7KAIgti",
        "outputId": "20f6b0d7-fdcd-4d95-8cb0-9a3044a62a4d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        }
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Jr = sympy.sqrt(kp)*rho\n",
        "Jr"
      ],
      "metadata": {
        "id": "rbH2VnQ3NuGN",
        "outputId": "6ba3b4ff-f4fc-4ac1-b696-275b9541a80d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 114
        }
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{\\sqrt{k_{p}}}{\\sqrt{\\frac{\\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right)\\right) \\left(\\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right)^{2} + \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right)^{2}\\right)}{\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)} + \\frac{\\left(- \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right)\\right) \\left(\\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right)^{2} + \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)^{2}\\right)}{\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)} + \\frac{\\left(\\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right) \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right)^{2} + \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right)^{2}\\right)}{\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)} + \\left(\\frac{\\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right)^{2} + \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right)^{2}\\right) \\left(- \\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + \\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} - {x_{r}}_{i - 1} + {x_{r}}_{i}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)} + \\frac{\\left(\\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right)^{2} + \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)^{2}\\right) \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} - \\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i + 1} - {x_{r}}_{i}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)} + \\frac{\\left(\\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right)^{2} + \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right)^{2}\\right) \\left(- \\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + \\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} - {x_{r}}_{i + 1} + {x_{r}}_{i - 1}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)}\\right)^{2} + \\left(\\frac{\\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right)^{2} + \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right)^{2}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} - \\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i - 1} - {y_{r}}_{i}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)} + \\frac{\\left(\\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right)^{2} + \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)^{2}\\right) \\left(- \\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + \\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} - {y_{r}}_{i + 1} + {y_{r}}_{i}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)} + \\frac{\\left(\\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right)^{2} + \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right)^{2}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} - \\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i + 1} - {y_{r}}_{i - 1}\\right)}{2 \\left(\\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right) - \\left(\\left({x_{l}}_{i + 1} - {x_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {x_{r}}_{i + 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) - \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) + \\left(\\left({x_{l}}_{i - 1} - {x_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {x_{r}}_{i - 1}\\right) \\left(\\left({y_{l}}_{i} - {y_{r}}_{i}\\right) {\\alpha}_{i} + {y_{r}}_{i}\\right) + \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i + 1} - {y_{r}}_{i + 1}\\right) {\\alpha}_{i + 1} + {y_{r}}_{i + 1}\\right) - \\left(\\left({x_{l}}_{i} - {x_{r}}_{i}\\right) {\\alpha}_{i} + {x_{r}}_{i}\\right) \\left(\\left({y_{l}}_{i - 1} - {y_{r}}_{i - 1}\\right) {\\alpha}_{i - 1} + {y_{r}}_{i - 1}\\right)\\right)}\\right)^{2}}}$",
            "text/plain": [
              "sqrt(k_p)/sqrt((((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]))*(((x_l[i] - x_r[i])*alpha[i] + x_r[i])**2 + ((y_l[i] - y_r[i])*alpha[i] + y_r[i])**2)/(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])) + (-((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]))*(((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])**2 + ((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])**2)/(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])) + (((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])**2 + ((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1])**2)/(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])) + ((((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])**2 + ((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1])**2)*(-(x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + (x_l[i] - x_r[i])*alpha[i] - x_r[i - 1] + x_r[i])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))) + (((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])**2 + ((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])**2)*((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] - (x_l[i] - x_r[i])*alpha[i] + x_r[i + 1] - x_r[i])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))) + (((x_l[i] - x_r[i])*alpha[i] + x_r[i])**2 + ((y_l[i] - y_r[i])*alpha[i] + y_r[i])**2)*(-(x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + (x_l[i - 1] - x_r[i - 1])*alpha[i - 1] - x_r[i + 1] + x_r[i - 1])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))))**2 + ((((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])**2 + ((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1])**2)*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] - (y_l[i] - y_r[i])*alpha[i] + y_r[i - 1] - y_r[i])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))) + (((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])**2 + ((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1])**2)*(-(y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + (y_l[i] - y_r[i])*alpha[i] - y_r[i + 1] + y_r[i])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))) + (((x_l[i] - x_r[i])*alpha[i] + x_r[i])**2 + ((y_l[i] - y_r[i])*alpha[i] + y_r[i])**2)*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] - (y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i + 1] - y_r[i - 1])/(2*(((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]) - ((x_l[i + 1] - x_r[i + 1])*alpha[i + 1] + x_r[i + 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) - ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) + ((x_l[i - 1] - x_r[i - 1])*alpha[i - 1] + x_r[i - 1])*((y_l[i] - y_r[i])*alpha[i] + y_r[i]) + ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i + 1] - y_r[i + 1])*alpha[i + 1] + y_r[i + 1]) - ((x_l[i] - x_r[i])*alpha[i] + x_r[i])*((y_l[i - 1] - y_r[i - 1])*alpha[i - 1] + y_r[i - 1]))))**2)"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gradient"
      ],
      "metadata": {
        "id": "mF5RpmXSNnw9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def to_matlab(der):\n",
        "  return sympy.ccode(der) \\\n",
        "    .replace(\"x_l[i]\", \"leftpoints(idx, 1)\") \\\n",
        "    .replace(\"x_l[i + 1]\", \"leftpoints(idx+1, 1)\") \\\n",
        "    .replace(\"x_r[i]\", \"rightpoints(idx, 1)\") \\\n",
        "    .replace(\"x_r[i + 1]\", \"rightpoints(idx+1, 1)\") \\\n",
        "    .replace(\"y_l[i]\", \"leftpoints(idx, 2)\") \\\n",
        "    .replace(\"y_l[i + 1]\", \"leftpoints(idx+1, 2)\") \\\n",
        "    .replace(\"y_r[i]\", \"rightpoints(idx, 2)\") \\\n",
        "    .replace(\"y_r[i + 1]\", \"rightpoints(idx+1, 2)\") \\\n",
        "    .replace(\"x_l[i - 1]\", \"leftpoints(idx-1, 1)\") \\\n",
        "    .replace(\"y_l[i - 1]\", \"leftpoints(idx-1, 2)\") \\\n",
        "    .replace(\"x_r[i - 1]\", \"rightpoints(idx-1, 1)\") \\\n",
        "    .replace(\"y_r[i - 1]\", \"rightpoints(idx-1, 2)\") \\\n",
        "    .replace(\"alpha[i]\", \"alpha(idx)\") \\\n",
        "    .replace(\"alpha[i + 1]\", \"alpha(idx+1)\") \\\n",
        "    .replace(\"alpha[i - 1]\", \"alpha(idx-1)\") \\\n",
        "    .replace(\"pow\", \"power\")"
      ],
      "metadata": {
        "id": "nr-fDDJ3IxEO"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# d/a\n",
        "gradient_jr = Jr.diff(a[i])\n",
        "gradient_code_jr = to_matlab(gradient_jr)\n",
        "gradient_code_jr"
      ],
      "metadata": {
        "id": "OeyGK1mxNp7b",
        "outputId": "cd3cd186-322c-46f2-d61e-1e72ee9baeaf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'sqrt(k_p)*(-1.0/2.0*((-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) + ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(2*leftpoints(idx, 1) - 2*rightpoints(idx, 1)) + ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(2*leftpoints(idx, 2) - 2*rightpoints(idx, 2)))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) + ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(2*leftpoints(idx, 1) - 2*rightpoints(idx, 1)) + ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(2*leftpoints(idx, 2) - 2*rightpoints(idx, 2)))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(leftpoints(idx, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(2*leftpoints(idx, 1) - 2*rightpoints(idx, 1)) + ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(2*leftpoints(idx, 2) - 2*rightpoints(idx, 2)))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-leftpoints(idx, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(leftpoints(idx, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - rightpoints(idx+1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(leftpoints(idx, 2) - rightpoints(idx, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(leftpoints(idx, 1) - rightpoints(idx, 1)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(-leftpoints(idx, 1) + rightpoints(idx, 1)))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)))/power((((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2), 3.0/2.0)'"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# d/a+1\n",
        "gradient_jr = Jr.diff(a[i+1])\n",
        "gradient_code_jr = to_matlab(gradient_jr)\n",
        "gradient_code_jr"
      ],
      "metadata": {
        "id": "4g0iaWz8N_LV",
        "outputId": "3b5ea738-7ee1-46cd-ece5-5c1970a4a6b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'sqrt(k_p)*(-1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1)) + ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2)))*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*((-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) + ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1)) + ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2)))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(2*leftpoints(idx+1, 1) - 2*rightpoints(idx+1, 1)) + ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(2*leftpoints(idx+1, 2) - 2*rightpoints(idx+1, 2)))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-leftpoints(idx+1, 2) + rightpoints(idx+1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx-1, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*(leftpoints(idx+1, 2) - rightpoints(idx+1, 2)) - ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(leftpoints(idx+1, 1) - rightpoints(idx+1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(-leftpoints(idx+1, 1) + rightpoints(idx+1, 1)))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)))/power((((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2), 3.0/2.0)'"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# d/a-1\n",
        "gradient_jr = Jr.diff(a[i-1])\n",
        "gradient_code_jr = to_matlab(gradient_jr)\n",
        "gradient_code_jr"
      ],
      "metadata": {
        "id": "Q_wnzZiZODKq",
        "outputId": "71abae22-a1ce-4878-f791-52cbb00d2b64",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'sqrt(k_p)*(-1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1)) + ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(2*leftpoints(idx-1, 2) - 2*rightpoints(idx-1, 2)))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) + ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*(((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) - 1.0/2.0*((-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) + ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1)) + ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(2*leftpoints(idx-1, 2) - 2*rightpoints(idx-1, 2)))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)) - 1.0/2.0*((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))))*((((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*(2*leftpoints(idx-1, 1) - 2*rightpoints(idx-1, 1)) + ((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))*(2*leftpoints(idx-1, 2) - 2*rightpoints(idx-1, 2)))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-leftpoints(idx-1, 2) + rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - (-(leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx, 1))*(leftpoints(idx-1, 2) - rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2))*(-leftpoints(idx-1, 1) + rightpoints(idx-1, 1)) - ((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2))*(leftpoints(idx-1, 1) - rightpoints(idx-1, 1)))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/power(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)), 2)))/power((((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (-((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)))*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)))*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*(-(leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) - rightpoints(idx-1, 1) + rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) - (leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx+1, 1) - rightpoints(idx, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*(-(leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + (leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) - rightpoints(idx+1, 1) + rightpoints(idx-1, 1))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2) + power((1.0/2.0)*(power((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1), 2) + power((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2), 2))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) - (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx-1, 2) - rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1), 2) + power((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2), 2))*(-(leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + (leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) - rightpoints(idx+1, 2) + rightpoints(idx, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))) + (1.0/2.0)*(power((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1), 2) + power((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2), 2))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) - (leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx+1, 2) - rightpoints(idx-1, 2))/(((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2)) - ((leftpoints(idx+1, 1) - rightpoints(idx+1, 1))*alpha(idx+1) + rightpoints(idx+1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) - ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) + ((leftpoints(idx-1, 1) - rightpoints(idx-1, 1))*alpha(idx-1) + rightpoints(idx-1, 1))*((leftpoints(idx, 2) - rightpoints(idx, 2))*alpha(idx) + rightpoints(idx, 2)) + ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx+1, 2) - rightpoints(idx+1, 2))*alpha(idx+1) + rightpoints(idx+1, 2)) - ((leftpoints(idx, 1) - rightpoints(idx, 1))*alpha(idx) + rightpoints(idx, 1))*((leftpoints(idx-1, 2) - rightpoints(idx-1, 2))*alpha(idx-1) + rightpoints(idx-1, 2))), 2), 3.0/2.0)'"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    }
  ]
}