heart_example.py

import numpy as np

# 1. Define the Bounding Box
BdBox = [-10, 10, -14, 8]
#
# 2. Create a signed distance function

from pyPolyMesher.dFunctions import dLine, dIntersect, dCircle, dUnion


def SDF2(p, r=5.5):
    """
    Calculate the signed distance from a point P to a heart shape defined by two circles and three line segments.

    The heart shape consists of two circles representing the left and right sides, and three line segments representing the bottom tip and the tangent lines connecting the circles.

    Parameters:
        p (tuple): A tuple containing the coordinates (x, y) of the point P.
        r (float): The radius of the heart shape. Default is 5.5.

    Returns:
        float: The signed distance from the point P to the heart shape. Negative values indicate that the point is inside the heart shape, zero indicates that the point is on the boundary, and positive values indicate that the point is outside the heart shape.

    Note:
        For more information please refer to: https://sadjadabedi.ir/post/constructing-complex-shapes-with-signed-distance-functions-the-heart-example/
    """
    # Some experimental ratio for the center of circles based on their radius
    a = r * 3 / 4

    circle1 = dCircle(p, -a, 0, r)  # Left Circle
    circle2 = dCircle(p, a, 0, r)  # Right Circle

    d2c = np.sqrt(
        (a - 0) ** 2 + (0 - 2 * a - r) ** 2
    )  # Distance from bottom tip to center of circles
    d2t = np.sqrt(d2c**2 - r**2)  # Distance to tangent point of circle

    tpr = find_tangent_point(
        a, 0, r, 0, -2 * a - r, d2t
    )  # Tangent point on right circle

    line1 = dLine(p, -tpr[0], tpr[1], 0, -2 * a - r)
    line2 = dLine(p, 0, -2 * a - r, tpr[0], tpr[1])
    line3 = dLine(p, tpr[0], tpr[1], -tpr[0], tpr[1])

    #    Create a triangle which base is the line that
    #    connects tangent points and the vertex point is heart bottom tip

    dl = dIntersect(line1, line2, line3)

    d = dUnion(circle1, circle2, dl)

    return d


def find_tangent_point(x1, y1, d1, x2, y2, d2):
    """
    Find the tangent point that has radius(d1) distance from center of circle
    and calculated distance (d2) from the bottom tip of the heart. The result is
    limited to desired tangent point.


    Inspired from following gist:
    https://gist.github.com/jupdike/bfe5eb23d1c395d8a0a1a4ddd94882ac?permalink_comment_id=4545858#gistcomment-4545858
    """

    centerdx = x1 - x2
    centerdy = y1 - y2
    R = np.sqrt(centerdx**2 + centerdy**2)

    if not (abs(d1 - d2) <= R <= d1 + d2):
        # No intersections
        return []

    d1d2 = d1**2 - d2**2
    a = d1d2 / (2 * R**2)

    c = np.sqrt(2 * (d1**2 + d2**2) / R**2 - (d1d2**2) / R**4 - 1)

    fx = (x1 + x2) / 2 + a * (x2 - x1)
    gx = c * (y2 - y1) / 2
    # ix1 = fx + gx
    ix2 = fx - gx

    fy = (y1 + y2) / 2 + a * (y2 - y1)
    gy = c * (x1 - x2) / 2
    # iy1 = fy + gy
    iy2 = fy - gy

    return [ix2, iy2]


# 4. Create Domain object
from pyPolyMesher import Domain

NewDomain = Domain("My New Domain", BdBox, SDF2)

# 5. Plot the domain
NewDomain.Plot()

# 6. Generate mesh
from pyPolyMesher import PolyMesher

Node, Element, Supp, Load, P = PolyMesher(NewDomain, 100, 300, anim=False)