bezier.js

//
// interpolates between a set of colors uzing a bezier spline
//

// @requires utils lab
import Color from '../Color.js';
import '../io/lab/index.js';
import scale from './scale.js';

// nth row of the pascal triangle
const binom_row = function (n) {
    let row = [1, 1];
    for (let i = 1; i < n; i++) {
        let newrow = [1];
        for (let j = 1; j <= row.length; j++) {
            newrow[j] = (row[j] || 0) + row[j - 1];
        }
        row = newrow;
    }
    return row;
};

const bezier = function (colors) {
    let I, lab0, lab1, lab2;
    colors = colors.map((c) => new Color(c));
    if (colors.length === 2) {
        // linear interpolation
        [lab0, lab1] = colors.map((c) => c.lab());
        I = function (t) {
            const lab = [0, 1, 2].map((i) => lab0[i] + t * (lab1[i] - lab0[i]));
            return new Color(lab, 'lab');
        };
    } else if (colors.length === 3) {
        // quadratic bezier interpolation
        [lab0, lab1, lab2] = colors.map((c) => c.lab());
        I = function (t) {
            const lab = [0, 1, 2].map(
                (i) =>
                    (1 - t) * (1 - t) * lab0[i] +
                    2 * (1 - t) * t * lab1[i] +
                    t * t * lab2[i]
            );
            return new Color(lab, 'lab');
        };
    } else if (colors.length === 4) {
        // cubic bezier interpolation
        let lab3;
        [lab0, lab1, lab2, lab3] = colors.map((c) => c.lab());
        I = function (t) {
            const lab = [0, 1, 2].map(
                (i) =>
                    (1 - t) * (1 - t) * (1 - t) * lab0[i] +
                    3 * (1 - t) * (1 - t) * t * lab1[i] +
                    3 * (1 - t) * t * t * lab2[i] +
                    t * t * t * lab3[i]
            );
            return new Color(lab, 'lab');
        };
    } else if (colors.length >= 5) {
        // general case (degree n bezier)
        let labs, row, n;
        labs = colors.map((c) => c.lab());
        n = colors.length - 1;
        row = binom_row(n);
        I = function (t) {
            const u = 1 - t;
            const lab = [0, 1, 2].map((i) =>
                labs.reduce(
                    (sum, el, j) =>
                        sum + row[j] * u ** (n - j) * t ** j * el[i],
                    0
                )
            );
            return new Color(lab, 'lab');
        };
    } else {
        throw new RangeError('No point in running bezier with only one color.');
    }
    return I;
};

export default (colors) => {
    const f = bezier(colors);
    f.scale = () => scale(f);
    return f;
};