Generates a bezier curve, at a given sample-rate.

generate-bezier.js

module.exports = {
    getPoints: getPoints
};

/**
 * Generates a bezier curve at sameple rate nSamples, given an array of points
 * @param   {Number} nSamples
 * @param   {Array<Number>} points
 * @returns {Array<Number>}
 */
function getPoints(nSamples, points) {
    var output = [];
    var xy_items = points.length / 2;
    var pascal_row = pascalsTriangle.getRow(xy_items - 1);

    for (var i = 0; i < nSamples; i++) {
        var t = (1.0 / (nSamples - 1)) * i;
        var sumx = 0;
        var sumy = 0;

        for (var j = 0; j < xy_items; j++) {
            var coef = (
                pascal_row[j] *
                Math.pow(t, j) *
                Math.pow(1 - t, xy_items - (j + 1))
            );

            sumx += coef * points[j * 2];
            sumy += coef * points[j * 2 + 1];
        }

        output.push(sumx);
        output.push(sumy);
    }

    return output;
}

var pascalsTriangle = {
    getRow: function (n) {
        var row = [1];
        var numerator = n;
        var x = 1;
        var l = Math.floor((n / 2) + 1);
        var i;

        // Fill first half of array.
        for (i = 1; i < l; i++, numerator--) {
            x = Math.round((x * numerator) / i);
            row.push(x);
        }

        // Depending on if n is even or odd will determine whether or not we need
        // to read from one space back in row, or two.
        x = n % 2 === 1 ? i - 1 : i - 2;

        // Fill second half of array.
        for (; i <= n; i++, x--) {
            row.push(row[x]);
        }

        return row;
    }
};