fonteditor-core/src/math/bezierCubic2Q2.js

fonts (ttf, woff, woff2, eot, svg, otf) parse, write, transform, glyph adjust.

/**
 * @file 三次贝塞尔转二次贝塞尔
 * @author mengke01(kekee000@gmail.com)
 *
 * references:
 * https://github.com/search?utf8=%E2%9C%93&q=svg2ttf
 * http://www.caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
 *
 */

function toQuad(p1, c1, c2, p2) {
    // Quad control point is (3*c2 - p2 + 3*c1 - p1)/4
    const x = (3 * c2.x - p2.x + 3 * c1.x - p1.x) / 4;
    const y = (3 * c2.y - p2.y + 3 * c1.y - p1.y) / 4;
    return [
        p1,
        {x, y},
        p2
    ];
}


/**
 * 三次贝塞尔转二次贝塞尔
 *
 * @param {Object} p1 开始点
 * @param {Object} c1 控制点1
 * @param {Object} c2 控制点2
 * @param {Object} p2 结束点
 * @return {Array} 二次贝塞尔控制点
 */
export default function bezierCubic2Q2(p1, c1, c2, p2) {

    // 判断极端情况，控制点和起止点一样
    if (p1.x === c1.x && p1.y === c1.y && c2.x === p2.x && c2.y === p2.y) {
        return [
            [
                p1,
                {
                    x: (p1.x + p2.x) / 2,
                    y: (p1.y + p2.y) / 2
                },
                p2
            ]
        ];
    }

    const mx = p2.x - 3 * c2.x + 3 * c1.x - p1.x;
    const my = p2.y - 3 * c2.y + 3 * c1.y - p1.y;

    // control points near
    if (mx * mx + my * my <= 4) {
        return [
            toQuad(p1, c1, c2, p2)
        ];
    }

    // Split to 2 qubic beziers by midpoints
    // (p2 + 3*c2 + 3*c1 + p1)/8
    const mp = {
        x: (p2.x + 3 * c2.x + 3 * c1.x + p1.x) / 8,
        y: (p2.y + 3 * c2.y + 3 * c1.y + p1.y) / 8
    };

    return [
        toQuad(
            p1,
            {
                x: (p1.x + c1.x) / 2,
                y: (p1.y + c1.y) / 2

            },
            {
                x: (p1.x + 2 * c1.x + c2.x) / 4,
                y: (p1.y + 2 * c1.y + c2.y) / 4
            },
            mp
        ),
        toQuad(
            mp,
            {
                x: (p2.x + c1.x + 2 * c2.x) / 4,
                y: (p2.y + c1.y + 2 * c2.y) / 4

            },
            {
                x: (p2.x + c2.x) / 2,
                y: (p2.y + c2.y) / 2
            },
            p2
        )
    ];
}