zrender/src/tool/convertPath.ts

A lightweight graphic library providing 2d draw for Apache ECharts

import { cubicSubdivide } from '../core/curve';
import PathProxy from '../core/PathProxy';

const CMD = PathProxy.CMD;

function aroundEqual(a: number, b: number) {
    return Math.abs(a - b) < 1e-5;
}

export function pathToBezierCurves(path: PathProxy) {

    const data = path.data;
    const len = path.len();

    const bezierArrayGroups: number[][] = [];
    let currentSubpath: number[];

    let xi = 0;
    let yi = 0;
    let x0 = 0;
    let y0 = 0;

    function createNewSubpath(x: number, y: number) {
        // More than one M command
        if (currentSubpath && currentSubpath.length > 2) {
            bezierArrayGroups.push(currentSubpath);
        }
        currentSubpath = [x, y];
    }

    function addLine(x0: number, y0: number, x1: number, y1: number) {
        if (!(aroundEqual(x0, x1) && aroundEqual(y0, y1))) {
            currentSubpath.push(x0, y0, x1, y1, x1, y1);
        }
    }

    function addArc(startAngle: number, endAngle: number, cx: number, cy: number, rx: number, ry: number) {
        // https://stackoverflow.com/questions/1734745/how-to-create-circle-with-b%C3%A9zier-curves
        const delta = Math.abs(endAngle - startAngle);
        const len = Math.tan(delta / 4) * 4 / 3;
        const dir = endAngle < startAngle ? -1 : 1;

        const c1 = Math.cos(startAngle);
        const s1 = Math.sin(startAngle);
        const c2 = Math.cos(endAngle);
        const s2 = Math.sin(endAngle);

        const x1 = c1 * rx + cx;
        const y1 = s1 * ry + cy;

        const x4 = c2 * rx + cx;
        const y4 = s2 * ry + cy;

        const hx = rx * len * dir;
        const hy = ry * len * dir;
        currentSubpath.push(
            // Move control points on tangent.
            x1 - hx * s1, y1 + hy * c1,
            x4 + hx * s2, y4 - hy * c2,
            x4, y4
        );
    }

    let x1;
    let y1;
    let x2;
    let y2;

    for (let i = 0; i < len;) {
        const cmd = data[i++];
        const isFirst = i === 1;

        if (isFirst) {
            // 如果第一个命令是 L, C, Q
            // 则 previous point 同绘制命令的第一个 point
            // 第一个命令为 Arc 的情况下会在后面特殊处理
            xi = data[i];
            yi = data[i + 1];

            x0 = xi;
            y0 = yi;

            if (cmd === CMD.L || cmd === CMD.C || cmd === CMD.Q) {
                // Start point
                currentSubpath = [x0, y0];
            }
        }

        switch (cmd) {
            case CMD.M:
                // moveTo 命令重新创建一个新的 subpath, 并且更新新的起点
                // 在 closePath 的时候使用
                xi = x0 = data[i++];
                yi = y0 = data[i++];

                createNewSubpath(x0, y0);
                break;
            case CMD.L:
                x1 = data[i++];
                y1 = data[i++];
                addLine(xi, yi, x1, y1);
                xi = x1;
                yi = y1;
                break;
            case CMD.C:
                currentSubpath.push(
                    data[i++], data[i++], data[i++], data[i++],
                    xi = data[i++], yi = data[i++]
                );
                break;
            case CMD.Q:
                x1 = data[i++];
                y1 = data[i++];
                x2 = data[i++];
                y2 = data[i++];
                currentSubpath.push(
                    // Convert quadratic to cubic
                    xi + 2 / 3 * (x1 - xi), yi + 2 / 3 * (y1 - yi),
                    x2 + 2 / 3 * (x1 - x2), y2 + 2 / 3 * (y1 - y2),
                    x2, y2
                );
                xi = x2;
                yi = y2;
                break;
            case CMD.A:
                const cx = data[i++];
                const cy = data[i++];
                const rx = data[i++];
                const ry = data[i++];
                const startAngle = data[i++];
                const endAngle = data[i++] + startAngle;

                // TODO Arc rotation
                i += 1;
                const anticlockwise = !data[i++];

                x1 = Math.cos(startAngle) * rx + cx;
                y1 = Math.sin(startAngle) * ry + cy;
                if (isFirst) {
                    // 直接使用 arc 命令
                    // 第一个命令起点还未定义
                    x0 = x1;
                    y0 = y1;
                    createNewSubpath(x0, y0);
                }
                else {
                    // Connect a line between current point to arc start point.
                    addLine(xi, yi, x1, y1);
                }

                xi = Math.cos(endAngle) * rx + cx;
                yi = Math.sin(endAngle) * ry + cy;

                const step = (anticlockwise ? -1 : 1) * Math.PI / 2;

                for (let angle = startAngle; anticlockwise ? angle > endAngle : angle < endAngle; angle += step) {
                    const nextAngle = anticlockwise ? Math.max(angle + step, endAngle)
                        : Math.min(angle + step, endAngle);
                    addArc(angle, nextAngle, cx, cy, rx, ry);
                }

                break;
            case CMD.R:
                x0 = xi = data[i++];
                y0 = yi = data[i++];
                x1 = x0 + data[i++];
                y1 = y0 + data[i++];

                // rect is an individual path.
                createNewSubpath(x1, y0);
                addLine(x1, y0, x1, y1);
                addLine(x1, y1, x0, y1);
                addLine(x0, y1, x0, y0);
                addLine(x0, y0, x1, y0);
                break;
            case CMD.Z:
                currentSubpath && addLine(xi, yi, x0, y0);
                xi = x0;
                yi = y0;
                break;
        }
    }

    if (currentSubpath && currentSubpath.length > 2) {
        bezierArrayGroups.push(currentSubpath);
    }

    return bezierArrayGroups;
}

function adpativeBezier(
    x0: number, y0: number, x1: number, y1: number, x2: number, y2: number, x3: number, y3: number,
    out: number[], scale: number
) {
    // This bezier is used to simulates a line when converting path to beziers.
    if (aroundEqual(x0, x1) && aroundEqual(y0, y1) && aroundEqual(x2, x3) && aroundEqual(y2, y3)) {
        out.push(x3, y3);
        return;
    }

    const PIXEL_DISTANCE = 2 / scale;
    const PIXEL_DISTANCE_SQR = PIXEL_DISTANCE * PIXEL_DISTANCE;

    // Determine if curve is straight enough
    let dx = x3 - x0;
    let dy = y3 - y0;
    const d = Math.sqrt(dx * dx + dy * dy);
    dx /= d;
    dy /= d;

    const dx1 = x1 - x0;
    const dy1 = y1 - y0;
    const dx2 = x2 - x3;
    const dy2 = y2 - y3;

    const cp1LenSqr = dx1 * dx1 + dy1 * dy1;
    const cp2LenSqr = dx2 * dx2 + dy2 * dy2;

    if (cp1LenSqr < PIXEL_DISTANCE_SQR && cp2LenSqr < PIXEL_DISTANCE_SQR) {
        // Add small segment
        out.push(x3, y3);
        return;
    }

    // Project length of cp1
    const projLen1 = dx * dx1 + dy * dy1;
    // Project length of cp2
    const projLen2 = -dx * dx2 - dy * dy2;

    // Distance from cp1 to start-end line.
    const d1Sqr = cp1LenSqr - projLen1 * projLen1;
    // Distance from cp2 to start-end line.
    const d2Sqr = cp2LenSqr - projLen2 * projLen2;

    // IF the cp1 and cp2 is near to the start-line enough
    // We treat it straight enough
    if (d1Sqr < PIXEL_DISTANCE_SQR && projLen1 >= 0
        && d2Sqr < PIXEL_DISTANCE_SQR && projLen2 >= 0
    ) {
        out.push(x3, y3);
        return;
    }


    const tmpSegX: number[] = [];
    const tmpSegY: number[] = [];
    // Subdivide
    cubicSubdivide(x0, x1, x2, x3, 0.5, tmpSegX);
    cubicSubdivide(y0, y1, y2, y3, 0.5, tmpSegY);

    adpativeBezier(
        tmpSegX[0], tmpSegY[0], tmpSegX[1], tmpSegY[1], tmpSegX[2], tmpSegY[2], tmpSegX[3], tmpSegY[3],
        out, scale
    );
    adpativeBezier(
        tmpSegX[4], tmpSegY[4], tmpSegX[5], tmpSegY[5], tmpSegX[6], tmpSegY[6], tmpSegX[7], tmpSegY[7],
        out, scale
    );
}

export function pathToPolygons(path: PathProxy, scale?: number) {
    // TODO Optimize simple case like path is polygon and rect?
    const bezierArrayGroups = pathToBezierCurves(path);

    const polygons: number[][] = [];

    scale = scale || 1;

    for (let i = 0; i < bezierArrayGroups.length; i++) {
        const beziers = bezierArrayGroups[i];
        const polygon: number[] = [];
        let x0 = beziers[0];
        let y0 = beziers[1];

        polygon.push(x0, y0);

        for (let k = 2; k < beziers.length;) {

            const x1 = beziers[k++];
            const y1 = beziers[k++];
            const x2 = beziers[k++];
            const y2 = beziers[k++];
            const x3 = beziers[k++];
            const y3 = beziers[k++];

            adpativeBezier(x0, y0, x1, y1, x2, y2, x3, y3, polygon, scale);

            x0 = x3;
            y0 = y3;
        }

        polygons.push(polygon);
    }
    return polygons;
}