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Co-Authored-By: 狸花猫/Claude-Qwen3.6-Plus 🐾
119 lines
4.3 KiB
JavaScript
119 lines
4.3 KiB
JavaScript
"use strict";
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Object.defineProperty(exports, "__esModule", { value: true });
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var util_1 = require("./util");
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var line_1 = require("./line");
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var bezier_1 = require("./bezier");
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function cubicAt(p0, p1, p2, p3, t) {
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var onet = 1 - t; // t * t * t 的性能大概是 Math.pow(t, 3) 的三倍
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return onet * onet * onet * p0 + 3 * p1 * t * onet * onet + 3 * p2 * t * t * onet + p3 * t * t * t;
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}
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function derivativeAt(p0, p1, p2, p3, t) {
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var onet = 1 - t;
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return 3 * (onet * onet * (p1 - p0) + 2 * onet * t * (p2 - p1) + t * t * (p3 - p2));
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}
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function extrema(p0, p1, p2, p3) {
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var a = -3 * p0 + 9 * p1 - 9 * p2 + 3 * p3;
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var b = 6 * p0 - 12 * p1 + 6 * p2;
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var c = 3 * p1 - 3 * p0;
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var extremas = [];
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var t1;
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var t2;
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var discSqrt;
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if (util_1.isNumberEqual(a, 0)) {
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if (!util_1.isNumberEqual(b, 0)) {
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t1 = -c / b;
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if (t1 >= 0 && t1 <= 1) {
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extremas.push(t1);
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}
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}
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}
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else {
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var disc = b * b - 4 * a * c;
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if (util_1.isNumberEqual(disc, 0)) {
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extremas.push(-b / (2 * a));
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}
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else if (disc > 0) {
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discSqrt = Math.sqrt(disc);
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t1 = (-b + discSqrt) / (2 * a);
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t2 = (-b - discSqrt) / (2 * a);
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if (t1 >= 0 && t1 <= 1) {
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extremas.push(t1);
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}
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if (t2 >= 0 && t2 <= 1) {
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extremas.push(t2);
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}
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}
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}
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return extremas;
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}
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// 分割贝塞尔曲线
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function divideCubic(x1, y1, x2, y2, x3, y3, x4, y4, t) {
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// 划分点
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var xt = cubicAt(x1, x2, x3, x4, t);
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var yt = cubicAt(y1, y2, y3, y4, t);
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// 计算两点之间的差值点
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var c1 = line_1.default.pointAt(x1, y1, x2, y2, t);
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var c2 = line_1.default.pointAt(x2, y2, x3, y3, t);
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var c3 = line_1.default.pointAt(x3, y3, x4, y4, t);
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var c12 = line_1.default.pointAt(c1.x, c1.y, c2.x, c2.y, t);
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var c23 = line_1.default.pointAt(c2.x, c2.y, c3.x, c3.y, t);
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return [
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[x1, y1, c1.x, c1.y, c12.x, c12.y, xt, yt],
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[xt, yt, c23.x, c23.y, c3.x, c3.y, x4, y4],
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];
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}
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// 使用迭代法取贝塞尔曲线的长度，二阶和三阶分开写，更清晰和便于调试
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function cubicLength(x1, y1, x2, y2, x3, y3, x4, y4, iterationCount) {
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if (iterationCount === 0) {
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return bezier_1.snapLength([x1, x2, x3, x4], [y1, y2, y3, y4]);
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}
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var cubics = divideCubic(x1, y1, x2, y2, x3, y3, x4, y4, 0.5);
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var left = cubics[0];
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var right = cubics[1];
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left.push(iterationCount - 1);
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right.push(iterationCount - 1);
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return cubicLength.apply(null, left) + cubicLength.apply(null, right);
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}
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exports.default = {
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extrema: extrema,
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box: function (x1, y1, x2, y2, x3, y3, x4, y4) {
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var xArr = [x1, x4];
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var yArr = [y1, y4];
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var xExtrema = extrema(x1, x2, x3, x4);
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var yExtrema = extrema(y1, y2, y3, y4);
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for (var i = 0; i < xExtrema.length; i++) {
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xArr.push(cubicAt(x1, x2, x3, x4, xExtrema[i]));
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}
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for (var i = 0; i < yExtrema.length; i++) {
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yArr.push(cubicAt(y1, y2, y3, y4, yExtrema[i]));
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}
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return util_1.getBBoxByArray(xArr, yArr);
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},
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length: function (x1, y1, x2, y2, x3, y3, x4, y4) {
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// 迭代三次，划分成 8 段求长度
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return cubicLength(x1, y1, x2, y2, x3, y3, x4, y4, 3);
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},
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nearestPoint: function (x1, y1, x2, y2, x3, y3, x4, y4, x0, y0, length) {
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return bezier_1.nearestPoint([x1, x2, x3, x4], [y1, y2, y3, y4], x0, y0, cubicAt, length);
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},
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pointDistance: function (x1, y1, x2, y2, x3, y3, x4, y4, x0, y0, length) {
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var point = this.nearestPoint(x1, y1, x2, y2, x3, y3, x4, y4, x0, y0, length);
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return util_1.distance(point.x, point.y, x0, y0);
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},
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interpolationAt: cubicAt,
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pointAt: function (x1, y1, x2, y2, x3, y3, x4, y4, t) {
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return {
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x: cubicAt(x1, x2, x3, x4, t),
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y: cubicAt(y1, y2, y3, y4, t),
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};
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},
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divide: function (x1, y1, x2, y2, x3, y3, x4, y4, t) {
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return divideCubic(x1, y1, x2, y2, x3, y3, x4, y4, t);
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},
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tangentAngle: function (x1, y1, x2, y2, x3, y3, x4, y4, t) {
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var dx = derivativeAt(x1, x2, x3, x4, t);
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var dy = derivativeAt(y1, y2, y3, y4, t);
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return util_1.piMod(Math.atan2(dy, dx));
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},
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};
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//# sourceMappingURL=cubic.js.map
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