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Co-Authored-By: 狸花猫/Claude-Qwen3.6-Plus 🐾
92 lines
3.2 KiB
JavaScript
92 lines
3.2 KiB
JavaScript
import line from './line';
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import { distance, isNumberEqual, getBBoxByArray, piMod } from './util';
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import { nearestPoint } from './bezier';
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// 差值公式
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function quadraticAt(p0, p1, p2, t) {
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var onet = 1 - t;
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return onet * onet * p0 + 2 * t * onet * p1 + t * t * p2;
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}
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// 求极值
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function extrema(p0, p1, p2) {
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var a = p0 + p2 - 2 * p1;
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if (isNumberEqual(a, 0)) {
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return [0.5];
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}
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var rst = (p0 - p1) / a;
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if (rst <= 1 && rst >= 0) {
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return [rst];
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}
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return [];
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}
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function derivativeAt(p0, p1, p2, t) {
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return 2 * (1 - t) * (p1 - p0) + 2 * t * (p2 - p1);
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}
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// 分割贝塞尔曲线
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function divideQuadratic(x1, y1, x2, y2, x3, y3, t) {
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// 划分点
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var xt = quadraticAt(x1, x2, x3, t);
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var yt = quadraticAt(y1, y2, y3, t);
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// 分割的第一条曲线的控制点
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var controlPoint1 = line.pointAt(x1, y1, x2, y2, t);
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// 分割的第二条曲线的控制点
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var controlPoint2 = line.pointAt(x2, y2, x3, y3, t);
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return [
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[x1, y1, controlPoint1.x, controlPoint1.y, xt, yt],
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[xt, yt, controlPoint2.x, controlPoint2.y, x3, y3],
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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
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function quadraticLength(x1, y1, x2, y2, x3, y3, iterationCount) {
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if (iterationCount === 0) {
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return (distance(x1, y1, x2, y2) + distance(x2, y2, x3, y3) + distance(x1, y1, x3, y3)) / 2;
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}
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var quadratics = divideQuadratic(x1, y1, x2, y2, x3, y3, 0.5);
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var left = quadratics[0];
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var right = quadratics[1];
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left.push(iterationCount - 1);
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right.push(iterationCount - 1);
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return quadraticLength.apply(null, left) + quadraticLength.apply(null, right);
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}
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export default {
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box: function (x1, y1, x2, y2, x3, y3) {
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var xExtrema = extrema(x1, x2, x3)[0];
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var yExtrema = extrema(y1, y2, y3)[0];
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// 控制点不加入 box 的计算
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var xArr = [x1, x3];
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var yArr = [y1, y3];
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if (xExtrema !== undefined) {
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xArr.push(quadraticAt(x1, x2, x3, xExtrema));
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}
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if (yExtrema !== undefined) {
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yArr.push(quadraticAt(y1, y2, y3, yExtrema));
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}
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return getBBoxByArray(xArr, yArr);
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},
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length: function (x1, y1, x2, y2, x3, y3) {
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return quadraticLength(x1, y1, x2, y2, x3, y3, 3);
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},
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nearestPoint: function (x1, y1, x2, y2, x3, y3, x0, y0) {
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return nearestPoint([x1, x2, x3], [y1, y2, y3], x0, y0, quadraticAt);
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},
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pointDistance: function (x1, y1, x2, y2, x3, y3, x0, y0) {
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var point = this.nearestPoint(x1, y1, x2, y2, x3, y3, x0, y0);
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return distance(point.x, point.y, x0, y0);
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},
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interpolationAt: quadraticAt,
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pointAt: function (x1, y1, x2, y2, x3, y3, t) {
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return {
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x: quadraticAt(x1, x2, x3, t),
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y: quadraticAt(y1, y2, y3, t),
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};
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},
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divide: function (x1, y1, x2, y2, x3, y3, t) {
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return divideQuadratic(x1, y1, x2, y2, x3, y3, t);
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},
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tangentAngle: function (x1, y1, x2, y2, x3, y3, t) {
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var dx = derivativeAt(x1, x2, x3, t);
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var dy = derivativeAt(y1, y2, y3, t);
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var angle = Math.atan2(dy, dx);
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return piMod(angle);
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},
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};
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//# sourceMappingURL=quadratic.js.map
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