187 lines
6.9 KiB
JavaScript
187 lines
6.9 KiB
JavaScript
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"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 ellipse_1 = require("./ellipse");
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// 偏导数 x
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function derivativeXAt(cx, cy, rx, ry, xRotation, startAngle, endAngle, angle) {
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return -1 * rx * Math.cos(xRotation) * Math.sin(angle) - ry * Math.sin(xRotation) * Math.cos(angle);
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}
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// 偏导数 y
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function derivativeYAt(cx, cy, rx, ry, xRotation, startAngle, endAngle, angle) {
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return -1 * rx * Math.sin(xRotation) * Math.sin(angle) + ry * Math.cos(xRotation) * Math.cos(angle);
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}
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// x 的极值
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function xExtrema(rx, ry, xRotation) {
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return Math.atan((-ry / rx) * Math.tan(xRotation));
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}
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// y 的极值
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function yExtrema(rx, ry, xRotation) {
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return Math.atan(ry / (rx * Math.tan(xRotation)));
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}
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// 根据角度求 x 坐标
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function xAt(cx, cy, rx, ry, xRotation, angle) {
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return rx * Math.cos(xRotation) * Math.cos(angle) - ry * Math.sin(xRotation) * Math.sin(angle) + cx;
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}
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// 根据角度求 y 坐标
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function yAt(cx, cy, rx, ry, xRotation, angle) {
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return rx * Math.sin(xRotation) * Math.cos(angle) + ry * Math.cos(xRotation) * Math.sin(angle) + cy;
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}
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// 获取点在椭圆上的角度
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function getAngle(rx, ry, x0, y0) {
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var angle = Math.atan2(y0 * rx, x0 * ry);
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// 转换到 0 - 2PI 内
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return (angle + Math.PI * 2) % (Math.PI * 2);
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}
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// 根据角度获取，x,y
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function getPoint(rx, ry, angle) {
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return {
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x: rx * Math.cos(angle),
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y: ry * Math.sin(angle),
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};
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}
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// 旋转
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function rotate(x, y, angle) {
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var cos = Math.cos(angle);
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var sin = Math.sin(angle);
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return [x * cos - y * sin, x * sin + y * cos];
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}
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exports.default = {
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/**
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* 计算包围盒
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* @param {number} cx 圆心 x
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* @param {number} cy 圆心 y
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* @param {number} rx x 轴方向的半径
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* @param {number} ry y 轴方向的半径
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* @param {number} xRotation 旋转角度
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* @param {number} startAngle 起始角度
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* @param {number} endAngle 结束角度
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* @return {object} 包围盒对象
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*/
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box: function (cx, cy, rx, ry, xRotation, startAngle, endAngle) {
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var xDim = xExtrema(rx, ry, xRotation);
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var minX = Infinity;
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var maxX = -Infinity;
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var xs = [startAngle, endAngle];
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for (var i = -Math.PI * 2; i <= Math.PI * 2; i += Math.PI) {
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var xAngle = xDim + i;
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if (startAngle < endAngle) {
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if (startAngle < xAngle && xAngle < endAngle) {
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xs.push(xAngle);
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}
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}
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else {
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if (endAngle < xAngle && xAngle < startAngle) {
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xs.push(xAngle);
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}
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}
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}
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for (var i = 0; i < xs.length; i++) {
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var x = xAt(cx, cy, rx, ry, xRotation, xs[i]);
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if (x < minX) {
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minX = x;
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}
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if (x > maxX) {
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maxX = x;
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}
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}
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var yDim = yExtrema(rx, ry, xRotation);
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var minY = Infinity;
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var maxY = -Infinity;
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var ys = [startAngle, endAngle];
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for (var i = -Math.PI * 2; i <= Math.PI * 2; i += Math.PI) {
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var yAngle = yDim + i;
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if (startAngle < endAngle) {
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if (startAngle < yAngle && yAngle < endAngle) {
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ys.push(yAngle);
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}
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}
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else {
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if (endAngle < yAngle && yAngle < startAngle) {
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ys.push(yAngle);
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}
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}
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}
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for (var i = 0; i < ys.length; i++) {
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var y = yAt(cx, cy, rx, ry, xRotation, ys[i]);
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if (y < minY) {
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minY = y;
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}
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if (y > maxY) {
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maxY = y;
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}
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}
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return {
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x: minX,
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y: minY,
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width: maxX - minX,
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height: maxY - minY,
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};
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},
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/**
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* 获取圆弧的长度，计算圆弧长度时不考虑旋转角度，
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* 仅跟 rx, ry, startAngle, endAngle 相关
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* @param {number} cx 圆心 x
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* @param {number} cy 圆心 y
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* @param {number} rx x 轴方向的半径
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* @param {number} ry y 轴方向的半径
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* @param {number} xRotation 旋转角度
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* @param {number} startAngle 起始角度
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* @param {number} endAngle 结束角度
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*/
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length: function (cx, cy, rx, ry, xRotation, startAngle, endAngle) { },
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/**
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* 获取指定点到圆弧的最近距离的点
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* @param {number} cx 圆心 x
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* @param {number} cy 圆心 y
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* @param {number} rx x 轴方向的半径
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* @param {number} ry y 轴方向的半径
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* @param {number} xRotation 旋转角度
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* @param {number} startAngle 起始角度
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* @param {number} endAngle 结束角度
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* @param {number} x0 指定点的 x
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* @param {number} y0 指定点的 y
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* @return {object} 到指定点最近距离的点
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*/
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nearestPoint: function (cx, cy, rx, ry, xRotation, startAngle, endAngle, x0, y0) {
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// 将最近距离问题转换成到椭圆中心 0,0 没有旋转的椭圆问题
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var relativeVector = rotate(x0 - cx, y0 - cy, -xRotation);
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var x1 = relativeVector[0], y1 = relativeVector[1];
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// 计算点到椭圆的最近的点
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var relativePoint = ellipse_1.default.nearestPoint(0, 0, rx, ry, x1, y1);
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// 获取点在椭圆上的角度
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var angle = getAngle(rx, ry, relativePoint.x, relativePoint.y);
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// 点没有在圆弧上
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if (angle < startAngle) {
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// 小于起始圆弧
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relativePoint = getPoint(rx, ry, startAngle);
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}
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else if (angle > endAngle) {
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// 大于结束圆弧
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relativePoint = getPoint(rx, ry, endAngle);
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}
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// 旋转到 xRotation 的角度
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var vector = rotate(relativePoint.x, relativePoint.y, xRotation);
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return {
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x: vector[0] + cx,
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y: vector[1] + cy,
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};
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},
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pointDistance: function (cx, cy, rx, ry, xRotation, startAngle, endAngle, x0, y0) {
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var nearestPoint = this.nearestPoint(cx, cy, rx, ry, x0, y0);
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return util_1.distance(nearestPoint.x, nearestPoint.y, x0, y0);
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},
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pointAt: function (cx, cy, rx, ry, xRotation, startAngle, endAngle, t) {
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var angle = (endAngle - startAngle) * t + startAngle;
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return {
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x: xAt(cx, cy, rx, ry, xRotation, angle),
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y: yAt(cx, cy, rx, ry, xRotation, angle),
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};
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},
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tangentAngle: function (cx, cy, rx, ry, xRotation, startAngle, endAngle, t) {
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var angle = (endAngle - startAngle) * t + startAngle;
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var dx = derivativeXAt(cx, cy, rx, ry, xRotation, startAngle, endAngle, angle);
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var dy = derivativeYAt(cx, cy, rx, ry, xRotation, startAngle, endAngle, angle);
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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=arc.js.map
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