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