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META-INF.assets.rjzjh.zrender.core.curve.js Maven / Gradle / Ivy
/**
* 曲线辅助模块
* @module zrender/core/curve
* @author pissang(https://www.github.com/pissang)
*/
define(function(require) {
'use strict';
var vec2 = require('./vector');
var v2Create = vec2.create;
var v2DistSquare = vec2.distSquare;
var mathPow = Math.pow;
var mathSqrt = Math.sqrt;
var EPSILON = 1e-8;
var EPSILON_NUMERIC = 1e-4;
var THREE_SQRT = mathSqrt(3);
var ONE_THIRD = 1 / 3;
// 临时变量
var _v0 = v2Create();
var _v1 = v2Create();
var _v2 = v2Create();
// var _v3 = vec2.create();
function isAroundZero(val) {
return val > -EPSILON && val < EPSILON;
}
function isNotAroundZero(val) {
return val > EPSILON || val < -EPSILON;
}
/**
* 计算三次贝塞尔值
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} p3
* @param {number} t
* @return {number}
*/
function cubicAt(p0, p1, p2, p3, t) {
var onet = 1 - t;
return onet * onet * (onet * p0 + 3 * t * p1)
+ t * t * (t * p3 + 3 * onet * p2);
}
/**
* 计算三次贝塞尔导数值
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} p3
* @param {number} t
* @return {number}
*/
function cubicDerivativeAt(p0, p1, p2, p3, t) {
var onet = 1 - t;
return 3 * (
((p1 - p0) * onet + 2 * (p2 - p1) * t) * onet
+ (p3 - p2) * t * t
);
}
/**
* 计算三次贝塞尔方程根，使用盛金公式
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} p3
* @param {number} val
* @param {Array.} roots
* @return {number} 有效根数目
*/
function cubicRootAt(p0, p1, p2, p3, val, roots) {
// Evaluate roots of cubic functions
var a = p3 + 3 * (p1 - p2) - p0;
var b = 3 * (p2 - p1 * 2 + p0);
var c = 3 * (p1 - p0);
var d = p0 - val;
var A = b * b - 3 * a * c;
var B = b * c - 9 * a * d;
var C = c * c - 3 * b * d;
var n = 0;
if (isAroundZero(A) && isAroundZero(B)) {
if (isAroundZero(b)) {
roots[0] = 0;
}
else {
var t1 = -c / b; //t1, t2, t3, b is not zero
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
}
}
else {
var disc = B * B - 4 * A * C;
if (isAroundZero(disc)) {
var K = B / A;
var t1 = -b / a + K; // t1, a is not zero
var t2 = -K / 2; // t2, t3
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
if (t2 >= 0 && t2 <= 1) {
roots[n++] = t2;
}
}
else if (disc > 0) {
var discSqrt = mathSqrt(disc);
var Y1 = A * b + 1.5 * a * (-B + discSqrt);
var Y2 = A * b + 1.5 * a * (-B - discSqrt);
if (Y1 < 0) {
Y1 = -mathPow(-Y1, ONE_THIRD);
}
else {
Y1 = mathPow(Y1, ONE_THIRD);
}
if (Y2 < 0) {
Y2 = -mathPow(-Y2, ONE_THIRD);
}
else {
Y2 = mathPow(Y2, ONE_THIRD);
}
var t1 = (-b - (Y1 + Y2)) / (3 * a);
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
}
else {
var T = (2 * A * b - 3 * a * B) / (2 * mathSqrt(A * A * A));
var theta = Math.acos(T) / 3;
var ASqrt = mathSqrt(A);
var tmp = Math.cos(theta);
var t1 = (-b - 2 * ASqrt * tmp) / (3 * a);
var t2 = (-b + ASqrt * (tmp + THREE_SQRT * Math.sin(theta))) / (3 * a);
var t3 = (-b + ASqrt * (tmp - THREE_SQRT * Math.sin(theta))) / (3 * a);
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
if (t2 >= 0 && t2 <= 1) {
roots[n++] = t2;
}
if (t3 >= 0 && t3 <= 1) {
roots[n++] = t3;
}
}
}
return n;
}
/**
* 计算三次贝塞尔方程极限值的位置
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} p3
* @param {Array.} extrema
* @return {number} 有效数目
*/
function cubicExtrema(p0, p1, p2, p3, extrema) {
var b = 6 * p2 - 12 * p1 + 6 * p0;
var a = 9 * p1 + 3 * p3 - 3 * p0 - 9 * p2;
var c = 3 * p1 - 3 * p0;
var n = 0;
if (isAroundZero(a)) {
if (isNotAroundZero(b)) {
var t1 = -c / b;
if (t1 >= 0 && t1 <=1) {
extrema[n++] = t1;
}
}
}
else {
var disc = b * b - 4 * a * c;
if (isAroundZero(disc)) {
extrema[0] = -b / (2 * a);
}
else if (disc > 0) {
var discSqrt = mathSqrt(disc);
var t1 = (-b + discSqrt) / (2 * a);
var t2 = (-b - discSqrt) / (2 * a);
if (t1 >= 0 && t1 <= 1) {
extrema[n++] = t1;
}
if (t2 >= 0 && t2 <= 1) {
extrema[n++] = t2;
}
}
}
return n;
}
/**
* 细分三次贝塞尔曲线
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} p3
* @param {number} t
* @param {Array.} out
*/
function cubicSubdivide(p0, p1, p2, p3, t, out) {
var p01 = (p1 - p0) * t + p0;
var p12 = (p2 - p1) * t + p1;
var p23 = (p3 - p2) * t + p2;
var p012 = (p12 - p01) * t + p01;
var p123 = (p23 - p12) * t + p12;
var p0123 = (p123 - p012) * t + p012;
// Seg0
out[0] = p0;
out[1] = p01;
out[2] = p012;
out[3] = p0123;
// Seg1
out[4] = p0123;
out[5] = p123;
out[6] = p23;
out[7] = p3;
}
/**
* 投射点到三次贝塞尔曲线上，返回投射距离。
* 投射点有可能会有一个或者多个，这里只返回其中距离最短的一个。
* @param {number} x0
* @param {number} y0
* @param {number} x1
* @param {number} y1
* @param {number} x2
* @param {number} y2
* @param {number} x3
* @param {number} y3
* @param {number} x
* @param {number} y
* @param {Array.} [out] 投射点
* @return {number}
*/
function cubicProjectPoint(
x0, y0, x1, y1, x2, y2, x3, y3,
x, y, out
) {
// http://pomax.github.io/bezierinfo/#projections
var t;
var interval = 0.005;
var d = Infinity;
var prev;
var next;
var d1;
var d2;
_v0[0] = x;
_v0[1] = y;
// 先粗略估计一下可能的最小距离的 t 值
// PENDING
for (var _t = 0; _t < 1; _t += 0.05) {
_v1[0] = cubicAt(x0, x1, x2, x3, _t);
_v1[1] = cubicAt(y0, y1, y2, y3, _t);
d1 = v2DistSquare(_v0, _v1);
if (d1 < d) {
t = _t;
d = d1;
}
}
d = Infinity;
// At most 32 iteration
for (var i = 0; i < 32; i++) {
if (interval < EPSILON_NUMERIC) {
break;
}
prev = t - interval;
next = t + interval;
// t - interval
_v1[0] = cubicAt(x0, x1, x2, x3, prev);
_v1[1] = cubicAt(y0, y1, y2, y3, prev);
d1 = v2DistSquare(_v1, _v0);
if (prev >= 0 && d1 < d) {
t = prev;
d = d1;
}
else {
// t + interval
_v2[0] = cubicAt(x0, x1, x2, x3, next);
_v2[1] = cubicAt(y0, y1, y2, y3, next);
d2 = v2DistSquare(_v2, _v0);
if (next <= 1 && d2 < d) {
t = next;
d = d2;
}
else {
interval *= 0.5;
}
}
}
// t
if (out) {
out[0] = cubicAt(x0, x1, x2, x3, t);
out[1] = cubicAt(y0, y1, y2, y3, t);
}
// console.log(interval, i);
return mathSqrt(d);
}
/**
* 计算二次方贝塞尔值
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} t
* @return {number}
*/
function quadraticAt(p0, p1, p2, t) {
var onet = 1 - t;
return onet * (onet * p0 + 2 * t * p1) + t * t * p2;
}
/**
* 计算二次方贝塞尔导数值
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} t
* @return {number}
*/
function quadraticDerivativeAt(p0, p1, p2, t) {
return 2 * ((1 - t) * (p1 - p0) + t * (p2 - p1));
}
/**
* 计算二次方贝塞尔方程根
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} t
* @param {Array.} roots
* @return {number} 有效根数目
*/
function quadraticRootAt(p0, p1, p2, val, roots) {
var a = p0 - 2 * p1 + p2;
var b = 2 * (p1 - p0);
var c = p0 - val;
var n = 0;
if (isAroundZero(a)) {
if (isNotAroundZero(b)) {
var t1 = -c / b;
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
}
}
else {
var disc = b * b - 4 * a * c;
if (isAroundZero(disc)) {
var t1 = -b / (2 * a);
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
}
else if (disc > 0) {
var discSqrt = mathSqrt(disc);
var t1 = (-b + discSqrt) / (2 * a);
var t2 = (-b - discSqrt) / (2 * a);
if (t1 >= 0 && t1 <= 1) {
roots[n++] = t1;
}
if (t2 >= 0 && t2 <= 1) {
roots[n++] = t2;
}
}
}
return n;
}
/**
* 计算二次贝塞尔方程极限值
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @return {number}
*/
function quadraticExtremum(p0, p1, p2) {
var divider = p0 + p2 - 2 * p1;
if (divider === 0) {
// p1 is center of p0 and p2
return 0.5;
}
else {
return (p0 - p1) / divider;
}
}
/**
* 细分二次贝塞尔曲线
* @memberOf module:zrender/core/curve
* @param {number} p0
* @param {number} p1
* @param {number} p2
* @param {number} t
* @param {Array.} out
*/
function quadraticSubdivide(p0, p1, p2, t, out) {
var p01 = (p1 - p0) * t + p0;
var p12 = (p2 - p1) * t + p1;
var p012 = (p12 - p01) * t + p01;
// Seg0
out[0] = p0;
out[1] = p01;
out[2] = p012;
// Seg1
out[3] = p012;
out[4] = p12;
out[5] = p2;
}
/**
* 投射点到二次贝塞尔曲线上，返回投射距离。
* 投射点有可能会有一个或者多个，这里只返回其中距离最短的一个。
* @param {number} x0
* @param {number} y0
* @param {number} x1
* @param {number} y1
* @param {number} x2
* @param {number} y2
* @param {number} x
* @param {number} y
* @param {Array.} out 投射点
* @return {number}
*/
function quadraticProjectPoint(
x0, y0, x1, y1, x2, y2,
x, y, out
) {
// http://pomax.github.io/bezierinfo/#projections
var t;
var interval = 0.005;
var d = Infinity;
_v0[0] = x;
_v0[1] = y;
// 先粗略估计一下可能的最小距离的 t 值
// PENDING
for (var _t = 0; _t < 1; _t += 0.05) {
_v1[0] = quadraticAt(x0, x1, x2, _t);
_v1[1] = quadraticAt(y0, y1, y2, _t);
var d1 = v2DistSquare(_v0, _v1);
if (d1 < d) {
t = _t;
d = d1;
}
}
d = Infinity;
// At most 32 iteration
for (var i = 0; i < 32; i++) {
if (interval < EPSILON_NUMERIC) {
break;
}
var prev = t - interval;
var next = t + interval;
// t - interval
_v1[0] = quadraticAt(x0, x1, x2, prev);
_v1[1] = quadraticAt(y0, y1, y2, prev);
var d1 = v2DistSquare(_v1, _v0);
if (prev >= 0 && d1 < d) {
t = prev;
d = d1;
}
else {
// t + interval
_v2[0] = quadraticAt(x0, x1, x2, next);
_v2[1] = quadraticAt(y0, y1, y2, next);
var d2 = v2DistSquare(_v2, _v0);
if (next <= 1 && d2 < d) {
t = next;
d = d2;
}
else {
interval *= 0.5;
}
}
}
// t
if (out) {
out[0] = quadraticAt(x0, x1, x2, t);
out[1] = quadraticAt(y0, y1, y2, t);
}
// console.log(interval, i);
return mathSqrt(d);
}
return {
cubicAt: cubicAt,
cubicDerivativeAt: cubicDerivativeAt,
cubicRootAt: cubicRootAt,
cubicExtrema: cubicExtrema,
cubicSubdivide: cubicSubdivide,
cubicProjectPoint: cubicProjectPoint,
quadraticAt: quadraticAt,
quadraticDerivativeAt: quadraticDerivativeAt,
quadraticRootAt: quadraticRootAt,
quadraticExtremum: quadraticExtremum,
quadraticSubdivide: quadraticSubdivide,
quadraticProjectPoint: quadraticProjectPoint
};
});
