127 lines
5.6 KiB
TypeScript
127 lines
5.6 KiB
TypeScript
module es {
|
||
/**
|
||
* 三次方和二次方贝塞尔帮助器(cubic and quadratic bezier helper)
|
||
*/
|
||
export class Bezier {
|
||
/**
|
||
* 求解二次曲折线
|
||
* @param p0
|
||
* @param p1
|
||
* @param p2
|
||
* @param t
|
||
*/
|
||
public static getPoint(p0: Vector2, p1: Vector2, p2: Vector2, t: number): Vector2 {
|
||
t = MathHelper.clamp01(t);
|
||
let oneMinusT = 1 - t;
|
||
return new Vector2(oneMinusT * oneMinusT).multiply(p0)
|
||
.addEqual(new Vector2(2 * oneMinusT * t).multiply(p1))
|
||
.addEqual(new Vector2(t * t).multiply(p2));
|
||
}
|
||
|
||
/**
|
||
* 求解一个立方体曲率
|
||
* @param start
|
||
* @param firstControlPoint
|
||
* @param secondControlPoint
|
||
* @param end
|
||
* @param t
|
||
*/
|
||
public static getPointThree(start: Vector2, firstControlPoint: Vector2, secondControlPoint: Vector2,
|
||
end: Vector2, t: number): Vector2 {
|
||
t = MathHelper.clamp01(t);
|
||
let oneMinusT = 1 - t;
|
||
return new Vector2(oneMinusT * oneMinusT * oneMinusT).multiply(start)
|
||
.addEqual(new Vector2(3 * oneMinusT * oneMinusT * t).multiply(firstControlPoint))
|
||
.addEqual(new Vector2(3 * oneMinusT * t * t).multiply(secondControlPoint))
|
||
.addEqual(new Vector2(t * t * t).multiply(end));
|
||
}
|
||
|
||
/**
|
||
* 得到二次贝塞尔函数的一阶导数
|
||
* @param p0
|
||
* @param p1
|
||
* @param p2
|
||
* @param t
|
||
*/
|
||
public static getFirstDerivative(p0: Vector2, p1: Vector2, p2: Vector2, t: number) {
|
||
return new Vector2(2 * (1 - t)).multiply(Vector2.subtract(p1, p0))
|
||
.addEqual(new Vector2(2 * t).multiply(Vector2.subtract(p2, p1)));
|
||
}
|
||
|
||
/**
|
||
* 得到一个三次贝塞尔函数的一阶导数
|
||
* @param start
|
||
* @param firstControlPoint
|
||
* @param secondControlPoint
|
||
* @param end
|
||
* @param t
|
||
*/
|
||
public static getFirstDerivativeThree(start: Vector2, firstControlPoint: Vector2, secondControlPoint: Vector2,
|
||
end: Vector2, t: number) {
|
||
t = MathHelper.clamp01(t);
|
||
let oneMunusT = 1 - t;
|
||
return new Vector2(3 * oneMunusT * oneMunusT).multiply(Vector2.subtract(firstControlPoint, start))
|
||
.addEqual(new Vector2(6 * oneMunusT * t).multiply(Vector2.subtract(secondControlPoint, firstControlPoint)))
|
||
.addEqual(new Vector2(3 * t * t).multiply(Vector2.subtract(end, secondControlPoint)));
|
||
}
|
||
|
||
/**
|
||
* 递归地细分bezier曲线，直到满足距离校正
|
||
* 在这种算法中，平面切片的点要比曲面切片少。返回完成后应返回到ListPool的合并列表。
|
||
* @param start
|
||
* @param firstCtrlPoint
|
||
* @param secondCtrlPoint
|
||
* @param end
|
||
* @param distanceTolerance
|
||
*/
|
||
public static getOptimizedDrawingPoints(start: Vector2, firstCtrlPoint: Vector2, secondCtrlPoint: Vector2,
|
||
end: Vector2, distanceTolerance: number = 1) {
|
||
let points = ListPool.obtain<Vector2>();
|
||
points.push(start);
|
||
this.recursiveGetOptimizedDrawingPoints(start, firstCtrlPoint, secondCtrlPoint, end, points, distanceTolerance);
|
||
points.push(end);
|
||
|
||
return points;
|
||
}
|
||
|
||
/**
|
||
* 递归地细分bezier曲线，直到满足距离校正。在这种算法中，平面切片的点要比曲面切片少。
|
||
* @param start
|
||
* @param firstCtrlPoint
|
||
* @param secondCtrlPoint
|
||
* @param end
|
||
* @param points
|
||
* @param distanceTolerance
|
||
*/
|
||
private static recursiveGetOptimizedDrawingPoints(start: Vector2, firstCtrlPoint: Vector2, secondCtrlPoint: Vector2,
|
||
end: Vector2, points: Vector2[], distanceTolerance: number) {
|
||
// 计算线段的所有中点
|
||
let pt12 = Vector2.divideScaler(Vector2.add(start, firstCtrlPoint), 2);
|
||
let pt23 = Vector2.divideScaler(Vector2.add(firstCtrlPoint, secondCtrlPoint), 2);
|
||
let pt34 = Vector2.divideScaler(Vector2.add(secondCtrlPoint, end), 2);
|
||
|
||
// 计算新半直线的中点
|
||
let pt123 = Vector2.divideScaler(Vector2.add(pt12, pt23), 2);
|
||
let pt234 = Vector2.divideScaler(Vector2.add(pt23, pt34), 2);
|
||
|
||
// 最后再细分最后两个中点。如果我们满足我们的距离公差，这将是我们使用的最后一点。
|
||
let pt1234 = Vector2.divideScaler(Vector2.add(pt123, pt234), 2);
|
||
|
||
// 试着用一条直线来近似整个三次曲线
|
||
let deltaLine = Vector2.subtract(end, start);
|
||
|
||
let d2 = Math.abs(((firstCtrlPoint.x, end.x) * deltaLine.y - (firstCtrlPoint.y - end.y) * deltaLine.x));
|
||
let d3 = Math.abs(((secondCtrlPoint.x - end.x) * deltaLine.y - (secondCtrlPoint.y - end.y) * deltaLine.x));
|
||
|
||
if ((d2 + d3) * (d2 + d3) < distanceTolerance * (deltaLine.x * deltaLine.x + deltaLine.y * deltaLine.y)) {
|
||
points.push(pt1234);
|
||
return;
|
||
}
|
||
|
||
// 继续细分
|
||
this.recursiveGetOptimizedDrawingPoints(start, pt12, pt123, pt1234, points, distanceTolerance);
|
||
this.recursiveGetOptimizedDrawingPoints(pt1234, pt234, pt34, end, points, distanceTolerance);
|
||
}
|
||
}
|
||
}
|