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新增bezierSpline提供了一系列立方贝塞尔点，并提供了帮助方法来访问贝塞尔

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This commit is contained in:
yhh
2020-12-10 10:53:05 +08:00
parent 8230d9cd9b
commit f38b5261d5
5 changed files with 330 additions and 51 deletions
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51
source/src/Math/Bezier.ts
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@@ -13,8 +13,27 @@ module es {
public static getPoint(p0: Vector2, p1: Vector2, p2: Vector2, t: number): Vector2 {
t = MathHelper.clamp01(t);
let oneMinusT = 1 - t;
return Vector2.add(Vector2.add(Vector2.multiply(new Vector2(oneMinusT * oneMinusT), p0),
Vector2.multiply(new Vector2(2 * oneMinusT * t), p1)), Vector2.multiply(new Vector2(t * t), p2));
return new Vector2(oneMinusT * oneMinusT).multiply(p0)
.add(new Vector2(2 * oneMinusT * t).multiply(p1))
.add(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)
.add(new Vector2(3 * oneMinusT * oneMinusT * t).multiply(firstControlPoint))
.add(new Vector2(3 * oneMinusT * t * t).multiply(secondControlPoint))
.add(new Vector2(t * t * t).multiply(end));
}
/**
@@ -25,8 +44,8 @@ module es {
* @param t
*/
public static getFirstDerivative(p0: Vector2, p1: Vector2, p2: Vector2, t: number) {
return Vector2.add(Vector2.multiply(new Vector2(2 * (1 - t)), Vector2.subtract(p1, p0)),
Vector2.multiply(new Vector2(2 * t), Vector2.subtract(p2, p1)));
return new Vector2(2 * (1 - t)).multiply(Vector2.subtract(p1, p0))
.add(new Vector2(2 * t).multiply(Vector2.subtract(p2, p1)));
}
/**
@@ -41,27 +60,9 @@ module es {
end: Vector2, t: number) {
t = MathHelper.clamp01(t);
let oneMunusT = 1 - t;
return Vector2.add(Vector2.add(Vector2.multiply(new Vector2(3 * oneMunusT * oneMunusT), Vector2.subtract(firstControlPoint, start)),
Vector2.multiply(new Vector2(6 * oneMunusT * t), Vector2.subtract(secondControlPoint, firstControlPoint))),
Vector2.multiply(new Vector2(3 * t * t), Vector2.subtract(end, secondControlPoint)));
}
/**
* 计算一个三次贝塞尔
* @param start
* @param firstControlPoint
* @param secondControlPoint
* @param end
* @param t
*/
public static getPointThree(start: Vector2, firstControlPoint: Vector2, secondControlPoint: Vector2,
end: Vector2, t: number) {
t = MathHelper.clamp01(t);
let oneMunusT = 1 - t;
return Vector2.add(Vector2.add(Vector2.add(Vector2.multiply(new Vector2(oneMunusT * oneMunusT * oneMunusT), start),
Vector2.multiply(new Vector2(3 * oneMunusT * oneMunusT * t), firstControlPoint)),
Vector2.multiply(new Vector2(3 * oneMunusT * t * t), secondControlPoint)),
Vector2.multiply(new Vector2(t * t * t), end));
return new Vector2(3 * oneMunusT * oneMunusT).multiply(Vector2.subtract(firstControlPoint, start))
.add(new Vector2(6 * oneMunusT * t).multiply(Vector2.subtract(secondControlPoint, firstControlPoint)))
.add(new Vector2(3 * t * t).multiply(Vector2.subtract(end, secondControlPoint)));
}
/**