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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
View File

@@ -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)));
}
/**

114
source/src/Math/BezierSpline.ts Normal file
View File

@@ -0,0 +1,114 @@
module es {
/**
* 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
*/
export class BezierSpline {
public _points: FastList<Vector2> = new FastList<Vector2>();
public _curveCount: number = 0;
/**
* 在这个过程中，t被修改为在曲线段的范围内。
* @param t
*/
public pointIndexAtTime(t: Ref<number>): number {
let i = 0;
if (t.value >= 1) {
t.value = 1;
i = this._points.length - 4;
} else {
t.value = MathHelper.clamp01(t.value) * this._curveCount;
i = ~~t;
t.value -= i;
i *= 3;
}
return i;
}
/**
* 设置一个控制点，考虑到这是否是一个共享点，如果是，则适当调整
* @param index
* @param point
*/
public setControlPoint(index: number, point: Vector2) {
if (index % 3 == 0) {
let delta = Vector2.subtract(point, this._points.buffer[index]);
if (index > 0)
this._points.buffer[index - 1].add(delta);
if (index + 1 < this._points.length)
this._points.buffer[index + 1].add(delta);
}
this._points.buffer[index] = point;
}
/**
* 得到时间t的贝塞尔曲线上的点
* @param t
*/
public getPointAtTime(t: number): Vector2{
let i = this.pointIndexAtTime(new Ref(t));
return Bezier.getPointThree(this._points.buffer[i], this._points.buffer[i + 1], this._points.buffer[i + 2],
this._points.buffer[i + 3], t);
}
/**
* 得到贝塞尔在时间t的速度（第一导数）
* @param t
*/
public getVelocityAtTime(t: number): Vector2 {
let i = this.pointIndexAtTime(new Ref(t));
return Bezier.getFirstDerivativeThree(this._points.buffer[i], this._points.buffer[i + 1], this._points.buffer[i + 2],
this._points.buffer[i + 3], t);
}
/**
* 得到时间t时贝塞尔的方向（归一化第一导数）
* @param t
*/
public getDirectionAtTime(t: number) {
return Vector2.normalize(this.getVelocityAtTime(t));
}
/**
* 在贝塞尔曲线上添加一条曲线
* @param start
* @param firstControlPoint
* @param secondControlPoint
* @param end
*/
public addCurve(start: Vector2, firstControlPoint: Vector2, secondControlPoint: Vector2, end: Vector2) {
// 只有当这是第一条曲线时，我们才会添加起始点。对于其他所有的曲线，前一个曲线的终点应该等于新曲线的起点。
if (this._points.length == 0)
this._points.add(start);
this._points.add(firstControlPoint);
this._points.add(secondControlPoint);
this._points.add(end);
this._curveCount = (this._points.length - 1) / 3;
}
/**
* 重置bezier，移除所有点
*/
public reset() {
this._points.clear();
}
/**
* 将splitine分解成totalSegments部分，并返回使用线条绘制所需的所有点
* @param totalSegments
*/
public getDrawingPoints(totalSegments: number): Vector2[] {
let points: Vector2[] = [];
for (let i = 0; i < totalSegments; i ++) {
let t = i / totalSegments;
points[i] = this.getPointAtTime(t);
}
return points;
}
}
}