在雨松blog上看到一个bezier的class,转过来发现其实不是什么特殊算法,是bezier曲线
using UnityEngine;
[System.Serializable]public class Bezier : System.Object{ public Vector3 p0; public Vector3 p1; public Vector3 p2; public Vector3 p3; public float ti = 0f; private Vector3 b0 = Vector3.zero; private Vector3 b1 = Vector3.zero; private Vector3 b2 = Vector3.zero; private Vector3 b3 = Vector3.zero; private float Ax; private float Ay; private float Az; private float Bx; private float By; private float Bz; private float Cx; private float Cy; private float Cz; // Init function v0 = 1st point, v1 = handle of the 1st point , v2 = handle of the 2nd point, v3 = 2nd point // handle1 = v0 + v1 // handle2 = v3 + v2 public Bezier( Vector3 v0, Vector3 v1, Vector3 v2, Vector3 v3 ) { this.p0 = v0; this.p1 = v1; this.p2 = v2; this.p3 = v3; } // 0.0 >= t <= 1.0 public Vector3 GetPointAtTime( float t ) { this.CheckConstant(); float t2 = t * t; float t3 = t * t * t; float x = this.Ax * t3 + this.Bx * t2 + this.Cx * t + p0.x; float y = this.Ay * t3 + this.By * t2 + this.Cy * t + p0.y; float z = this.Az * t3 + this.Bz * t2 + this.Cz * t + p0.z; return new Vector3( x, y, z ); } private void SetConstant() { this.Cx = 3f * ( ( this.p0.x + this.p1.x ) - this.p0.x ); this.Bx = 3f * ( ( this.p3.x + this.p2.x ) - ( this.p0.x + this.p1.x ) ) - this.Cx; this.Ax = this.p3.x - this.p0.x - this.Cx - this.Bx; this.Cy = 3f * ( ( this.p0.y + this.p1.y ) - this.p0.y ); this.By = 3f * ( ( this.p3.y + this.p2.y ) - ( this.p0.y + this.p1.y ) ) - this.Cy; this.Ay = this.p3.y - this.p0.y - this.Cy - this.By; this.Cz = 3f * ( ( this.p0.z + this.p1.z ) - this.p0.z ); this.Bz = 3f * ( ( this.p3.z + this.p2.z ) - ( this.p0.z + this.p1.z ) ) - this.Cz; this.Az = this.p3.z - this.p0.z - this.Cz - this.Bz; } // Check if p0, p1, p2 or p3 have changed private void CheckConstant() { if( this.p0 != this.b0 || this.p1 != this.b1 || this.p2 != this.b2 || this.p3 != this.b3 ) { this.SetConstant(); this.b0 = this.p0; this.b1 = this.p1; this.b2 = this.p2; this.b3 = this.p3; } }}
private Vector3 GetPoint(float t)
{
int numSections = getPoints.Length - 3;
int tSec = (int)Math.Floor(t * numSections);
int currPt = numSections - 1;
if (currPt > tSec)
{
currPt = tSec;
}
float u = t * numSections - currPt;
Vector3 a = getPoints[currPt];
Vector3 b = getPoints[currPt + 1];
Vector3 c = getPoints[currPt + 2];
Vector3 d = getPoints[currPt + 3];
return .5f * (
(-a + 3f * b - 3f * c + d) * (u * u * u)
+ (2f * a - 5f * b + 4f * c - d) * (u * u)
+ (-a + c) * u
+ 2f * b
);
}
以上的代码可以在0到1之间,沿路径平均细分出曲线
偶然看到的,然后google了一下
发现源头是unity的官方开发人写出来的
然后突然发现itween,hotween,一些赛车塔防的路径都是用这个算法的
当然,我还是没太理解这个算法
补充:
设 已知 的四点为 (x0,y0),(x1,y1),(x2,y2),(x3,y3),其中 0 和 3 是端点,
1,2是控制点,则 该曲线上的所有点表示为:
x = (1-t)^3 *x0 + 3*t*(1-t)^2 *x1 + 3*t^2*(1-t) *x2 + t^3 *x3
y = (1-t)^3 *y0 + 3*t*(1-t)^2 *y1 + 3*t^2*(1-t) *y2 + t^3 *y3
其中 0 <= t <= 1.
应该是beizier曲线的算法
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