毫无状态的度过一段时间，今天把贝塞尔曲线实现吧。之前自己推导了一阶，二阶，三阶的贝塞尔方程式，接下来只需要将其实现就好。
在网上找了文章截了两张图（一阶和二阶）：
贝塞尔一阶.png
贝塞尔二阶.png
三阶（没找到，明天上传自己推导的吧）
还有可以参考雨松大神的文章（PS：但是好像有点错误）
链接：http://www.xuanyusong.com/archives/1548
接下来就是三阶的代码：
using UnityEngine;
[System.Serializable]
public class Bezier : System.Object
{
//定义四个点，起点终点，两个控制点
public Vector3 p0;
public Vector3 p1;
public Vector3 p2;
public Vector3 p3;
public float ti = 0f;
//定义几个私有的向量来存储那些点
private Vector3 b0 = Vector3.zero;
private Vector3 b1 = Vector3.zero;
private Vector3 b2 = Vector3.zero;
private Vector3 b3 = Vector3.zero;
//四个点之间的三个比例点的坐标
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;
//初始化这四个点
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
//获取t时刻的点
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.p1.x - this.p0.x);
this.Bx = 3f * (this.p2.x - this.p1.x) - this.Cx;
this.Ax = this.p3.x - this.p0.x - this.Cx - this.Bx;
this.Cy = 3f * (this.p1.y - this.p0.y);
this.By = 3f * (this.p2.y - this.p1.y) - this.Cy;
this.Ay = this.p3.y - this.p0.y - this.Cy - this.By;
this.Cz = 3f * (this.p1.z- this.p0.z);
this.Bz = 3f * (this.p2.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;
}
}
}
这个实际上是在雨松大神的基础上修正的（PS：微笑脸），但是重要的贝塞尔的理解（PS：微笑脸）
