贝塞尔曲线

using UnityEngine;


[System.Serializable]
//贝塞尔曲线类
public class Bezier : System.Object

{

public Vector3 Point0;

public Vector3 Point1;

public Vector3 Point2;

public Vector3 Point3;

private Vector3 comparisonPoint0 = Vector3.zero;

private Vector3 comparisonPoint1 = Vector3.zero;

private Vector3 comparisonPoint2 = Vector3.zero;

private Vector3 comparisonPoint3 = 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;



//得到四个点的坐标，起始点，中间两个点和末尾的点
public void SetPoint( Vector3 point0, Vector3 point1, Vector3 point2, Vector3 point3 )

{

this.Point0 = point0;

this.Point1 = point1;

this.Point2 = point2;

this.Point3 = point3;

}

// 0.0 <= t <= 1.0
//确定对应点的坐标
public Vector3 GetOnPathPoint( float t )

{

this.CheckPointChange();

float t2 = t * t;

float t3 = t * t * t;

float x = this.Ax * t3 + this.Bx * t2 + this.Cx * t + Point0.x;

float y = this.Ay * t3 + this.By * t2 + this.Cy * t + Point0.y;

float z = this.Az * t3 + this.Bz * t2 + this.Cz * t + Point0.z;

return new Vector3( x, y, z );

}
//对系数赋值
private void SetCoefficient()

{

this.Cx = 3f * (  this.Point1.x  - this.Point0.x );

this.Bx = 3f * (  this.Point2.x  -  this.Point1.x  ) - this.Cx;

this.Ax = this.Point3.x - this.Point0.x - this.Cx - this.Bx;

this.Cy = 3f * (  this.Point1.y  - this.Point0.y );

this.By = 3f * (  this.Point2.y  - this.Point1.y  ) - this.Cy;

this.Ay = this.Point3.y - this.Point0.y - this.Cy - this.By;

this.Cz = 3f * (  this.Point1.z  - this.Point0.z );

this.Bz = 3f * ( this.Point2.z - this.Point1.z  ) - this.Cz;

this.Az = this.Point3.z - this.Point0.z - this.Cz - this.Bz;

}

// Check if p0, p1, p2 or p3 have changed

private void CheckPointChange()

{

if( this.Point0 != this.comparisonPoint0 || this.Point1 != this.comparisonPoint1 || this.Point2 != this.comparisonPoint2 || this.Point3 != this.comparisonPoint3 )

{

this.SetCoefficient();

this.comparisonPoint0 = this.Point0;

this.comparisonPoint1 = this.Point1;

this.comparisonPoint2 = this.Point2;

this.comparisonPoint3 = this.Point3;

}

}

}

//调用的类

using UnityEngine;


public class MyBezier : MonoBehaviour
{


public Transform Head;
public Transform End;


private Vector3 point0;

public Vector3 point1;

public Vector3 point2;

private Vector3 point3;
//贝塞尔曲线算法类
private Bezier bezier;

//曲线的对象
// public GameObject BezierLine;

//曲线对象的曲线组件
public LineRenderer BezierLineRenderer;

void Awake(){
//为了让曲线更加美观，设置曲线由100个点来组成
BezierLineRenderer.SetVertexCount(100);
bezier = new Bezier( );
}

void Start()
{
drawLine();
}




void Update()
{


//当起始点或者末尾点的坐标改变时重新绘制线
if (point0 !=Head.position||point3 !=End.position) {
setPoint();
drawLine();
}


}
//对中间的点赋值
private void setPoint(){
point1 =Vector3.Lerp(point1,(Head.position + End.position) * 0.5f,0.1f);
point2 = point1;
}
//绘制线
private void drawLine(){
point0 =Head.position;
point3 =End.position;
bezier.SetPoint(point0,point1,point2,point3);
//循环100遍来绘制贝塞尔曲线每个线段
for(int i =0; i < 100; i++)
{
//参数的取值范围 0 - 1 返回曲线每一点的位置
//为了精确这里使用i * 0.01 得到当前点的坐标
Vector3 v = bezier.GetOnPathPoint( (float)(i *0.01) );
//把每条线段绘制出来 完成贝塞尔曲线的绘制
BezierLineRenderer.SetPosition(i,v);
}
}

}