贝塞尔曲线最近经常接触到，今天研究了一下。
- 原理
关于它的原理，网上有很多。
1.一阶
2.二阶
3.多阶
可以看到，多阶可以慢慢降阶为一阶贝塞尔曲线。
//一阶
private Vector3 BaseBezier(float t,Vector3 pos0,Vector3 pos1)
{
return pos0 + t * (pos1-pos0);
}
递归，降阶为一阶
//n阶
private Vector3 BezierPro(float t,params Vector3[] posArray)
{
int l = posArray.Length; if (l<)
{
return Vector3.zero;
}
else if (l == )
{
return BaseBezier(t, posArray[], posArray[]);
}
else
{
Vector3[] tempArray = new Vector3[l-];
for (int i = ; i < l-; i++)
{
tempArray[i] = BaseBezier(t, posArray[i], posArray[i + ]);
}
return BezierPro(t,tempArray);
} }
在unity里整合：
using UnityEngine;
using System.Collections;
using System.Linq;
[ExecuteInEditMode]
public class Bezier : MonoBehaviour {
public LineRenderer line;
public Transform[] PosArray; [Range(,)]
public int sampleCount;
// Use this for initialization
void Start () { } // Update is called once per frame
void Update () {
SetBezier();
} //一阶
private Vector3 BaseBezier(float t,Vector3 pos0,Vector3 pos1)
{
return pos0 + t * (pos1-pos0);
}
//n阶
private Vector3 BezierPro(float t,params Vector3[] posArray)
{
int l = posArray.Length; if (l<)
{
return Vector3.zero;
}
else if (l == )
{
return BaseBezier(t, posArray[], posArray[]);
}
else
{
Vector3[] tempArray = new Vector3[l-];
for (int i = ; i < l-; i++)
{
tempArray[i] = BaseBezier(t, posArray[i], posArray[i + ]);
}
return BezierPro(t,tempArray);
} } [ContextMenu("设置贝塞尔曲线")]
private void SetBezier()
{
if (PosArray.Length<)
{
return;
}
Vector3[] tempArray = new Vector3[PosArray.Length]; for (int i = ; i < PosArray.Length; i++)
{
tempArray[i] = PosArray[i].position;
} line.SetVertexCount(sampleCount);
for (int i = ; i < sampleCount; i++)
{
line.SetPosition(i, BezierPro( (float)i/(float)sampleCount, tempArray) );
}
}
}
效果展示