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。

1  //一阶
2     private Vector3 BaseBezier(float t,Vector3 pos0,Vector3 pos1)
3     {
4         return pos0 + t * (pos1-pos0);
5     }

 

 递归，降阶为一阶

 1  //n阶
 2     private Vector3 BezierPro(float t,params Vector3[] posArray)
 3     {
 4         int l = posArray.Length;
 5 
 6         if (l<2)
 7         {
 8             return Vector3.zero;
 9         }
10         else  if (l == 2)
11         {
12             return BaseBezier(t, posArray[0], posArray[1]);
13         }
14         else
15         {
16             Vector3[] tempArray = new Vector3[l-1];
17             for (int i = 0; i < l-1; i++)
18             {
19                 tempArray[i] = BaseBezier(t, posArray[i], posArray[i + 1]);
20             }
21             return BezierPro(t,tempArray);
22         }
23 
24     }

 

　　在unity里整合：

 1 using UnityEngine;
 2 using System.Collections;
 3 using System.Linq;
 4 [ExecuteInEditMode]
 5 public class Bezier : MonoBehaviour {
 6     public LineRenderer line;
 7     public Transform[] PosArray;
 8 
 9     [Range(0,100)]
10     public int sampleCount;
11     // Use this for initialization
12     void Start () {
13     
14     }
15     
16     // Update is called once per frame
17     void Update () {
18         SetBezier();
19     }
20 
21     //一阶
22     private Vector3 BaseBezier(float t,Vector3 pos0,Vector3 pos1)
23     {
24         return pos0 + t * (pos1-pos0);
25     }
26     //n阶
27     private Vector3 BezierPro(float t,params Vector3[] posArray)
28     {
29         int l = posArray.Length;
30 
31         if (l<2)
32         {
33             return Vector3.zero;
34         }
35         else  if (l == 2)
36         {
37             return BaseBezier(t, posArray[0], posArray[1]);
38         }
39         else
40         {
41             Vector3[] tempArray = new Vector3[l-1];
42             for (int i = 0; i < l-1; i++)
43             {
44                 tempArray[i] = BaseBezier(t, posArray[i], posArray[i + 1]);
45             }
46             return BezierPro(t,tempArray);
47         }
48 
49     }
50 
51     [ContextMenu("设置贝塞尔曲线")]
52     private void SetBezier()
53     {
54         if (PosArray.Length<2)
55         {
56             return;
57         }
58         Vector3[] tempArray = new Vector3[PosArray.Length];
59 
60         for (int i = 0; i < PosArray.Length; i++)
61         {
62             tempArray[i] = PosArray[i].position;
63         }
64 
65         line.SetVertexCount(sampleCount);
66         for (int i = 0; i < sampleCount; i++)
67         {
68             line.SetPosition(i, BezierPro( (float)i/(float)sampleCount, tempArray) );
69         }
70     }
71 }

 

 

 

效果展示