Unity3D 贝塞尔曲线

最近为了模拟法术的运行轨迹，打算使用了贝塞尔曲线，以前在 2D 开发项目中也经常使用贝塞尔曲线，但是在 3D 场景中贝塞尔曲线的实现还是稍稍有些麻烦，于是在网上收集 Unity3D 贝塞尔曲线的代码，原文链接：http://www.xuanyusong.com/archives/1548

Demo 过程如下：

示例代码：

01	using UnityEngine;

02	using System.Collections;

03

04	public class BezierPath : MonoBehaviour

05

{

06	public GameObject sphere;

07

08	public GameObject begin;

09	public GameObject control0;

10	public GameObject control1;

11	public GameObject end;

12

13	void Awake()

14

{

15	Bezier bezier = new Bezier (begin.transform.position, control0.transform.position, control1.transform.position, end.transform.position);

16

17	int pointSize = 20;

18	Vector3[] resultList = new Vector3[pointSize];

19

20	for(int index = 1; index <= pointSize; index ++)

21

{

22	resultList[index - 1] = bezier.GetPointAtTime((float)index / (float)pointSize);

23

}

24

25	foreach (Vector3 point in resultList)

26

{

27	GameObject gameObject = (GameObject)Instantiate(sphere);

28	gameObject.transform.localPosition = point;

29	gameObject.transform.localScale = new Vector3(0.5f, 0.5f, 0.5f);

30

}

31

}

32

}

Bezier.cs

view source print ?

01	using UnityEngine;

02

03	public class Bezier

04

{

05	public Vector3 p0;

06	public Vector3 p1;

07	public Vector3 p2;

08	public Vector3 p3;

09

10	private Vector3 b0 = Vector3.zero;

11	private Vector3 b1 = Vector3.zero;

12	private Vector3 b2 = Vector3.zero;

13	private Vector3 b3 = Vector3.zero;

14

15	private float Ax;

16	private float Ay;

17	private float Az;

18

19	private float Bx;

20	private float By;

21	private float Bz;

22

23	private float Cx;

24	private float Cy;

25	private float Cz;

26

27	/// <summary>

28

/// 构造函数

29	/// </summary>

30	/// <param name="v0">起始点</param>

31	/// <param name="v1">第一个控制点</param>

32	/// <param name="v2">第二个控制点（通过可省略，有 Vector3.Zero 代码）</param>

33	/// <param name="v3">结束点</param>

34	public Bezier( Vector3 v0, Vector3 v1, Vector3 v2, Vector3 v3 )

35

{

36	this.p0 = v0;

37	this.p1 = v1;

38	this.p2 = v2;

39	this.p3 = v3;

40

}

41

42	/// <summary>

43	/// 通过 t 获取节点

44	/// </summary>

45	/// <returns>The point at time.</returns>

46	/// <param name="t">t 的取值范围在 0.0 >= t <= 1.0</param>

47	public Vector3 GetPointAtTime( float t )

48

{

49	this.CheckConstant();

50

51	float t2 = t * t;

52	float t3 = t * t * t;

53	float x = this.Ax * t3 + this.Bx * t2 + this.Cx * t + p0.x;

54	float y = this.Ay * t3 + this.By * t2 + this.Cy * t + p0.y;

55	float z = this.Az * t3 + this.Bz * t2 + this.Cz * t + p0.z;

56	return new Vector3( x, y, z );

57

}

58

59	private void SetConstant()

60

{

61	this.Cx = 3f * ( ( this.p0.x + this.p1.x ) - this.p0.x );

62	this.Bx = 3f * ( ( this.p3.x + this.p2.x ) - ( this.p0.x +this.p1.x ) ) - this.Cx;

63	this.Ax = this.p3.x - this.p0.x - this.Cx - this.Bx;

64	this.Cy = 3f * ( ( this.p0.y + this.p1.y ) - this.p0.y );

65	this.By = 3f * ( ( this.p3.y + this.p2.y ) - ( this.p0.y +this.p1.y ) ) - this.Cy;

66	this.Ay = this.p3.y - this.p0.y - this.Cy - this.By;

67	this.Cz = 3f * ( ( this.p0.z + this.p1.z ) - this.p0.z );

68	this.Bz = 3f * ( ( this.p3.z + this.p2.z ) - ( this.p0.z +this.p1.z ) ) - this.Cz;

69	this.Az = this.p3.z - this.p0.z - this.Cz - this.Bz;

70

}

71

72	private void CheckConstant()

73

{

74	if( this.p0 != this.b0 || this.p1 != this.b1 || this.p2 != this.b2 || this.p3 != this.b3 )

75

{

76	this.SetConstant();

77

78	this.b0 = this.p0;

79	this.b1 = this.p1;

80	this.b2 = this.p2;

81	this.b3 = this.p3;

82

}

83

}

84

}