#### /Scripts/MathUtils.cs

C# | 157 lines | 116 code | 27 blank | 14 comment | 7 complexity | a4dc6f168596d7a670ef438dec315909 MD5 | raw file
```  1using UnityEngine;
2using System.Collections;
3using System.Collections.Generic;
4
5public class MathUtils
6{
7	public static float GetQuatLength(Quaternion q)
8	{
9		return Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
10	}
11
12	public static Quaternion GetQuatConjugate(Quaternion q)
13	{
14		return new Quaternion(-q.x, -q.y, -q.z, q.w);
15	}
16
17	/// <summary>
18	/// Logarithm of a unit quaternion. The result is not necessary a unit quaternion.
19	/// </summary>
20	public static Quaternion GetQuatLog(Quaternion q)
21	{
22		Quaternion res = q;
23		res.w = 0;
24
25		if (Mathf.Abs(q.w) < 1.0f)
26		{
27			float theta = Mathf.Acos(q.w);
28			float sin_theta = Mathf.Sin(theta);
29
30			if (Mathf.Abs(sin_theta) > 0.0001)
31			{
32				float coef = theta / sin_theta;
33				res.x = q.x * coef;
34				res.y = q.y * coef;
35				res.z = q.z * coef;
36			}
37		}
38
39		return res;
40	}
41
42	public static Quaternion GetQuatExp(Quaternion q)
43	{
44		Quaternion res = q;
45
46		float fAngle = Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z);
47		float fSin = Mathf.Sin(fAngle);
48
49		res.w = Mathf.Cos(fAngle);
50
51		if (Mathf.Abs(fSin) > 0.0001)
52		{
53			float coef = fSin / fAngle;
54			res.x = coef * q.x;
55			res.y = coef * q.y;
56			res.z = coef * q.z;
57		}
58
59		return res;
60	}
61
62	/// <summary>
64	/// </summary>
65	public static Quaternion GetQuatSquad(float t, Quaternion q0, Quaternion q1, Quaternion a0, Quaternion a1)
66	{
67		float slerpT = 2.0f * t * (1.0f - t);
68
69		Quaternion slerpP = Slerp(q0, q1, t);
70		Quaternion slerpQ = Slerp(a0, a1, t);
71
72		return Slerp(slerpP, slerpQ, slerpT);
73	}
74
75	public static Quaternion GetSquadIntermediate(Quaternion q0, Quaternion q1, Quaternion q2)
76	{
77		Quaternion q1Inv = GetQuatConjugate(q1);
78		Quaternion p0 = GetQuatLog(q1Inv * q0);
79		Quaternion p2 = GetQuatLog(q1Inv * q2);
80		Quaternion sum = new Quaternion(-0.25f * (p0.x + p2.x), -0.25f * (p0.y + p2.y), -0.25f * (p0.z + p2.z), -0.25f * (p0.w + p2.w));
81
82		return q1 * GetQuatExp(sum);
83	}
84
85	/// <summary>
86	/// Smooths the input parameter t.
87	/// If less than k1 ir greater than k2, it uses a sin.
88	/// Between k1 and k2 it uses linear interp.
89	/// </summary>
90	public static float Ease(float t, float k1, float k2)
91	{
92		float f; float s;
93
94		f = k1 * 2 / Mathf.PI + k2 - k1 + (1.0f - k2) * 2 / Mathf.PI;
95
96		if (t < k1)
97		{
98			s = k1 * (2 / Mathf.PI) * (Mathf.Sin((t / k1) * Mathf.PI / 2 - Mathf.PI / 2) + 1);
99		}
100		else
101			if (t < k2)
102			{
103				s = (2 * k1 / Mathf.PI + t - k1);
104			}
105			else
106			{
107				s = 2 * k1 / Mathf.PI + k2 - k1 + ((1 - k2) * (2 / Mathf.PI)) * Mathf.Sin(((t - k2) / (1.0f - k2)) * Mathf.PI / 2);
108			}
109
110		return (s / f);
111	}
112
113	/// <summary>
114	/// We need this because Quaternion.Slerp always uses the shortest arc.
115	/// </summary>
116	public static Quaternion Slerp(Quaternion p, Quaternion q, float t)
117	{
118		Quaternion ret;
119
120		float fCos = Quaternion.Dot(p, q);
121
122		if ((1.0f + fCos) > 0.00001)
123		{
124			float fCoeff0, fCoeff1;
125
126			if ((1.0f - fCos) > 0.00001)
127			{
128				float omega = Mathf.Acos(fCos);
129				float invSin = 1.0f / Mathf.Sin(omega);
130				fCoeff0 = Mathf.Sin((1.0f - t) * omega) * invSin;
131				fCoeff1 = Mathf.Sin(t * omega) * invSin;
132			}
133			else
134			{
135				fCoeff0 = 1.0f - t;
136				fCoeff1 = t;
137			}
138
139			ret.x = fCoeff0 * p.x + fCoeff1 * q.x;
140			ret.y = fCoeff0 * p.y + fCoeff1 * q.y;
141			ret.z = fCoeff0 * p.z + fCoeff1 * q.z;
142			ret.w = fCoeff0 * p.w + fCoeff1 * q.w;
143		}
144		else
145		{
146			float fCoeff0 = Mathf.Sin((1.0f - t) * Mathf.PI * 0.5f);
147			float fCoeff1 = Mathf.Sin(t * Mathf.PI * 0.5f);
148
149			ret.x = fCoeff0 * p.x - fCoeff1 * p.y;
150			ret.y = fCoeff0 * p.y + fCoeff1 * p.x;
151			ret.z = fCoeff0 * p.z - fCoeff1 * p.w;
152			ret.w = p.z;
153		}
154
155		return ret;
156	}
157}
```