summaryrefslogtreecommitdiffstats
path: root/depedencies/include/glm/gtx/quaternion.inl
blob: c86ec1872f10b9ade690b41e90607d880050de17 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
/// @ref gtx_quaternion
/// @file glm/gtx/quaternion.inl

#include <limits>
#include "../gtc/constants.hpp"

namespace glm
{
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> cross(tvec3<T, P> const& v, tquat<T, P> const& q)
	{
		return inverse(q) * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> cross(tquat<T, P> const& q, tvec3<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> squad
	(
		tquat<T, P> const & q1,
		tquat<T, P> const & q2,
		tquat<T, P> const & s1,
		tquat<T, P> const & s2,
		T const & h)
	{
		return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> intermediate
	(
		tquat<T, P> const & prev,
		tquat<T, P> const & curr,
		tquat<T, P> const & next
	)
	{
		tquat<T, P> invQuat = inverse(curr);
		return exp((log(next + invQuat) + log(prev + invQuat)) / static_cast<T>(-4)) * curr;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> exp(tquat<T, P> const& q)
	{
		tvec3<T, P> u(q.x, q.y, q.z);
		T const Angle = glm::length(u);
		if (Angle < epsilon<T>())
			return tquat<T, P>();

		tvec3<T, P> const v(u / Angle);
		return tquat<T, P>(cos(Angle), sin(Angle) * v);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> log(tquat<T, P> const& q)
	{
		tvec3<T, P> u(q.x, q.y, q.z);
		T Vec3Len = length(u);

		if (Vec3Len < epsilon<T>())
		{
			if(q.w > static_cast<T>(0))
				return tquat<T, P>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
			else if(q.w < static_cast<T>(0))
				return tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
			else
				return tquat<T, P>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity());
		}
		else
		{
			T t = atan(Vec3Len, T(q.w)) / Vec3Len;
			T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
			return tquat<T, P>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
		}
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> const & x, T const & y)
	{
		//Raising to the power of 0 should yield 1
		//Needed to prevent a division by 0 error later on
		if(y > -epsilon<T>() && y < epsilon<T>())
			return tquat<T, P>(1,0,0,0);

		//To deal with non-unit quaternions
		T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);

		//Equivalent to raising a real number to a power
		//Needed to prevent a division by 0 error later on
		if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
			return tquat<T, P>(pow(x.w, y),0,0,0);

		T Angle = acos(x.w / magnitude);
		T NewAngle = Angle * y;
		T Div = sin(NewAngle) / sin(Angle);
		T Mag = pow(magnitude, y - static_cast<T>(1));

		return tquat<T, P>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec3<T, P> rotate(tquat<T, P> const& q, tvec3<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tvec4<T, P> rotate(tquat<T, P> const& q, tvec4<T, P> const& v)
	{
		return q * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T extractRealComponent(tquat<T, P> const& q)
	{
		T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
		if(w < T(0))
			return T(0);
		else
			return -sqrt(w);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T length2(tquat<T, P> const& q)
	{
		return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> shortMix(tquat<T, P> const& x, tquat<T, P> const& y, T const& a)
	{
		if(a <= static_cast<T>(0)) return x;
		if(a >= static_cast<T>(1)) return y;

		T fCos = dot(x, y);
		tquat<T, P> y2(y); //BUG!!! tquat<T> y2;
		if(fCos < static_cast<T>(0))
		{
			y2 = -y;
			fCos = -fCos;
		}

		//if(fCos > 1.0f) // problem
		T k0, k1;
		if(fCos > (static_cast<T>(1) - epsilon<T>()))
		{
			k0 = static_cast<T>(1) - a;
			k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a;
		}
		else
		{
			T fSin = sqrt(T(1) - fCos * fCos);
			T fAngle = atan(fSin, fCos);
			T fOneOverSin = static_cast<T>(1) / fSin;
			k0 = sin((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
			k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
		}

		return tquat<T, P>(
			k0 * x.w + k1 * y2.w,
			k0 * x.x + k1 * y2.x,
			k0 * x.y + k1 * y2.y,
			k0 * x.z + k1 * y2.z);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> fastMix(tquat<T, P> const& x, tquat<T, P> const& y, T const & a)
	{
		return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> rotation(tvec3<T, P> const& orig, tvec3<T, P> const& dest)
	{
		T cosTheta = dot(orig, dest);
		tvec3<T, P> rotationAxis;

		if(cosTheta >= static_cast<T>(1) - epsilon<T>())
			return quat();

		if(cosTheta < static_cast<T>(-1) + epsilon<T>())
		{
			// special case when vectors in opposite directions :
			// there is no "ideal" rotation axis
			// So guess one; any will do as long as it's perpendicular to start
			// This implementation favors a rotation around the Up axis (Y),
			// since it's often what you want to do.
			rotationAxis = cross(tvec3<T, P>(0, 0, 1), orig);
			if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
				rotationAxis = cross(tvec3<T, P>(1, 0, 0), orig);

			rotationAxis = normalize(rotationAxis);
			return angleAxis(pi<T>(), rotationAxis);
		}

		// Implementation from Stan Melax's Game Programming Gems 1 article
		rotationAxis = cross(orig, dest);

		T s = sqrt((T(1) + cosTheta) * static_cast<T>(2));
		T invs = static_cast<T>(1) / s;

		return tquat<T, P>(
			s * static_cast<T>(0.5f), 
			rotationAxis.x * invs,
			rotationAxis.y * invs,
			rotationAxis.z * invs);
	}

}//namespace glm