1/// @ref gtx_rotate_vector
2
3namespace glm
4{
5	template<typename T, qualifier Q>
6	GLM_FUNC_QUALIFIER vec<3, T, Q> slerp
7	(
8		vec<3, T, Q> const& x,
9		vec<3, T, Q> const& y,
10		T const& a
11	)
12	{
13		// get cosine of angle between vectors (-1 -> 1)
14		T CosAlpha = dot(x, y);
15		// get angle (0 -> pi)
16		T Alpha = acos(CosAlpha);
17		// get sine of angle between vectors (0 -> 1)
18		T SinAlpha = sin(Alpha);
19		// this breaks down when SinAlpha = 0, i.e. Alpha = 0 or pi
20		T t1 = sin((static_cast<T>(1) - a) * Alpha) / SinAlpha;
21		T t2 = sin(a * Alpha) / SinAlpha;
22
23		// interpolate src vectors
24		return x * t1 + y * t2;
25	}
26
27	template<typename T, qualifier Q>
28	GLM_FUNC_QUALIFIER vec<2, T, Q> rotate
29	(
30		vec<2, T, Q> const& v,
31		T const& angle
32	)
33	{
34		vec<2, T, Q> Result;
35		T const Cos(cos(angle));
36		T const Sin(sin(angle));
37
38		Result.x = v.x * Cos - v.y * Sin;
39		Result.y = v.x * Sin + v.y * Cos;
40		return Result;
41	}
42
43	template<typename T, qualifier Q>
44	GLM_FUNC_QUALIFIER vec<3, T, Q> rotate
45	(
46		vec<3, T, Q> const& v,
47		T const& angle,
48		vec<3, T, Q> const& normal
49	)
50	{
51		return mat<3, 3, T, Q>(glm::rotate(angle, normal)) * v;
52	}
53	/*
54	template<typename T, qualifier Q>
55	GLM_FUNC_QUALIFIER vec<3, T, Q> rotateGTX(
56		const vec<3, T, Q>& x,
57		T angle,
58		const vec<3, T, Q>& normal)
59	{
60		const T Cos = cos(radians(angle));
61		const T Sin = sin(radians(angle));
62		return x * Cos + ((x * normal) * (T(1) - Cos)) * normal + cross(x, normal) * Sin;
63	}
64	*/
65	template<typename T, qualifier Q>
66	GLM_FUNC_QUALIFIER vec<4, T, Q> rotate
67	(
68		vec<4, T, Q> const& v,
69		T const& angle,
70		vec<3, T, Q> const& normal
71	)
72	{
73		return rotate(angle, normal) * v;
74	}
75
76	template<typename T, qualifier Q>
77	GLM_FUNC_QUALIFIER vec<3, T, Q> rotateX
78	(
79		vec<3, T, Q> const& v,
80		T const& angle
81	)
82	{
83		vec<3, T, Q> Result(v);
84		T const Cos(cos(angle));
85		T const Sin(sin(angle));
86
87		Result.y = v.y * Cos - v.z * Sin;
88		Result.z = v.y * Sin + v.z * Cos;
89		return Result;
90	}
91
92	template<typename T, qualifier Q>
93	GLM_FUNC_QUALIFIER vec<3, T, Q> rotateY
94	(
95		vec<3, T, Q> const& v,
96		T const& angle
97	)
98	{
99		vec<3, T, Q> Result = v;
100		T const Cos(cos(angle));
101		T const Sin(sin(angle));
102
103		Result.x =  v.x * Cos + v.z * Sin;
104		Result.z = -v.x * Sin + v.z * Cos;
105		return Result;
106	}
107
108	template<typename T, qualifier Q>
109	GLM_FUNC_QUALIFIER vec<3, T, Q> rotateZ
110	(
111		vec<3, T, Q> const& v,
112		T const& angle
113	)
114	{
115		vec<3, T, Q> Result = v;
116		T const Cos(cos(angle));
117		T const Sin(sin(angle));
118
119		Result.x = v.x * Cos - v.y * Sin;
120		Result.y = v.x * Sin + v.y * Cos;
121		return Result;
122	}
123
124	template<typename T, qualifier Q>
125	GLM_FUNC_QUALIFIER vec<4, T, Q> rotateX
126	(
127		vec<4, T, Q> const& v,
128		T const& angle
129	)
130	{
131		vec<4, T, Q> Result = v;
132		T const Cos(cos(angle));
133		T const Sin(sin(angle));
134
135		Result.y = v.y * Cos - v.z * Sin;
136		Result.z = v.y * Sin + v.z * Cos;
137		return Result;
138	}
139
140	template<typename T, qualifier Q>
141	GLM_FUNC_QUALIFIER vec<4, T, Q> rotateY
142	(
143		vec<4, T, Q> const& v,
144		T const& angle
145	)
146	{
147		vec<4, T, Q> Result = v;
148		T const Cos(cos(angle));
149		T const Sin(sin(angle));
150
151		Result.x =  v.x * Cos + v.z * Sin;
152		Result.z = -v.x * Sin + v.z * Cos;
153		return Result;
154	}
155
156	template<typename T, qualifier Q>
157	GLM_FUNC_QUALIFIER vec<4, T, Q> rotateZ
158	(
159		vec<4, T, Q> const& v,
160		T const& angle
161	)
162	{
163		vec<4, T, Q> Result = v;
164		T const Cos(cos(angle));
165		T const Sin(sin(angle));
166
167		Result.x = v.x * Cos - v.y * Sin;
168		Result.y = v.x * Sin + v.y * Cos;
169		return Result;
170	}
171
172	template<typename T, qualifier Q>
173	GLM_FUNC_QUALIFIER mat<4, 4, T, Q> orientation
174	(
175		vec<3, T, Q> const& Normal,
176		vec<3, T, Q> const& Up
177	)
178	{
179		if(all(equal(Normal, Up, epsilon<T>())))
180			return mat<4, 4, T, Q>(static_cast<T>(1));
181
182		vec<3, T, Q> RotationAxis = cross(Up, Normal);
183		T Angle = acos(dot(Normal, Up));
184
185		return rotate(Angle, RotationAxis);
186	}
187}//namespace glm
188