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
|
namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'mix' only accept floating-point inputs");
T const cosTheta = dot(x, y);
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > static_cast<T>(1) - epsilon<T>())
{
// Linear interpolation
return qua<T, Q>(
mix(x.w, y.w, a),
mix(x.x, y.x, a),
mix(x.y, y.y, a),
mix(x.z, y.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'lerp' only accept floating-point inputs");
// Lerp is only defined in [0, 1]
assert(a >= static_cast<T>(0));
assert(a <= static_cast<T>(1));
return x * (static_cast<T>(1) - a) + (y * a);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'slerp' only accept floating-point inputs");
qua<T, Q> z = y;
T cosTheta = dot(x, y);
// If cosTheta < 0, the interpolation will take the long way around the sphere.
// To fix this, one quat must be negated.
if(cosTheta < static_cast<T>(0))
{
z = -y;
cosTheta = -cosTheta;
}
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if(cosTheta > static_cast<T>(1) - epsilon<T>())
{
// Linear interpolation
return qua<T, Q>(
mix(x.w, z.w, a),
mix(x.x, z.x, a),
mix(x.y, z.y, a),
mix(x.z, z.z, a));
}
else
{
// Essential Mathematics, page 467
T angle = acos(cosTheta);
return (sin((static_cast<T>(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
}
}
template<typename T, typename S, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a, S k)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'slerp' only accept floating-point inputs");
GLM_STATIC_ASSERT(std::numeric_limits<S>::is_integer, "'slerp' only accept integer for spin count");
qua<T, Q> z = y;
T cosTheta = dot(x, y);
// If cosTheta < 0, the interpolation will take the long way around the sphere.
// To fix this, one quat must be negated.
if (cosTheta < static_cast<T>(0))
{
z = -y;
cosTheta = -cosTheta;
}
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
if (cosTheta > static_cast<T>(1) - epsilon<T>())
{
// Linear interpolation
return qua<T, Q>(
mix(x.w, z.w, a),
mix(x.x, z.x, a),
mix(x.y, z.y, a),
mix(x.z, z.z, a));
}
else
{
// Graphics Gems III, page 96
T angle = acos(cosTheta);
T phi = angle + k * glm::pi<T>();
return (sin(angle - a * phi)* x + sin(a * phi) * z) / sin(angle);
}
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> conjugate(qua<T, Q> const& q)
{
return qua<T, Q>(q.w, -q.x, -q.y, -q.z);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER qua<T, Q> inverse(qua<T, Q> const& q)
{
return conjugate(q) / dot(q, q);
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
}
}//namespace glm
#if GLM_CONFIG_SIMD == GLM_ENABLE
# include "quaternion_common_simd.inl"
#endif
|
