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matrix_interpolation.inl
1
2
3#include "../gtc/constants.hpp"
4
5namespace glm
6{
7 template<typename T, qualifier Q>
8 GLM_FUNC_QUALIFIER void axisAngle(mat<4, 4, T, Q> const& m, vec<3, T, Q> & axis, T& angle)
9 {
10 T epsilon = static_cast<T>(0.01);
11 T epsilon2 = static_cast<T>(0.1);
12
13 if((abs(m[1][0] - m[0][1]) < epsilon) && (abs(m[2][0] - m[0][2]) < epsilon) && (abs(m[2][1] - m[1][2]) < epsilon))
14 {
15 if ((abs(m[1][0] + m[0][1]) < epsilon2) && (abs(m[2][0] + m[0][2]) < epsilon2) && (abs(m[2][1] + m[1][2]) < epsilon2) && (abs(m[0][0] + m[1][1] + m[2][2] - static_cast<T>(3.0)) < epsilon2))
16 {
17 angle = static_cast<T>(0.0);
18 axis.x = static_cast<T>(1.0);
19 axis.y = static_cast<T>(0.0);
20 axis.z = static_cast<T>(0.0);
21 return;
22 }
23 angle = static_cast<T>(3.1415926535897932384626433832795);
24 T xx = (m[0][0] + static_cast<T>(1.0)) * static_cast<T>(0.5);
25 T yy = (m[1][1] + static_cast<T>(1.0)) * static_cast<T>(0.5);
26 T zz = (m[2][2] + static_cast<T>(1.0)) * static_cast<T>(0.5);
27 T xy = (m[1][0] + m[0][1]) * static_cast<T>(0.25);
28 T xz = (m[2][0] + m[0][2]) * static_cast<T>(0.25);
29 T yz = (m[2][1] + m[1][2]) * static_cast<T>(0.25);
30 if((xx > yy) && (xx > zz))
31 {
32 if(xx < epsilon)
33 {
34 axis.x = static_cast<T>(0.0);
35 axis.y = static_cast<T>(0.7071);
36 axis.z = static_cast<T>(0.7071);
37 }
38 else
39 {
40 axis.x = sqrt(xx);
41 axis.y = xy / axis.x;
42 axis.z = xz / axis.x;
43 }
44 }
45 else if (yy > zz)
46 {
47 if(yy < epsilon)
48 {
49 axis.x = static_cast<T>(0.7071);
50 axis.y = static_cast<T>(0.0);
51 axis.z = static_cast<T>(0.7071);
52 }
53 else
54 {
55 axis.y = sqrt(yy);
56 axis.x = xy / axis.y;
57 axis.z = yz / axis.y;
58 }
59 }
60 else
61 {
62 if (zz < epsilon)
63 {
64 axis.x = static_cast<T>(0.7071);
65 axis.y = static_cast<T>(0.7071);
66 axis.z = static_cast<T>(0.0);
67 }
68 else
69 {
70 axis.z = sqrt(zz);
71 axis.x = xz / axis.z;
72 axis.y = yz / axis.z;
73 }
74 }
75 return;
76 }
77 T s = sqrt((m[2][1] - m[1][2]) * (m[2][1] - m[1][2]) + (m[2][0] - m[0][2]) * (m[2][0] - m[0][2]) + (m[1][0] - m[0][1]) * (m[1][0] - m[0][1]));
78 if (glm::abs(s) < T(0.001))
79 s = static_cast<T>(1);
80 T const angleCos = (m[0][0] + m[1][1] + m[2][2] - static_cast<T>(1)) * static_cast<T>(0.5);
81 if(angleCos - static_cast<T>(1) < epsilon)
82 angle = pi<T>() * static_cast<T>(0.25);
83 else
84 angle = acos(angleCos);
85 axis.x = (m[1][2] - m[2][1]) / s;
86 axis.y = (m[2][0] - m[0][2]) / s;
87 axis.z = (m[0][1] - m[1][0]) / s;
88 }
89
90 template<typename T, qualifier Q>
91 GLM_FUNC_QUALIFIER mat<4, 4, T, Q> axisAngleMatrix(vec<3, T, Q> const& axis, T const angle)
92 {
93 T c = cos(angle);
94 T s = sin(angle);
95 T t = static_cast<T>(1) - c;
96 vec<3, T, Q> n = normalize(axis);
97
98 return mat<4, 4, T, Q>(
99 t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, static_cast<T>(0.0),
100 t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, static_cast<T>(0.0),
101 t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, static_cast<T>(0.0),
102 static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0));
103 }
104
105 template<typename T, qualifier Q>
106 GLM_FUNC_QUALIFIER mat<4, 4, T, Q> extractMatrixRotation(mat<4, 4, T, Q> const& m)
107 {
108 return mat<4, 4, T, Q>(
109 m[0][0], m[0][1], m[0][2], static_cast<T>(0.0),
110 m[1][0], m[1][1], m[1][2], static_cast<T>(0.0),
111 m[2][0], m[2][1], m[2][2], static_cast<T>(0.0),
112 static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(0.0), static_cast<T>(1.0));
113 }
114
115 template<typename T, qualifier Q>
116 GLM_FUNC_QUALIFIER mat<4, 4, T, Q> interpolate(mat<4, 4, T, Q> const& m1, mat<4, 4, T, Q> const& m2, T const delta)
117 {
118 mat<4, 4, T, Q> m1rot = extractMatrixRotation(m1);
119 mat<4, 4, T, Q> dltRotation = m2 * transpose(m1rot);
120 vec<3, T, Q> dltAxis;
121 T dltAngle;
122 axisAngle(dltRotation, dltAxis, dltAngle);
123 mat<4, 4, T, Q> out = axisAngleMatrix(dltAxis, dltAngle * delta) * m1rot;
124 out[3][0] = m1[3][0] + delta * (m2[3][0] - m1[3][0]);
125 out[3][1] = m1[3][1] + delta * (m2[3][1] - m1[3][1]);
126 out[3][2] = m1[3][2] + delta * (m2[3][2] - m1[3][2]);
127 return out;
128 }
129}//namespace glm
glm::abs
GLM_FUNC_DECL GLM_CONSTEXPR genType abs(genType x)
glm::sqrt
GLM_FUNC_QUALIFIER vec< L, T, Q > sqrt(vec< L, T, Q > const &x)
Definition func_exponential.inl:128
glm::normalize
GLM_FUNC_QUALIFIER vec< L, T, Q > normalize(vec< L, T, Q > const &x)
Definition func_geometric.inl:190
glm::sin
GLM_FUNC_QUALIFIER vec< L, T, Q > sin(vec< L, T, Q > const &v)
Definition func_trigonometric.inl:41
glm::cos
GLM_FUNC_QUALIFIER vec< L, T, Q > cos(vec< L, T, Q > const &v)
Definition func_trigonometric.inl:50
glm::acos
GLM_FUNC_QUALIFIER vec< L, T, Q > acos(vec< L, T, Q > const &v)
Definition func_trigonometric.inl:77
glm::angle
GLM_FUNC_DECL T angle(qua< T, Q > const &x)
Definition quaternion_trigonometric.inl:6
glm::axis
GLM_FUNC_DECL vec< 3, T, Q > axis(qua< T, Q > const &x)
Definition quaternion_trigonometric.inl:17
glm::epsilon
GLM_FUNC_DECL GLM_CONSTEXPR genType epsilon()
Return the epsilon constant for floating point types.
Definition scalar_constants.inl:6
glm::pi
GLM_FUNC_DECL GLM_CONSTEXPR genType pi()
Return the pi constant for floating point types.
Definition scalar_constants.inl:13
glm::axisAngleMatrix
GLM_FUNC_DECL mat< 4, 4, T, Q > axisAngleMatrix(vec< 3, T, Q > const &Axis, T const Angle)
Definition matrix_interpolation.inl:91
glm::extractMatrixRotation
GLM_FUNC_DECL mat< 4, 4, T, Q > extractMatrixRotation(mat< 4, 4, T, Q > const &Mat)
Definition matrix_interpolation.inl:106
glm::interpolate
GLM_FUNC_DECL mat< 4, 4, T, Q > interpolate(mat< 4, 4, T, Q > const &m1, mat< 4, 4, T, Q > const &m2, T const Delta)
Definition matrix_interpolation.inl:116
glm::axisAngle
GLM_FUNC_DECL void axisAngle(mat< 4, 4, T, Q > const &Mat, vec< 3, T, Q > &Axis, T &Angle)
Definition matrix_interpolation.inl:8
glm
Core features
Definition common.hpp:21
glm::mat
Definition qualifier.hpp:36
glm::vec
Definition qualifier.hpp:35
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