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117 lines
4.5 KiB
C++
117 lines
4.5 KiB
C++
///////////////////////////////////////////////////////////////////////////////////////////////////
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// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Created : 2011-03-05
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// Updated : 2011-03-05
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// Licence : This source is under MIT License
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// File : glm/gtx/matrix_interpolation.inl
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///////////////////////////////////////////////////////////////////////////////////////////////////
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namespace glm{
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namespace gtx{
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namespace matrix_interpolation
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{
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template <typename T>
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GLM_FUNC_QUALIFIER void axisAngle(
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detail::tmat4x4<T> const & mat,
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detail::tvec3<T> & axis,
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T & angle)
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{
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T epsilon = (T)0.01;
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T epsilon2 = (T)0.1;
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if ((fabs(mat[1][0] - mat[0][1]) < epsilon) && (fabs(mat[2][0] - mat[0][2]) < epsilon) && (fabs(mat[2][1] - mat[1][2]) < epsilon)) {
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if ((fabs(mat[1][0] + mat[0][1]) < epsilon2) && (fabs(mat[2][0] + mat[0][2]) < epsilon2) && (fabs(mat[2][1] + mat[1][2]) < epsilon2) && (fabs(mat[0][0] + mat[1][1] + mat[2][2] - (T)3.0) < epsilon2)) {
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angle = (T)0.0;
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axis.x = (T)1.0;
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axis.y = (T)0.0;
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axis.z = (T)0.0;
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return;
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}
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angle = M_1_PI;
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T xx = (mat[0][0] + (T)1.0) / (T)2.0;
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T yy = (mat[1][1] + (T)1.0) / (T)2.0;
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T zz = (mat[2][2] + (T)1.0) / (T)2.0;
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T xy = (mat[1][0] + mat[0][1]) / (T)4.0;
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T xz = (mat[2][0] + mat[0][2]) / (T)4.0;
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T yz = (mat[2][1] + mat[1][2]) / (T)4.0;
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if ((xx > yy) && (xx > zz)) {
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if (xx < epsilon) {
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axis.x = (T)0.0;
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axis.y = (T)0.7071;
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axis.z = (T)0.7071;
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} else {
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axis.x = sqrt(xx);
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axis.y = xy / axis.x;
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axis.z = xz / axis.x;
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}
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} else if (yy > zz) {
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if (yy < epsilon) {
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axis.x = (T)0.7071;
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axis.y = (T)0.0;
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axis.z = (T)0.7071;
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} else {
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axis.y = sqrt(yy);
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axis.x = xy / axis.y;
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axis.z = yz / axis.y;
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}
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} else {
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if (zz < epsilon) {
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axis.x = (T)0.7071;
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axis.y = (T)0.7071;
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axis.z = (T)0.0;
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} else {
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axis.z = sqrt(zz);
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axis.x = xz / axis.z;
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axis.y = yz / axis.z;
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}
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}
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return;
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}
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T s = sqrt((mat[2][1] - mat[1][2]) * (mat[2][1] - mat[1][2]) + (mat[2][0] - mat[0][2]) * (mat[2][0] - mat[0][2]) + (mat[1][0] - mat[0][1]) * (mat[1][0] - mat[0][1]));
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if (glm::abs(s) < T(0.001))
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s = (T)1.0;
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angle = acos((mat[0][0] + mat[1][1] + mat[2][2] - (T)1.0) / (T)2.0);
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axis.x = (mat[1][2] - mat[2][1]) / s;
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axis.y = (mat[2][0] - mat[0][2]) / s;
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axis.z = (mat[0][1] - mat[1][0]) / s;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x4<T> axisAngleMatrix(
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detail::tvec3<T> const & axis,
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T const angle)
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{
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T c = cos(angle);
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T s = sin(angle);
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T t = T(1) - c;
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detail::tvec3<T> n = normalize(axis);
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return detail::tmat4x4<T>(
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t * n.x * n.x + c, t * n.x * n.y + n.z * s, t * n.x * n.z - n.y * s, T(0),
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t * n.x * n.y - n.z * s, t * n.y * n.y + c, t * n.y * n.z + n.x * s, T(0),
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t * n.x * n.z + n.y * s, t * n.y * n.z - n.x * s, t * n.z * n.z + c, T(0),
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T(0), T(0), T(0), T(1)
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);
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x4<T> interpolate(
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detail::tmat4x4<T> const & m1,
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detail::tmat4x4<T> const & m2,
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T const delta)
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{
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detail::tmat4x4<T> dltRotation = m2 * transpose(m1);
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detail::tvec3<T> dltAxis;
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T dltAngle;
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axisAngle(dltRotation, dltAxis, dltAngle);
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detail::tmat4x4<T> out = axisAngleMatrix(dltAxis, dltAngle * delta) * rotationMatrix(m1);
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out[3][0] = m1[3][0] + delta * (m2[3][0] - m1[3][0]);
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out[3][1] = m1[3][1] + delta * (m2[3][1] - m1[3][1]);
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out[3][2] = m1[3][2] + delta * (m2[3][2] - m1[3][2]);
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return out;
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}
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}//namespace transform
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}//namespace gtx
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}//namespace glm
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