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118 lines
4.4 KiB
118 lines
4.4 KiB
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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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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inline 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 (fabs(s) < 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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inline 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 = 1.0 - 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, 0.0, |
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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, 0.0, |
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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, 0.0, |
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0.0, 0.0, 0.0, 1.0 |
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); |
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} |
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template <typename T> |
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inline 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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