1/// @ref gtx_matrix_decompose 2 3#include "../gtc/constants.hpp" 4#include "../gtc/epsilon.hpp" 5 6namespace glm{ 7namespace detail 8{ 9 /// Make a linear combination of two vectors and return the result. 10 // result = (a * ascl) + (b * bscl) 11 template<typename T, qualifier Q> 12 GLM_FUNC_QUALIFIER vec<3, T, Q> combine( 13 vec<3, T, Q> const& a, 14 vec<3, T, Q> const& b, 15 T ascl, T bscl) 16 { 17 return (a * ascl) + (b * bscl); 18 } 19 20 template<typename T, qualifier Q> 21 GLM_FUNC_QUALIFIER vec<3, T, Q> scale(vec<3, T, Q> const& v, T desiredLength) 22 { 23 return v * desiredLength / length(v); 24 } 25}//namespace detail 26 27 // Matrix decompose 28 // http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp 29 // Decomposes the mode matrix to translations,rotation scale components 30 31 template<typename T, qualifier Q> 32 GLM_FUNC_QUALIFIER bool decompose(mat<4, 4, T, Q> const& ModelMatrix, vec<3, T, Q> & Scale, qua<T, Q> & Orientation, vec<3, T, Q> & Translation, vec<3, T, Q> & Skew, vec<4, T, Q> & Perspective) 33 { 34 mat<4, 4, T, Q> LocalMatrix(ModelMatrix); 35 36 // Normalize the matrix. 37 if(epsilonEqual(LocalMatrix[3][3], static_cast<T>(0), epsilon<T>())) 38 return false; 39 40 for(length_t i = 0; i < 4; ++i) 41 for(length_t j = 0; j < 4; ++j) 42 LocalMatrix[i][j] /= LocalMatrix[3][3]; 43 44 // perspectiveMatrix is used to solve for perspective, but it also provides 45 // an easy way to test for singularity of the upper 3x3 component. 46 mat<4, 4, T, Q> PerspectiveMatrix(LocalMatrix); 47 48 for(length_t i = 0; i < 3; i++) 49 PerspectiveMatrix[i][3] = static_cast<T>(0); 50 PerspectiveMatrix[3][3] = static_cast<T>(1); 51 52 /// TODO: Fixme! 53 if(epsilonEqual(determinant(PerspectiveMatrix), static_cast<T>(0), epsilon<T>())) 54 return false; 55 56 // First, isolate perspective. This is the messiest. 57 if( 58 epsilonNotEqual(LocalMatrix[0][3], static_cast<T>(0), epsilon<T>()) || 59 epsilonNotEqual(LocalMatrix[1][3], static_cast<T>(0), epsilon<T>()) || 60 epsilonNotEqual(LocalMatrix[2][3], static_cast<T>(0), epsilon<T>())) 61 { 62 // rightHandSide is the right hand side of the equation. 63 vec<4, T, Q> RightHandSide; 64 RightHandSide[0] = LocalMatrix[0][3]; 65 RightHandSide[1] = LocalMatrix[1][3]; 66 RightHandSide[2] = LocalMatrix[2][3]; 67 RightHandSide[3] = LocalMatrix[3][3]; 68 69 // Solve the equation by inverting PerspectiveMatrix and multiplying 70 // rightHandSide by the inverse. (This is the easiest way, not 71 // necessarily the best.) 72 mat<4, 4, T, Q> InversePerspectiveMatrix = glm::inverse(PerspectiveMatrix);// inverse(PerspectiveMatrix, inversePerspectiveMatrix); 73 mat<4, 4, T, Q> TransposedInversePerspectiveMatrix = glm::transpose(InversePerspectiveMatrix);// transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix); 74 75 Perspective = TransposedInversePerspectiveMatrix * RightHandSide; 76 // v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint); 77 78 // Clear the perspective partition 79 LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = static_cast<T>(0); 80 LocalMatrix[3][3] = static_cast<T>(1); 81 } 82 else 83 { 84 // No perspective. 85 Perspective = vec<4, T, Q>(0, 0, 0, 1); 86 } 87 88 // Next take care of translation (easy). 89 Translation = vec<3, T, Q>(LocalMatrix[3]); 90 LocalMatrix[3] = vec<4, T, Q>(0, 0, 0, LocalMatrix[3].w); 91 92 vec<3, T, Q> Row[3], Pdum3; 93 94 // Now get scale and shear. 95 for(length_t i = 0; i < 3; ++i) 96 for(length_t j = 0; j < 3; ++j) 97 Row[i][j] = LocalMatrix[i][j]; 98 99 // Compute X scale factor and normalize first row. 100 Scale.x = length(Row[0]);// v3Length(Row[0]); 101 102 Row[0] = detail::scale(Row[0], static_cast<T>(1)); 103 104 // Compute XY shear factor and make 2nd row orthogonal to 1st. 105 Skew.z = dot(Row[0], Row[1]); 106 Row[1] = detail::combine(Row[1], Row[0], static_cast<T>(1), -Skew.z); 107 108 // Now, compute Y scale and normalize 2nd row. 109 Scale.y = length(Row[1]); 110 Row[1] = detail::scale(Row[1], static_cast<T>(1)); 111 Skew.z /= Scale.y; 112 113 // Compute XZ and YZ shears, orthogonalize 3rd row. 114 Skew.y = glm::dot(Row[0], Row[2]); 115 Row[2] = detail::combine(Row[2], Row[0], static_cast<T>(1), -Skew.y); 116 Skew.x = glm::dot(Row[1], Row[2]); 117 Row[2] = detail::combine(Row[2], Row[1], static_cast<T>(1), -Skew.x); 118 119 // Next, get Z scale and normalize 3rd row. 120 Scale.z = length(Row[2]); 121 Row[2] = detail::scale(Row[2], static_cast<T>(1)); 122 Skew.y /= Scale.z; 123 Skew.x /= Scale.z; 124 125 // At this point, the matrix (in rows[]) is orthonormal. 126 // Check for a coordinate system flip. If the determinant 127 // is -1, then negate the matrix and the scaling factors. 128 Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3); 129 if(dot(Row[0], Pdum3) < 0) 130 { 131 for(length_t i = 0; i < 3; i++) 132 { 133 Scale[i] *= static_cast<T>(-1); 134 Row[i] *= static_cast<T>(-1); 135 } 136 } 137 138 // Now, get the rotations out, as described in the gem. 139 140 // FIXME - Add the ability to return either quaternions (which are 141 // easier to recompose with) or Euler angles (rx, ry, rz), which 142 // are easier for authors to deal with. The latter will only be useful 143 // when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I 144 // will leave the Euler angle code here for now. 145 146 // ret.rotateY = asin(-Row[0][2]); 147 // if (cos(ret.rotateY) != 0) { 148 // ret.rotateX = atan2(Row[1][2], Row[2][2]); 149 // ret.rotateZ = atan2(Row[0][1], Row[0][0]); 150 // } else { 151 // ret.rotateX = atan2(-Row[2][0], Row[1][1]); 152 // ret.rotateZ = 0; 153 // } 154 155 int i, j, k = 0; 156 float root, trace = Row[0].x + Row[1].y + Row[2].z; 157 if(trace > static_cast<T>(0)) 158 { 159 root = sqrt(trace + static_cast<T>(1.0)); 160 Orientation.w = static_cast<T>(0.5) * root; 161 root = static_cast<T>(0.5) / root; 162 Orientation.x = root * (Row[1].z - Row[2].y); 163 Orientation.y = root * (Row[2].x - Row[0].z); 164 Orientation.z = root * (Row[0].y - Row[1].x); 165 } // End if > 0 166 else 167 { 168 static int Next[3] = {1, 2, 0}; 169 i = 0; 170 if(Row[1].y > Row[0].x) i = 1; 171 if(Row[2].z > Row[i][i]) i = 2; 172 j = Next[i]; 173 k = Next[j]; 174 175 root = sqrt(Row[i][i] - Row[j][j] - Row[k][k] + static_cast<T>(1.0)); 176 177 Orientation[i] = static_cast<T>(0.5) * root; 178 root = static_cast<T>(0.5) / root; 179 Orientation[j] = root * (Row[i][j] + Row[j][i]); 180 Orientation[k] = root * (Row[i][k] + Row[k][i]); 181 Orientation.w = root * (Row[j][k] - Row[k][j]); 182 } // End if <= 0 183 184 return true; 185 } 186}//namespace glm 187