| 1 | /// @ref gtx_matrix_decompose |
| 2 | |
| 3 | #include "../gtc/constants.hpp" |
| 4 | #include "../gtc/epsilon.hpp" |
| 5 | |
| 6 | namespace glm{ |
| 7 | namespace 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 |