| 1 | /// @ref gtc_matrix_inverse |
| 2 | |
| 3 | namespace glm |
| 4 | { |
| 5 | template<typename T, qualifier Q> |
| 6 | GLM_FUNC_QUALIFIER mat<3, 3, T, Q> affineInverse(mat<3, 3, T, Q> const& m) |
| 7 | { |
| 8 | mat<2, 2, T, Q> const Inv(inverse(mat<2, 2, T, Q>(m))); |
| 9 | |
| 10 | return mat<3, 3, T, Q>( |
| 11 | vec<3, T, Q>(Inv[0], static_cast<T>(0)), |
| 12 | vec<3, T, Q>(Inv[1], static_cast<T>(0)), |
| 13 | vec<3, T, Q>(-Inv * vec<2, T, Q>(m[2]), static_cast<T>(1))); |
| 14 | } |
| 15 | |
| 16 | template<typename T, qualifier Q> |
| 17 | GLM_FUNC_QUALIFIER mat<4, 4, T, Q> affineInverse(mat<4, 4, T, Q> const& m) |
| 18 | { |
| 19 | mat<3, 3, T, Q> const Inv(inverse(mat<3, 3, T, Q>(m))); |
| 20 | |
| 21 | return mat<4, 4, T, Q>( |
| 22 | vec<4, T, Q>(Inv[0], static_cast<T>(0)), |
| 23 | vec<4, T, Q>(Inv[1], static_cast<T>(0)), |
| 24 | vec<4, T, Q>(Inv[2], static_cast<T>(0)), |
| 25 | vec<4, T, Q>(-Inv * vec<3, T, Q>(m[3]), static_cast<T>(1))); |
| 26 | } |
| 27 | |
| 28 | template<typename T, qualifier Q> |
| 29 | GLM_FUNC_QUALIFIER mat<2, 2, T, Q> inverseTranspose(mat<2, 2, T, Q> const& m) |
| 30 | { |
| 31 | T Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1]; |
| 32 | |
| 33 | mat<2, 2, T, Q> Inverse( |
| 34 | + m[1][1] / Determinant, |
| 35 | - m[0][1] / Determinant, |
| 36 | - m[1][0] / Determinant, |
| 37 | + m[0][0] / Determinant); |
| 38 | |
| 39 | return Inverse; |
| 40 | } |
| 41 | |
| 42 | template<typename T, qualifier Q> |
| 43 | GLM_FUNC_QUALIFIER mat<3, 3, T, Q> inverseTranspose(mat<3, 3, T, Q> const& m) |
| 44 | { |
| 45 | T Determinant = |
| 46 | + m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1]) |
| 47 | - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0]) |
| 48 | + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); |
| 49 | |
| 50 | mat<3, 3, T, Q> Inverse; |
| 51 | Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]); |
| 52 | Inverse[0][1] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]); |
| 53 | Inverse[0][2] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]); |
| 54 | Inverse[1][0] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]); |
| 55 | Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]); |
| 56 | Inverse[1][2] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]); |
| 57 | Inverse[2][0] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]); |
| 58 | Inverse[2][1] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]); |
| 59 | Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]); |
| 60 | Inverse /= Determinant; |
| 61 | |
| 62 | return Inverse; |
| 63 | } |
| 64 | |
| 65 | template<typename T, qualifier Q> |
| 66 | GLM_FUNC_QUALIFIER mat<4, 4, T, Q> inverseTranspose(mat<4, 4, T, Q> const& m) |
| 67 | { |
| 68 | T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3]; |
| 69 | T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3]; |
| 70 | T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2]; |
| 71 | T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3]; |
| 72 | T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2]; |
| 73 | T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1]; |
| 74 | T SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3]; |
| 75 | T SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3]; |
| 76 | T SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2]; |
| 77 | T SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3]; |
| 78 | T SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2]; |
| 79 | T SubFactor11 = m[1][0] * m[3][1] - m[3][0] * m[1][1]; |
| 80 | T SubFactor12 = m[1][2] * m[2][3] - m[2][2] * m[1][3]; |
| 81 | T SubFactor13 = m[1][1] * m[2][3] - m[2][1] * m[1][3]; |
| 82 | T SubFactor14 = m[1][1] * m[2][2] - m[2][1] * m[1][2]; |
| 83 | T SubFactor15 = m[1][0] * m[2][3] - m[2][0] * m[1][3]; |
| 84 | T SubFactor16 = m[1][0] * m[2][2] - m[2][0] * m[1][2]; |
| 85 | T SubFactor17 = m[1][0] * m[2][1] - m[2][0] * m[1][1]; |
| 86 | |
| 87 | mat<4, 4, T, Q> Inverse; |
| 88 | Inverse[0][0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02); |
| 89 | Inverse[0][1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04); |
| 90 | Inverse[0][2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05); |
| 91 | Inverse[0][3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05); |
| 92 | |
| 93 | Inverse[1][0] = - (m[0][1] * SubFactor00 - m[0][2] * SubFactor01 + m[0][3] * SubFactor02); |
| 94 | Inverse[1][1] = + (m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04); |
| 95 | Inverse[1][2] = - (m[0][0] * SubFactor01 - m[0][1] * SubFactor03 + m[0][3] * SubFactor05); |
| 96 | Inverse[1][3] = + (m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05); |
| 97 | |
| 98 | Inverse[2][0] = + (m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08); |
| 99 | Inverse[2][1] = - (m[0][0] * SubFactor06 - m[0][2] * SubFactor09 + m[0][3] * SubFactor10); |
| 100 | Inverse[2][2] = + (m[0][0] * SubFactor07 - m[0][1] * SubFactor09 + m[0][3] * SubFactor11); |
| 101 | Inverse[2][3] = - (m[0][0] * SubFactor08 - m[0][1] * SubFactor10 + m[0][2] * SubFactor11); |
| 102 | |
| 103 | Inverse[3][0] = - (m[0][1] * SubFactor12 - m[0][2] * SubFactor13 + m[0][3] * SubFactor14); |
| 104 | Inverse[3][1] = + (m[0][0] * SubFactor12 - m[0][2] * SubFactor15 + m[0][3] * SubFactor16); |
| 105 | Inverse[3][2] = - (m[0][0] * SubFactor13 - m[0][1] * SubFactor15 + m[0][3] * SubFactor17); |
| 106 | Inverse[3][3] = + (m[0][0] * SubFactor14 - m[0][1] * SubFactor16 + m[0][2] * SubFactor17); |
| 107 | |
| 108 | T Determinant = |
| 109 | + m[0][0] * Inverse[0][0] |
| 110 | + m[0][1] * Inverse[0][1] |
| 111 | + m[0][2] * Inverse[0][2] |
| 112 | + m[0][3] * Inverse[0][3]; |
| 113 | |
| 114 | Inverse /= Determinant; |
| 115 | |
| 116 | return Inverse; |
| 117 | } |
| 118 | }//namespace glm |