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/// @ref gtc_matrix_inverse
namespace glm
{
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<3, 3, T, Q> affineInverse(mat<3, 3, T, Q> const& m)
{
mat<2, 2, T, Q> const Inv(inverse(mat<2, 2, T, Q>(m)));
return mat<3, 3, T, Q>(
vec<3, T, Q>(Inv[0], static_cast<T>(0)),
vec<3, T, Q>(Inv[1], static_cast<T>(0)),
vec<3, T, Q>(-Inv * vec<2, T, Q>(m[2]), static_cast<T>(1)));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> affineInverse(mat<4, 4, T, Q> const& m)
{
mat<3, 3, T, Q> const Inv(inverse(mat<3, 3, T, Q>(m)));
return mat<4, 4, T, Q>(
vec<4, T, Q>(Inv[0], static_cast<T>(0)),
vec<4, T, Q>(Inv[1], static_cast<T>(0)),
vec<4, T, Q>(Inv[2], static_cast<T>(0)),
vec<4, T, Q>(-Inv * vec<3, T, Q>(m[3]), static_cast<T>(1)));
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<2, 2, T, Q> inverseTranspose(mat<2, 2, T, Q> const& m)
{
T Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1];
mat<2, 2, T, Q> Inverse(
+ m[1][1] / Determinant,
- m[0][1] / Determinant,
- m[1][0] / Determinant,
+ m[0][0] / Determinant);
return Inverse;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<3, 3, T, Q> inverseTranspose(mat<3, 3, T, Q> const& m)
{
T Determinant =
+ m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
- m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
+ m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
mat<3, 3, T, Q> Inverse;
Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
Inverse[0][1] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
Inverse[0][2] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
Inverse[1][0] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
Inverse[1][2] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
Inverse[2][0] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
Inverse[2][1] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
Inverse /= Determinant;
return Inverse;
}
template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER mat<4, 4, T, Q> inverseTranspose(mat<4, 4, T, Q> const& m)
{
T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
T SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
T SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
T SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
T SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
T SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
T SubFactor11 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
T SubFactor12 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
T SubFactor13 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
T SubFactor14 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
T SubFactor15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
T SubFactor16 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
T SubFactor17 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
mat<4, 4, T, Q> Inverse;
Inverse[0][0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02);
Inverse[0][1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04);
Inverse[0][2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05);
Inverse[0][3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05);
Inverse[1][0] = - (m[0][1] * SubFactor00 - m[0][2] * SubFactor01 + m[0][3] * SubFactor02);
Inverse[1][1] = + (m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04);
Inverse[1][2] = - (m[0][0] * SubFactor01 - m[0][1] * SubFactor03 + m[0][3] * SubFactor05);
Inverse[1][3] = + (m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05);
Inverse[2][0] = + (m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08);
Inverse[2][1] = - (m[0][0] * SubFactor06 - m[0][2] * SubFactor09 + m[0][3] * SubFactor10);
Inverse[2][2] = + (m[0][0] * SubFactor07 - m[0][1] * SubFactor09 + m[0][3] * SubFactor11);
Inverse[2][3] = - (m[0][0] * SubFactor08 - m[0][1] * SubFactor10 + m[0][2] * SubFactor11);
Inverse[3][0] = - (m[0][1] * SubFactor12 - m[0][2] * SubFactor13 + m[0][3] * SubFactor14);
Inverse[3][1] = + (m[0][0] * SubFactor12 - m[0][2] * SubFactor15 + m[0][3] * SubFactor16);
Inverse[3][2] = - (m[0][0] * SubFactor13 - m[0][1] * SubFactor15 + m[0][3] * SubFactor17);
Inverse[3][3] = + (m[0][0] * SubFactor14 - m[0][1] * SubFactor16 + m[0][2] * SubFactor17);
T Determinant =
+ m[0][0] * Inverse[0][0]
+ m[0][1] * Inverse[0][1]
+ m[0][2] * Inverse[0][2]
+ m[0][3] * Inverse[0][3];
Inverse /= Determinant;
return Inverse;
}
}//namespace glm
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