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159 lines
6.7 KiB
159 lines
6.7 KiB
///////////////////////////////////////////////////////////////////////////////////
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/// OpenGL Mathematics (glm.g-truc.net)
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///
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/// Copyright (c) 2005 - 2013 G-Truc Creation (www.g-truc.net)
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/// Permission is hereby granted, free of charge, to any person obtaining a copy
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/// of this software and associated documentation files (the "Software"), to deal
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/// in the Software without restriction, including without limitation the rights
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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/// copies of the Software, and to permit persons to whom the Software is
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/// furnished to do so, subject to the following conditions:
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///
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/// The above copyright notice and this permission notice shall be included in
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/// all copies or substantial portions of the Software.
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///
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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/// THE SOFTWARE.
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///
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/// @ref gtc_matrix_inverse
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/// @file glm/gtc/matrix_inverse.inl
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/// @date 2005-12-21 / 2011-06-15
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/// @author Christophe Riccio
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///////////////////////////////////////////////////////////////////////////////////
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namespace glm
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{
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat3x3<T> affineInverse
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(
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detail::tmat3x3<T> const & m
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)
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{
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detail::tmat3x3<T> Result(m);
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Result[2] = detail::tvec3<T>(0, 0, 1);
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Result = transpose(Result);
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detail::tvec3<T> Translation = Result * detail::tvec3<T>(-detail::tvec2<T>(m[2]), m[2][2]);
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Result[2] = Translation;
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return Result;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x4<T> affineInverse
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(
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detail::tmat4x4<T> const & m
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)
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{
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detail::tmat4x4<T> Result(m);
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Result[3] = detail::tvec4<T>(0, 0, 0, 1);
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Result = transpose(Result);
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detail::tvec4<T> Translation = Result * detail::tvec4<T>(-detail::tvec3<T>(m[3]), m[3][3]);
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Result[3] = Translation;
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return Result;
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tmat2x2<valType> inverseTranspose
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(
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detail::tmat2x2<valType> const & m
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)
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{
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valType Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1];
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detail::tmat2x2<valType> Inverse(
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+ m[1][1] / Determinant,
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- m[0][1] / Determinant,
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- m[1][0] / Determinant,
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+ m[0][0] / Determinant);
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return Inverse;
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tmat3x3<valType> inverseTranspose
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(
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detail::tmat3x3<valType> const & m
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)
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{
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valType Determinant =
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+ m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
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- m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
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+ m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
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detail::tmat3x3<valType> Inverse;
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Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
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Inverse[0][1] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
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Inverse[0][2] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
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Inverse[1][0] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
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Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
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Inverse[1][2] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
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Inverse[2][0] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
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Inverse[2][1] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
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Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
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Inverse /= Determinant;
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return Inverse;
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}
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template <typename valType>
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GLM_FUNC_QUALIFIER detail::tmat4x4<valType> inverseTranspose
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(
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detail::tmat4x4<valType> const & m
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)
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{
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valType SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
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valType SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
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valType SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
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valType SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
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valType SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
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valType SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
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valType SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
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valType SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
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valType SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
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valType SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
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valType SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
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valType SubFactor11 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
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valType SubFactor12 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
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valType SubFactor13 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
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valType SubFactor14 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
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valType SubFactor15 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
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valType SubFactor16 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
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valType SubFactor17 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
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valType SubFactor18 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
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detail::tmat4x4<valType> Inverse;
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Inverse[0][0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02);
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Inverse[0][1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04);
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Inverse[0][2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05);
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Inverse[0][3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05);
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Inverse[1][0] = - (m[0][1] * SubFactor00 - m[0][2] * SubFactor01 + m[0][3] * SubFactor02);
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Inverse[1][1] = + (m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04);
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Inverse[1][2] = - (m[0][0] * SubFactor01 - m[0][1] * SubFactor03 + m[0][3] * SubFactor05);
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Inverse[1][3] = + (m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05);
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Inverse[2][0] = + (m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08);
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Inverse[2][1] = - (m[0][0] * SubFactor06 - m[0][2] * SubFactor09 + m[0][3] * SubFactor10);
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Inverse[2][2] = + (m[0][0] * SubFactor11 - m[0][1] * SubFactor09 + m[0][3] * SubFactor12);
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Inverse[2][3] = - (m[0][0] * SubFactor08 - m[0][1] * SubFactor10 + m[0][2] * SubFactor12);
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Inverse[3][0] = - (m[0][1] * SubFactor13 - m[0][2] * SubFactor14 + m[0][3] * SubFactor15);
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Inverse[3][1] = + (m[0][0] * SubFactor13 - m[0][2] * SubFactor16 + m[0][3] * SubFactor17);
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Inverse[3][2] = - (m[0][0] * SubFactor14 - m[0][1] * SubFactor16 + m[0][3] * SubFactor18);
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Inverse[3][3] = + (m[0][0] * SubFactor15 - m[0][1] * SubFactor17 + m[0][2] * SubFactor18);
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valType Determinant =
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+ m[0][0] * Inverse[0][0]
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+ m[0][1] * Inverse[0][1]
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+ m[0][2] * Inverse[0][2]
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+ m[0][3] * Inverse[0][3];
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Inverse /= Determinant;
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return Inverse;
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}
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}//namespace glm
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