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582 lines
16 KiB
582 lines
16 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 core
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/// @file glm/core/func_matrix.inl
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/// @date 2008-03-08 / 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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// matrixCompMult
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template <typename matType>
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GLM_FUNC_QUALIFIER matType matrixCompMult
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(
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matType const & x,
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matType const & y
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)
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{
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GLM_STATIC_ASSERT(detail::type<typename matType::value_type>::is_float, "'matrixCompMult' only accept floating-point inputs");
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matType result(matType::null);
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for(typename matType::size_type i = 0; i < matType::row_size(); ++i)
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result[i] = x[i] * y[i];
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return result;
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}
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// outerProduct
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat2x2<T> outerProduct
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(
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detail::tvec2<T> const & c,
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detail::tvec2<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat2x2<T> m(detail::tmat2x2<T>::null);
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m[0][0] = c[0] * r[0];
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m[0][1] = c[1] * r[0];
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m[1][0] = c[0] * r[1];
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m[1][1] = c[1] * r[1];
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat3x3<T> outerProduct
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(
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detail::tvec3<T> const & c,
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detail::tvec3<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat3x3<T> m(detail::tmat3x3<T>::null);
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for(typename detail::tmat3x3<T>::size_type i(0); i < m.length(); ++i)
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m[i] = c * r[i];
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x4<T> outerProduct
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(
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detail::tvec4<T> const & c,
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detail::tvec4<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat4x4<T> m(detail::tmat4x4<T>::null);
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for(typename detail::tmat4x4<T>::size_type i(0); i < m.length(); ++i)
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m[i] = c * r[i];
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat2x3<T> outerProduct
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(
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detail::tvec3<T> const & c,
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detail::tvec2<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat2x3<T> m(detail::tmat2x3<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[0][2] = c.z * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[1][2] = c.z * r.y;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat3x2<T> outerProduct
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(
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detail::tvec2<T> const & c,
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detail::tvec3<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat3x2<T> m(detail::tmat3x2<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[2][0] = c.x * r.z;
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m[2][1] = c.y * r.z;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat2x4<T> outerProduct
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(
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detail::tvec4<T> const & c,
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detail::tvec2<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat2x4<T> m(detail::tmat2x4<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[0][2] = c.z * r.x;
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m[0][3] = c.w * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[1][2] = c.z * r.y;
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m[1][3] = c.w * r.y;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x2<T> outerProduct
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(
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detail::tvec2<T> const & c,
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detail::tvec4<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat4x2<T> m(detail::tmat4x2<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[2][0] = c.x * r.z;
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m[2][1] = c.y * r.z;
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m[3][0] = c.x * r.w;
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m[3][1] = c.y * r.w;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat3x4<T> outerProduct
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(
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detail::tvec4<T> const & c,
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detail::tvec3<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat3x4<T> m(detail::tmat3x4<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[0][2] = c.z * r.x;
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m[0][3] = c.w * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[1][2] = c.z * r.y;
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m[1][3] = c.w * r.y;
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m[2][0] = c.x * r.z;
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m[2][1] = c.y * r.z;
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m[2][2] = c.z * r.z;
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m[2][3] = c.w * r.z;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat4x3<T> outerProduct
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(
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detail::tvec3<T> const & c,
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detail::tvec4<T> const & r
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'outerProduct' only accept floating-point inputs");
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detail::tmat4x3<T> m(detail::tmat4x3<T>::null);
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m[0][0] = c.x * r.x;
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m[0][1] = c.y * r.x;
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m[0][2] = c.z * r.x;
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m[1][0] = c.x * r.y;
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m[1][1] = c.y * r.y;
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m[1][2] = c.z * r.y;
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m[2][0] = c.x * r.z;
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m[2][1] = c.y * r.z;
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m[2][2] = c.z * r.z;
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m[3][0] = c.x * r.w;
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m[3][1] = c.y * r.w;
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m[3][2] = c.z * r.w;
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return m;
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tmat2x2<T> transpose
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(
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detail::tmat2x2<T> const & m
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)
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{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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detail::tmat2x2<T> result(detail::tmat2x2<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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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::tmat3x3<T> transpose
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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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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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detail::tmat3x3<T> result(detail::tmat3x3<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[0][2] = m[2][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[1][2] = m[2][1];
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result[2][0] = m[0][2];
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result[2][1] = m[1][2];
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result[2][2] = m[2][2];
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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> transpose
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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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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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|
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detail::tmat4x4<T> result(detail::tmat4x4<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[0][2] = m[2][0];
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result[0][3] = m[3][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[1][2] = m[2][1];
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result[1][3] = m[3][1];
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result[2][0] = m[0][2];
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result[2][1] = m[1][2];
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result[2][2] = m[2][2];
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result[2][3] = m[3][2];
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result[3][0] = m[0][3];
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result[3][1] = m[1][3];
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result[3][2] = m[2][3];
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result[3][3] = m[3][3];
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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::tmat2x3<T> transpose
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(
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detail::tmat3x2<T> const & m
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|
)
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|
{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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|
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detail::tmat2x3<T> result(detail::tmat2x3<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[0][2] = m[2][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[1][2] = m[2][1];
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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::tmat3x2<T> transpose
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(
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detail::tmat2x3<T> const & m
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|
)
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|
{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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detail::tmat3x2<T> result(detail::tmat3x2<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[2][0] = m[0][2];
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result[2][1] = m[1][2];
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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::tmat2x4<T> transpose
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|
(
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detail::tmat4x2<T> const & m
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|
)
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|
{
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GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
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|
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detail::tmat2x4<T> result(detail::tmat2x4<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[0][2] = m[2][0];
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result[0][3] = m[3][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[1][2] = m[2][1];
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result[1][3] = m[3][1];
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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::tmat4x2<T> transpose
|
|
(
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|
detail::tmat2x4<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
|
|
|
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detail::tmat4x2<T> result(detail::tmat4x2<T>::null);
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result[0][0] = m[0][0];
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result[0][1] = m[1][0];
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result[1][0] = m[0][1];
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result[1][1] = m[1][1];
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result[2][0] = m[0][2];
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result[2][1] = m[1][2];
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|
result[3][0] = m[0][3];
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result[3][1] = m[1][3];
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|
return result;
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER detail::tmat3x4<T> transpose
|
|
(
|
|
detail::tmat4x3<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
|
|
|
|
detail::tmat3x4<T> result(detail::tmat3x4<T>::null);
|
|
result[0][0] = m[0][0];
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|
result[0][1] = m[1][0];
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|
result[0][2] = m[2][0];
|
|
result[0][3] = m[3][0];
|
|
result[1][0] = m[0][1];
|
|
result[1][1] = m[1][1];
|
|
result[1][2] = m[2][1];
|
|
result[1][3] = m[3][1];
|
|
result[2][0] = m[0][2];
|
|
result[2][1] = m[1][2];
|
|
result[2][2] = m[2][2];
|
|
result[2][3] = m[3][2];
|
|
return result;
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER detail::tmat4x3<T> transpose
|
|
(
|
|
detail::tmat3x4<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'transpose' only accept floating-point inputs");
|
|
|
|
detail::tmat4x3<T> result(detail::tmat4x3<T>::null);
|
|
result[0][0] = m[0][0];
|
|
result[0][1] = m[1][0];
|
|
result[0][2] = m[2][0];
|
|
result[1][0] = m[0][1];
|
|
result[1][1] = m[1][1];
|
|
result[1][2] = m[2][1];
|
|
result[2][0] = m[0][2];
|
|
result[2][1] = m[1][2];
|
|
result[2][2] = m[2][2];
|
|
result[3][0] = m[0][3];
|
|
result[3][1] = m[1][3];
|
|
result[3][2] = m[2][3];
|
|
return result;
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER typename detail::tmat2x2<T>::value_type determinant
|
|
(
|
|
detail::tmat2x2<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'determinant' only accept floating-point inputs");
|
|
|
|
return m[0][0] * m[1][1] - m[1][0] * m[0][1];
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER typename detail::tmat3x3<T>::value_type determinant
|
|
(
|
|
detail::tmat3x3<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'determinant' only accept floating-point inputs");
|
|
|
|
return
|
|
+ m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
|
|
- m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
|
|
+ m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER typename detail::tmat4x4<T>::value_type determinant
|
|
(
|
|
detail::tmat4x4<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'determinant' only accept floating-point inputs");
|
|
|
|
T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
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T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
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T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
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T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
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T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
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T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
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|
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detail::tvec4<T> DetCof(
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+ (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02),
|
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- (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04),
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+ (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05),
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- (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05));
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|
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return m[0][0] * DetCof[0]
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+ m[0][1] * DetCof[1]
|
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+ m[0][2] * DetCof[2]
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+ m[0][3] * DetCof[3];
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|
}
|
|
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|
template <typename T>
|
|
GLM_FUNC_QUALIFIER detail::tmat2x2<T> inverse
|
|
(
|
|
detail::tmat2x2<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'inverse' only accept floating-point inputs");
|
|
|
|
//valType Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1];
|
|
T Determinant = determinant(m);
|
|
|
|
detail::tmat2x2<T> Inverse(
|
|
+ m[1][1] / Determinant,
|
|
- m[0][1] / Determinant,
|
|
- m[1][0] / Determinant,
|
|
+ m[0][0] / Determinant);
|
|
|
|
return Inverse;
|
|
}
|
|
|
|
template <typename T>
|
|
GLM_FUNC_QUALIFIER detail::tmat3x3<T> inverse
|
|
(
|
|
detail::tmat3x3<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'inverse' only accept floating-point inputs");
|
|
|
|
//valType Determinant = m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
|
|
// - m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
|
|
// + m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
|
|
|
|
T Determinant = determinant(m);
|
|
|
|
detail::tmat3x3<T> Inverse(detail::tmat3x3<T>::null);
|
|
Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
|
|
Inverse[1][0] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
|
|
Inverse[2][0] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
|
|
Inverse[0][1] = - (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[2][1] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
|
|
Inverse[0][2] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
|
|
Inverse[1][2] = - (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>
|
|
GLM_FUNC_QUALIFIER detail::tmat4x4<T> inverse
|
|
(
|
|
detail::tmat4x4<T> const & m
|
|
)
|
|
{
|
|
GLM_STATIC_ASSERT(detail::type<T>::is_float, "'inverse' only accept floating-point inputs");
|
|
|
|
T Coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
|
|
T Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
|
|
T Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
|
|
|
|
T Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
|
|
T Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
|
|
T Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
|
|
|
|
T Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
|
|
T Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
|
|
T Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
|
|
|
|
T Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
|
|
T Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
|
|
T Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
|
|
|
|
T Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
|
|
T Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
|
|
T Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
|
|
|
|
T Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
|
|
T Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
|
|
T Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
|
|
|
|
detail::tvec4<T> const SignA(+1, -1, +1, -1);
|
|
detail::tvec4<T> const SignB(-1, +1, -1, +1);
|
|
|
|
detail::tvec4<T> Fac0(Coef00, Coef00, Coef02, Coef03);
|
|
detail::tvec4<T> Fac1(Coef04, Coef04, Coef06, Coef07);
|
|
detail::tvec4<T> Fac2(Coef08, Coef08, Coef10, Coef11);
|
|
detail::tvec4<T> Fac3(Coef12, Coef12, Coef14, Coef15);
|
|
detail::tvec4<T> Fac4(Coef16, Coef16, Coef18, Coef19);
|
|
detail::tvec4<T> Fac5(Coef20, Coef20, Coef22, Coef23);
|
|
|
|
detail::tvec4<T> Vec0(m[1][0], m[0][0], m[0][0], m[0][0]);
|
|
detail::tvec4<T> Vec1(m[1][1], m[0][1], m[0][1], m[0][1]);
|
|
detail::tvec4<T> Vec2(m[1][2], m[0][2], m[0][2], m[0][2]);
|
|
detail::tvec4<T> Vec3(m[1][3], m[0][3], m[0][3], m[0][3]);
|
|
|
|
detail::tvec4<T> Inv0 = SignA * (Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
|
|
detail::tvec4<T> Inv1 = SignB * (Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
|
|
detail::tvec4<T> Inv2 = SignA * (Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
|
|
detail::tvec4<T> Inv3 = SignB * (Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);
|
|
|
|
detail::tmat4x4<T> Inverse(Inv0, Inv1, Inv2, Inv3);
|
|
|
|
detail::tvec4<T> Row0(Inverse[0][0], Inverse[1][0], Inverse[2][0], Inverse[3][0]);
|
|
|
|
T Determinant = glm::dot(m[0], Row0);
|
|
|
|
Inverse /= Determinant;
|
|
|
|
return Inverse;
|
|
}
|
|
}//namespace glm
|