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+///////////////////////////////////////////////////////////////////////////////////
+/// OpenGL Mathematics (glm.g-truc.net)
+///
+/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
+/// Permission is hereby granted, free of charge, to any person obtaining a copy
+/// of this software and associated documentation files (the "Software"), to deal
+/// in the Software without restriction, including without limitation the rights
+/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+/// copies of the Software, and to permit persons to whom the Software is
+/// furnished to do so, subject to the following conditions:
+///
+/// The above copyright notice and this permission notice shall be included in
+/// all copies or substantial portions of the Software.
+///
+/// Restrictions:
+/// By making use of the Software for military purposes, you choose to make
+/// a Bunny unhappy.
+///
+/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+/// THE SOFTWARE.
+///
+/// @ref gtx_matrix_query
+/// @file glm/gtx/matrix_query.inl
+/// @date 2007-03-05 / 2007-03-05
+/// @author Christophe Riccio
+///////////////////////////////////////////////////////////////////////////////////
+
+namespace glm
+{
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNull(tmat2x2<T, P> const & m, T const & epsilon)
+ {
+ bool result = true;
+ for(detail::component_count_t i = 0; result && i < 2 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNull(tmat3x3<T, P> const & m, T const & epsilon)
+ {
+ bool result = true;
+ for(detail::component_count_t i = 0; result && i < 3 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNull(tmat4x4<T, P> const & m, T const & epsilon)
+ {
+ bool result = true;
+ for(detail::component_count_t i = 0; result && i < 4 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename T, precision P, template <typename, precision> class matType>
+ GLM_FUNC_QUALIFIER bool isIdentity(matType<T, P> const & m, T const & epsilon)
+ {
+ bool result = true;
+ for(detail::component_count_t i(0); result && i < detail::component_count(m[0]); ++i)
+ {
+ for(detail::component_count_t j(0); result && j < i ; ++j)
+ result = abs(m[i][j]) <= epsilon;
+ if(result)
+ result = abs(m[i][i] - 1) <= epsilon;
+ for(detail::component_count_t j(i + 1); result && j < detail::component_count(m); ++j)
+ result = abs(m[i][j]) <= epsilon;
+ }
+ return result;
+ }
+
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNormalized(tmat2x2<T, P> const & m, T const & epsilon)
+ {
+ bool result(true);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ {
+ typename tmat2x2<T, P>::col_type v;
+ for(detail::component_count_t j(0); j < detail::component_count(m); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNormalized(tmat3x3<T, P> const & m, T const & epsilon)
+ {
+ bool result(true);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ {
+ typename tmat3x3<T, P>::col_type v;
+ for(detail::component_count_t j(0); j < detail::component_count(m); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename T, precision P>
+ GLM_FUNC_QUALIFIER bool isNormalized(tmat4x4<T, P> const & m, T const & epsilon)
+ {
+ bool result(true);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m); ++i)
+ {
+ typename tmat4x4<T, P>::col_type v;
+ for(detail::component_count_t j(0); j < detail::component_count(m); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename T, precision P, template <typename, precision> class matType>
+ GLM_FUNC_QUALIFIER bool isOrthogonal(matType<T, P> const & m, T const & epsilon)
+ {
+ bool result(true);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m) - 1; ++i)
+ for(detail::component_count_t j(i + 1); result && j < detail::component_count(m); ++j)
+ result = areOrthogonal(m[i], m[j], epsilon);
+
+ if(result)
+ {
+ matType<T, P> tmp = transpose(m);
+ for(detail::component_count_t i(0); result && i < detail::component_count(m) - 1 ; ++i)
+ for(detail::component_count_t j(i + 1); result && j < detail::component_count(m); ++j)
+ result = areOrthogonal(tmp[i], tmp[j], epsilon);
+ }
+ return result;
+ }
+}//namespace glm