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+///////////////////////////////////////////////////////////////////////////////////////////////////
+// OpenGL Mathematics Copyright (c) 2005 - 2013 G-Truc Creation (www.g-truc.net)
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Created : 2007-03-05
+// Updated : 2007-03-05
+// Licence : This source is under MIT License
+// File : glm/gtx/matrix_query.inl
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Dependency:
+// - GLM core
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+namespace glm
+{
+ template<typename T>
+ GLM_FUNC_QUALIFIER bool isNull
+ (
+ detail::tmat2x2<T> const & m,
+ T const & epsilon)
+ {
+ bool result = true;
+ for(int i = 0; result && i < 2 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename T>
+ GLM_FUNC_QUALIFIER bool isNull
+ (
+ detail::tmat3x3<T> const & m,
+ T const & epsilon
+ )
+ {
+ bool result = true;
+ for(int i = 0; result && i < 3 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename T>
+ GLM_FUNC_QUALIFIER bool isNull
+ (
+ detail::tmat4x4<T> const & m,
+ T const & epsilon
+ )
+ {
+ bool result = true;
+ for(int i = 0; result && i < 4 ; ++i)
+ result = isNull(m[i], epsilon);
+ return result;
+ }
+
+ template<typename genType>
+ GLM_FUNC_QUALIFIER bool isIdentity
+ (
+ genType const & m,
+ typename genType::value_type const & epsilon
+ )
+ {
+ bool result = true;
+ for(typename genType::size_type i = typename genType::size_type(0); result && i < genType::col_size(); ++i)
+ {
+ for(typename genType::size_type j = typename genType::size_type(0); result && j < i ; ++j)
+ result = abs(m[i][j]) <= epsilon;
+ if(result)
+ result = abs(m[i][i] - typename genType::value_type(1)) <= epsilon;
+ for(typename genType::size_type j = i + typename genType::size_type(1); result && j < genType::row_size(); ++j)
+ result = abs(m[i][j]) <= epsilon;
+ }
+ return result;
+ }
+
+ template<typename genType>
+ GLM_FUNC_QUALIFIER bool isNormalized
+ (
+ detail::tmat2x2<genType> const & m,
+ genType const & epsilon
+ )
+ {
+ bool result(true);
+ for(typename detail::tmat2x2<genType>::size_type i(0); result && i < m.length(); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(typename detail::tmat2x2<genType>::size_type i(0); result && i < m.length(); ++i)
+ {
+ typename detail::tmat2x2<genType>::col_type v;
+ for(typename detail::tmat2x2<genType>::size_type j(0); j < m.length(); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename genType>
+ GLM_FUNC_QUALIFIER bool isNormalized
+ (
+ detail::tmat3x3<genType> const & m,
+ genType const & epsilon
+ )
+ {
+ bool result(true);
+ for(typename detail::tmat3x3<genType>::size_type i(0); result && i < m.length(); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(typename detail::tmat3x3<genType>::size_type i(0); result && i < m.length(); ++i)
+ {
+ typename detail::tmat3x3<genType>::col_type v;
+ for(typename detail::tmat3x3<genType>::size_type j(0); j < m.length(); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename genType>
+ GLM_FUNC_QUALIFIER bool isNormalized
+ (
+ detail::tmat4x4<genType> const & m,
+ genType const & epsilon
+ )
+ {
+ bool result(true);
+ for(typename detail::tmat4x4<genType>::size_type i(0); result && i < m.length(); ++i)
+ result = isNormalized(m[i], epsilon);
+ for(typename detail::tmat4x4<genType>::size_type i(0); result && i < m.length(); ++i)
+ {
+ typename detail::tmat4x4<genType>::col_type v;
+ for(typename detail::tmat4x4<genType>::size_type j(0); j < m.length(); ++j)
+ v[j] = m[j][i];
+ result = isNormalized(v, epsilon);
+ }
+ return result;
+ }
+
+ template<typename genType, template <typename> class matType>
+ GLM_FUNC_QUALIFIER bool isOrthogonal
+ (
+ matType<genType> const & m,
+ genType const & epsilon
+ )
+ {
+ bool result(true);
+ for(typename matType<genType>::size_type i(0); result && i < m.length() - 1; ++i)
+ for(typename matType<genType>::size_type j(i + 1); result && j < m.length(); ++j)
+ result = areOrthogonal(m[i], m[j], epsilon);
+
+ if(result)
+ {
+ matType<genType> tmp = transpose(m);
+ for(typename matType<genType>::size_type i(0); result && i < m.length() - 1 ; ++i)
+ for(typename matType<genType>::size_type j(i + 1); result && j < m.length(); ++j)
+ result = areOrthogonal(tmp[i], tmp[j], epsilon);
+ }
+ return result;
+ }
+}//namespace glm