Math: added Matrix::isOrthogonal().

src/Math/Matrix.h

@@ -102,6 +102,29 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
         /** @brief Copy constructor */
         inline constexpr Matrix(const RectangularMatrix<size, size, T>& other): RectangularMatrix<size, size, T>(other) {}
 
+        /**
+         * @brief Whether the matrix is orthogonal
+         *
+         * The matrix is orthogonal if its transpose is equal to its inverse: @f[
+         *      Q^T = Q^{-1}
+         * @f]
+         * @see transposed(), inverted()
+         */
+        bool isOrthogonal() const {
+            /* Normality */
+            for(std::size_t i = 0; i != size; ++i)
+                if(!TypeTraits<T>::equals((*this)[i].dot(), T(1)))
+                    return false;
+
+            /* Orthogonality */
+            for(std::size_t i = 0; i != size-1; ++i)
+                for(std::size_t j = i+1; j != size; ++j)
+                    if(!TypeTraits<T>::equals(Vector<size, T>::dot((*this)[i], (*this)[j]), T(0)))
+                        return false;
+
+            return true;
+        }
+
         /**
          * @brief Trace of the matrix
          *

src/Math/Test/MatrixTest.cpp

@@ -40,6 +40,8 @@ class MatrixTest: public Corrade::TestSuite::Tester {
         void constructConversion();
         void constructCopy();
 
+        void isOrthogonal();
+
         void trace();
         void ij();
         void determinant();
@@ -63,6 +65,8 @@ MatrixTest::MatrixTest() {
               &MatrixTest::constructConversion,
               &MatrixTest::constructCopy,
 
+              &MatrixTest::isOrthogonal,
+
               &MatrixTest::trace,
               &MatrixTest::ij,
               &MatrixTest::determinant,
@@ -139,6 +143,18 @@ void MatrixTest::constructCopy() {
                                Vector4(7.9f, -1.0f, 8.0f, -1.5f)));
 }
 
+void MatrixTest::isOrthogonal() {
+    CORRADE_VERIFY(!Matrix3(Vector3(1.0f, 0.0f, 0.0f),
+                            Vector3(0.0f, 1.0f, 0.0f),
+                            Vector3(0.0f, 0.1f, 1.0f)).isOrthogonal());
+    CORRADE_VERIFY(!Matrix3(Vector3(1.0f, 0.0f, 0.0f),
+                            Vector3(0.0f, 1.0f, 0.0f),
+                            Vector3(0.0f, 1.0f, 0.0f)).isOrthogonal());
+    CORRADE_VERIFY(Matrix3(Vector3(1.0f, 0.0f, 0.0f),
+                           Vector3(0.0f, 1.0f, 0.0f),
+                           Vector3(0.0f, 0.0f, 1.0f)).isOrthogonal());
+}
+
 void MatrixTest::trace() {
     Matrix<5, Int> m(
         Vector<5, Int>(1, 2,   3,  0,  0),