Math: added Matrix{3,4}::isRigidTransformation().

src/Math/Matrix.h

@@ -108,7 +108,8 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
          * The matrix is orthogonal if its transpose is equal to its inverse: @f[
          *      Q^T = Q^{-1}
          * @f]
-         * @see transposed(), inverted()
+         * @see transposed(), inverted(), Matrix3::isRigidTransformation(),
+         *      Matrix4::isRigidTransformation()
          */
         bool isOrthogonal() const {
             /* Normality */

src/Math/Matrix3.h

@@ -152,6 +152,17 @@ template<class T> class Matrix3: public Matrix<3, T> {
         /** @brief Copy constructor */
         inline constexpr Matrix3(const RectangularMatrix<3, 3, T>& other): Matrix<3, T>(other) {}
 
+        /**
+         * @brief Check whether the matrix represents rigid transformation
+         *
+         * Rigid transformation consists only of rotation and translation (i.e.
+         * no scaling or projection).
+         * @see isOrthogonal()
+         */
+        inline bool isRigidTransformation() const {
+            return rotationScaling().isOrthogonal() && row(2) == Vector3<T>(T(0), T(0), T(1));
+        }
+
         /**
          * @brief 2D rotation and scaling part of the matrix
          *

src/Math/Matrix4.h

@@ -283,6 +283,17 @@ template<class T> class Matrix4: public Matrix<4, T> {
         /** @brief Copy constructor */
         inline constexpr Matrix4(const RectangularMatrix<4, 4, T>& other): Matrix<4, T>(other) {}
 
+        /**
+         * @brief Check whether the matrix represents rigid transformation
+         *
+         * Rigid transformation consists only of rotation and translation (i.e.
+         * no scaling or projection).
+         * @see isOrthogonal()
+         */
+        inline bool isRigidTransformation() const {
+            return rotationScaling().isOrthogonal() && row(3) == Vector4<T>(T(0), T(0), T(0), T(1));
+        }
+
         /**
          * @brief 3D rotation and scaling part of the matrix
          *

src/Math/Test/Matrix3Test.cpp

@@ -40,6 +40,8 @@ class Matrix3Test: public Corrade::TestSuite::Tester {
         void constructConversion();
         void constructCopy();
 
+        void isRigidTransformation();
+
         void translation();
         void scaling();
         void rotation();
@@ -69,6 +71,8 @@ Matrix3Test::Matrix3Test() {
               &Matrix3Test::constructConversion,
               &Matrix3Test::constructCopy,
 
+              &Matrix3Test::isRigidTransformation,
+
               &Matrix3Test::translation,
               &Matrix3Test::scaling,
               &Matrix3Test::rotation,
@@ -143,6 +147,18 @@ void Matrix3Test::constructCopy() {
                                {7.9f, -1.0f, 8.0f}));
 }
 
+void Matrix3Test::isRigidTransformation() {
+    CORRADE_VERIFY(!Matrix3({1.0f, 0.0f, 0.0f},
+                            {0.1f, 1.0f, 0.0f},
+                            {5.0f, 4.0f, 1.0f}).isRigidTransformation());
+    CORRADE_VERIFY(!Matrix3({1.0f, 0.0f, 0.0f},
+                            {0.0f, 1.0f, 1.0f},
+                            {5.0f, 4.0f, 0.0f}).isRigidTransformation());
+    CORRADE_VERIFY(Matrix3({1.0f, 0.0f, 0.0f},
+                           {0.0f, 1.0f, 0.0f},
+                           {5.0f, 4.0f, 1.0f}).isRigidTransformation());
+}
+
 void Matrix3Test::translation() {
     constexpr Matrix3 a = Matrix3::translation({3.0f, 1.0f});
     CORRADE_COMPARE(a, Matrix3({1.0f, 0.0f, 0.0f},

src/Math/Test/Matrix4Test.cpp

@@ -40,6 +40,8 @@ class Matrix4Test: public Corrade::TestSuite::Tester {
         void constructConversion();
         void constructCopy();
 
+        void isRigidTransformation();
+
         void translation();
         void scaling();
         void rotation();
@@ -75,6 +77,8 @@ Matrix4Test::Matrix4Test() {
               &Matrix4Test::constructConversion,
               &Matrix4Test::constructCopy,
 
+              &Matrix4Test::isRigidTransformation,
+
               &Matrix4Test::translation,
               &Matrix4Test::scaling,
               &Matrix4Test::rotation,
@@ -164,6 +168,21 @@ void Matrix4Test::constructCopy() {
                                {7.9f, -1.0f, 8.0f, -1.5f}));
 }
 
+void Matrix4Test::isRigidTransformation() {
+    CORRADE_VERIFY(!Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
+                            {0.0f, 1.0f, 0.0f, 0.0f},
+                            {0.0f, 0.1f, 1.0f, 0.0f},
+                            {5.0f, 4.0f, 0.5f, 1.0f}).isRigidTransformation());
+    CORRADE_VERIFY(!Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
+                            {0.1f, 1.0f, 0.0f, 0.0f},
+                            {0.0f, 0.0f, 1.0f, 1.0f},
+                            {5.0f, 4.0f, 0.5f, 0.0f}).isRigidTransformation());
+    CORRADE_VERIFY(Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
+                           {0.0f, 1.0f, 0.0f, 0.0f},
+                           {0.0f, 0.0f, 1.0f, 0.0f},
+                           {5.0f, 4.0f, 0.5f, 1.0f}).isRigidTransformation());
+}
+
 void Matrix4Test::translation() {
     constexpr Matrix4 a = Matrix4::translation({3.0f, 1.0f, 2.0f});
     CORRADE_COMPARE(a, Matrix4({1.0f, 0.0f, 0.0f, 0.0f},