Math: slight improvement of Gram-Schmidt orthonormalization algorithm.

Using Vector::projectOntoNormalized(), as it is slightly faster, renamed
the functions to properly mention that this is orthonormalization.

src/Math/Algorithms/GramSchmidt.h

@@ -16,7 +16,7 @@
 */
 
 /** @file
- * @brief Function Magnum::Math::Algorithms::gramSchmidtInPlace(), Magnum::Math::Algorithms::gramSchmidt()
+ * @brief Function Magnum::Math::Algorithms::gramSchmidtOrthonormalizeInPlace(), Magnum::Math::Algorithms::gramSchmidtOrthonormalize()
  */
 
 #include "Math/RectangularMatrix.h"
@@ -24,26 +24,26 @@
 namespace Magnum { namespace Math { namespace Algorithms {
 
 /**
-@brief Gram-Schmidt matrix orthonormalization
+@brief In-place Gram-Schmidt matrix orthonormalization
 @param[in,out] matrix   Matrix to perform orthonormalization on
 */
-template<std::size_t cols, std::size_t rows, class T> void gramSchmidtInPlace(RectangularMatrix<cols, rows, T>& matrix) {
+template<std::size_t cols, std::size_t rows, class T> void gramSchmidtOrthonormalizeInPlace(RectangularMatrix<cols, rows, T>& matrix) {
     static_assert(cols <= rows, "Unsupported matrix aspect ratio");
     for(std::size_t i = 0; i != cols; ++i) {
         matrix[i] = matrix[i].normalized();
         for(std::size_t j = i+1; j != cols; ++j)
-            matrix[j] -= matrix[j].projected(matrix[i]);
+            matrix[j] -= matrix[j].projectedOntoNormalized(matrix[i]);
     }
 }
 
 /**
 @brief Gram-Schmidt matrix orthonormalization
 
-Unlike gramSchmidtInPlace() returns the modified matrix instead of performing
-the orthonormalization in-place.
+Unlike gramSchmidtOrthonormalizeInPlace() returns the modified matrix instead
+of performing the orthonormalization in-place.
 */
-template<std::size_t cols, std::size_t rows, class T> RectangularMatrix<cols, rows, T> gramSchmidt(RectangularMatrix<cols, rows, T> matrix) {
-    gramSchmidtInPlace(matrix);
+template<std::size_t cols, std::size_t rows, class T> RectangularMatrix<cols, rows, T> gramSchmidtOrthonormalize(RectangularMatrix<cols, rows, T> matrix) {
+    gramSchmidtOrthonormalizeInPlace(matrix);
     return matrix;
 }
 

src/Math/Algorithms/Test/GramSchmidtTest.cpp

@@ -23,22 +23,22 @@ class GramSchmidtTest: public Corrade::TestSuite::Tester {
     public:
         GramSchmidtTest();
 
-        void test();
+        void orthonormalize();
 };
 
 typedef RectangularMatrix<3, 3, float> Matrix3;
 typedef Vector<3, float> Vector3;
 
 GramSchmidtTest::GramSchmidtTest() {
-    addTests(&GramSchmidtTest::test);
+    addTests(&GramSchmidtTest::orthonormalize);
 }
 
-void GramSchmidtTest::test() {
+void GramSchmidtTest::orthonormalize() {
     Matrix3 m(Vector3(3.0f,  5.0f, 8.0f),
               Vector3(4.0f,  4.0f, 7.0f),
               Vector3(7.0f, -1.0f, 8.0f));
 
-    Matrix3 normalized = Algorithms::gramSchmidt(m);
+    Matrix3 normalized = Algorithms::gramSchmidtOrthonormalize(m);
 
     /* Verify the first vector is in direction of first original */
     CORRADE_COMPARE(normalized[0], m[0].normalized());

src/SceneGraph/EuclideanMatrixTransformation2D.h

@@ -85,7 +85,7 @@ class EuclideanMatrixTransformation2D: public AbstractTranslationRotation2D<T> {
          */
         EuclideanMatrixTransformation2D<T>* normalizeRotation() {
             setTransformation(Math::Matrix3<T>::from(
-                Math::Algorithms::gramSchmidt(_transformation.rotationScaling()),
+                Math::Algorithms::gramSchmidtOrthonormalize(_transformation.rotationScaling()),
                 _transformation.translation()));
             return this;
         }

src/SceneGraph/EuclideanMatrixTransformation3D.h

@@ -85,7 +85,7 @@ class EuclideanMatrixTransformation3D: public AbstractTranslationRotation3D<T> {
          */
         EuclideanMatrixTransformation3D<T>* normalizeRotation() {
             setTransformation(Math::Matrix4<T>::from(
-                Math::Algorithms::gramSchmidt(_transformation.rotationScaling()),
+                Math::Algorithms::gramSchmidtOrthonormalize(_transformation.rotationScaling()),
                 _transformation.translation()));
             return this;
         }