Math: converting DualQuaternion to matrix.

Also updated and simplified Quaternion to matrix test.

src/Math/DualQuaternion.h

@@ -20,6 +20,7 @@
  */
 
 #include "Math/Dual.h"
+#include "Math/Matrix4.h"
 #include "Math/Quaternion.h"
 
 namespace Magnum { namespace Math {
@@ -137,6 +138,15 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
             return (this->dual()*this->real().conjugated()).vector()*T(2);
         }
 
+        /**
+         * @brief Convert dual quaternion to transformation matrix
+         *
+         * @see Quaternion::matrix()
+         */
+        Matrix4<T> matrix() const {
+            return Matrix4<T>::from(this->real().matrix(), translation());
+        }
+
         /**
          * @brief Quaternion-conjugated dual quaternion
          *

src/Math/Quaternion.h

@@ -200,7 +200,7 @@ template<class T> class Quaternion {
         /**
          * @brief Convert quaternion to rotation matrix
          *
-         * @see Matrix4::from(const Matrix<3, T>&, const Vector3<T>&)
+         * @see DualQuaternion::matrix(), Matrix4::from(const Matrix<3, T>&, const Vector3<T>&)
          */
         Matrix<3, T> matrix() const {
             return {

src/Math/Test/DualQuaternionTest.cpp

@@ -18,7 +18,6 @@
 
 #include "Math/Constants.h"
 #include "Math/DualQuaternion.h"
-#include "Math/Matrix4.h"
 
 namespace Magnum { namespace Math { namespace Test {
 
@@ -40,6 +39,7 @@ class DualQuaternionTest: public Corrade::TestSuite::Tester {
         void rotation();
         void translation();
         void combinedTransformParts();
+        void matrix();
         void transformPointNormalized();
 
         void debug();
@@ -67,6 +67,7 @@ DualQuaternionTest::DualQuaternionTest() {
              &DualQuaternionTest::rotation,
              &DualQuaternionTest::translation,
              &DualQuaternionTest::combinedTransformParts,
+             &DualQuaternionTest::matrix,
              &DualQuaternionTest::transformPointNormalized,
 
              &DualQuaternionTest::debug);
@@ -159,6 +160,15 @@ void DualQuaternionTest::combinedTransformParts() {
     CORRADE_COMPARE(b.translation(), Quaternion::rotation(deg(23.0f), Vector3::xAxis()).rotateVectorNormalized(translation));
 }
 
+void DualQuaternionTest::matrix() {
+    DualQuaternion q = DualQuaternion::rotation(deg(23.0f), Vector3::xAxis())*DualQuaternion::translation({-1.0f, 2.0f, 3.0f});
+    Matrix4 m = Matrix4::rotationX(deg(23.0f))*Matrix4::translation({-1.0f, 2.0f, 3.0f});
+
+    /* Verify that negated dual quaternion gives the same transformation */
+    CORRADE_COMPARE(q.matrix(), m);
+    CORRADE_COMPARE((-q).matrix(), m);
+}
+
 void DualQuaternionTest::transformPointNormalized() {
     DualQuaternion a = DualQuaternion::translation({-1.0f, 2.0f, 3.0f})*DualQuaternion::rotation(deg(23.0f), Vector3::xAxis());
     DualQuaternion b = DualQuaternion::rotation(deg(23.0f), Vector3::xAxis())*DualQuaternion::translation({-1.0f, 2.0f, 3.0f});

src/Math/Test/QuaternionTest.cpp

@@ -239,14 +239,12 @@ void QuaternionTest::angle() {
 }
 
 void QuaternionTest::matrix() {
-    float angle = deg(37.0f);
+    Quaternion q = Quaternion::rotation(deg(37.0f), Vector3(1.0f/Constants<float>::sqrt3()));
-    Vector3 axis(1.0f/Constants<float>::sqrt3());
+    Matrix3 m = Matrix4::rotation(deg(37.0f), Vector3(1.0f/Constants<float>::sqrt3())).rotationScaling();
-    Quaternion q = Quaternion::rotation(angle, axis);
-    Matrix3 expected = Matrix4::rotation(angle, axis).rotationScaling();
-    CORRADE_COMPARE(q.matrix(), expected);
 
     /* Verify that negated quaternion gives the same rotation */
-    CORRADE_COMPARE((-q).matrix(), expected);
+    CORRADE_COMPARE(q.matrix(), m);
+    CORRADE_COMPARE((-q).matrix(), m);
 }
 
 void QuaternionTest::lerp() {