From 8e93520bd64e9daefea6e42a13d4b76fba6bf000 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Sun, 6 Jan 2013 15:40:28 +0100
Subject: [PATCH] Math: converting Quaternion to rotation matrix.

---
 src/Math/Quaternion.h                | 20 ++++++++++++++++++++
 src/Math/Test/MathQuaternionTest.cpp | 11 +++++++++++
 2 files changed, 31 insertions(+)

diff --git a/src/Math/Quaternion.h b/src/Math/Quaternion.h
index 5cdcb9dbe..81f0a7a88 100644
--- a/src/Math/Quaternion.h
+++ b/src/Math/Quaternion.h
@@ -25,6 +25,7 @@
 
 #include "Math/Math.h"
 #include "Math/MathTypeTraits.h"
+#include "Math/Matrix.h"
 #include "Math/Vector3.h"
 
 namespace Magnum { namespace Math {
@@ -92,6 +93,25 @@ template<class T> class Quaternion {
             return _vector/std::sqrt(1-pow<2>(_scalar));
         }
 
+        /**
+         * @brief Convert quaternion to rotation matrix
+         *
+         * @see Matrix4::from(const Matrix<3, T>&, const Vector3<T>&)
+         */
+        Matrix<3, T> matrix() const {
+            return { /* Column-major! */
+                T(1) - 2*pow<2>(_vector.y()) - 2*pow<2>(_vector.z()),
+                    2*_vector.x()*_vector.y() + 2*_vector.z()*_scalar,
+                        2*_vector.x()*_vector.z() - 2*_vector.y()*_scalar,
+                2*_vector.x()*_vector.y() - 2*_vector.z()*_scalar,
+                    T(1) - 2*pow<2>(_vector.x()) - 2*pow<2>(_vector.z()),
+                        2*_vector.y()*_vector.z() + 2*_vector.x()*_scalar,
+                2*_vector.x()*_vector.z() + 2*_vector.y()*_scalar,
+                    2*_vector.y()*_vector.z() - 2*_vector.x()*_scalar,
+                        T(1) - 2*pow<2>(_vector.x()) - 2*pow<2>(_vector.y())
+            };
+        }
+
         /**
          * @brief Multiply with scalar and assign
          *
diff --git a/src/Math/Test/MathQuaternionTest.cpp b/src/Math/Test/MathQuaternionTest.cpp
index 1b8a351eb..fe2360964 100644
--- a/src/Math/Test/MathQuaternionTest.cpp
+++ b/src/Math/Test/MathQuaternionTest.cpp
@@ -17,6 +17,7 @@
 #include <TestSuite/Tester.h>
 
 #include "Math/Constants.h"
+#include "Math/Matrix4.h"
 #include "Math/Quaternion.h"
 
 namespace Magnum { namespace Math { namespace Test {
@@ -34,6 +35,7 @@ class QuaternionTest: public Corrade::TestSuite::Tester {
         void inverted();
         void invertedNormalized();
         void rotation();
+        void matrix();
 
         void debug();
 };
@@ -51,6 +53,7 @@ QuaternionTest::QuaternionTest() {
              &QuaternionTest::inverted,
              &QuaternionTest::invertedNormalized,
              &QuaternionTest::rotation,
+             &QuaternionTest::matrix,
              &QuaternionTest::debug);
 }
 
@@ -132,6 +135,14 @@ void QuaternionTest::rotation() {
     CORRADE_COMPARE(q2.rotationAxis(), -axis);
 }
 
+void QuaternionTest::matrix() {
+    float angle = deg(37.0f);
+    Vector3 axis(1.0f/Constants<float>::sqrt3());
+    Quaternion q = Quaternion::fromRotation(angle, axis);
+    Matrix<3, float> expected = Matrix4<float>::rotation(angle, axis).rotationScaling();
+    CORRADE_COMPARE(q.matrix(), expected);
+}
+
 void QuaternionTest::debug() {
     std::ostringstream o;