Math: transforming vectors with complex numbers.

src/Math/Complex.h

@@ -340,6 +340,35 @@ template<class T> class Complex {
             return conjugated();
         }
 
+        /**
+         * @brief Rotate vector with complex number
+         *
+         * See transformVectorNormalized(), which is faster for normalized
+         * complex numbers. @f[
+         *      v' = \frac c {|c|} v = \frac c {|c|} (v_x + iv_y)
+         * @f]
+         * @see Complex(const Vector2&), operator Vector2(), Matrix3::transformVector()
+         */
+        inline Vector2<T> transformVector(const Vector2<T>& vector) const {
+            return Vector2<T>(normalized()*Complex<T>(vector));
+        }
+
+        /**
+         * @brief Rotate vector with normalized complex number
+         *
+         * Faster alternative to transformVector(), expects that the complex
+         * number is normalized. @f[
+         *      v' = \frac c {|c|} v = cv = c(v_x + iv_y)
+         * @f]
+         * @see Complex(const Vector2&), operator Vector2(), Matrix3::transformVector()
+         */
+        inline Vector2<T> transformVectorNormalized(const Vector2<T>& vector) const {
+            CORRADE_ASSERT(MathTypeTraits<T>::equals(dot(), T(1)),
+                           "Math::Complex::transformVectorNormalized(): complex number must be normalized",
+                           Vector2<T>(std::numeric_limits<T>::quiet_NaN()));
+            return Vector2<T>((*this)*Complex<T>(vector));
+        }
+
     private:
         T _real, _imaginary;
 };

src/Math/DualQuaternion.h

@@ -251,7 +251,8 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * quaternions. @f[
          *      v' = qv \overline{\hat q^{-1}} = q ([\boldsymbol 0, 1] + \epsilon [\boldsymbol v, 0]) \overline{\hat q^{-1}}
          * @f]
-         * @see DualQuaternion(const Vector3&), Matrix4::transformPoint(), Quaternion::transformVector()
+         * @see DualQuaternion(const Vector3&), dual(), Matrix4::transformPoint(),
+         *      Quaternion::transformVector()
          */
         inline Vector3<T> transformPoint(const Vector3<T>& vector) const {
             return ((*this)*DualQuaternion<T>(vector)*inverted().dualConjugated()).dual().vector();
@@ -264,7 +265,8 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * quaternion is normalized. @f[
          *      v' = qv \overline{\hat q^{-1}} = qv \overline{\hat q^*} = q ([\boldsymbol 0, 1] + \epsilon [\boldsymbol v, 0]) \overline{\hat q^*}
          * @f]
-         * @see DualQuaternion(const Vector3&), Matrix4::transformPoint(), Quaternion::transformVectorNormalized()
+         * @see DualQuaternion(const Vector3&), dual(), Matrix4::transformPoint(),
+         *      Quaternion::transformVectorNormalized()
          */
         inline Vector3<T> transformPointNormalized(const Vector3<T>& vector) const {
             CORRADE_ASSERT(MathTypeTraits<Dual<T>>::equals(lengthSquared(), Dual<T>(1)),

src/Math/Matrix3.h

@@ -212,10 +212,11 @@ template<class T> class Matrix3: public Matrix<3, T> {
         /**
          * @brief Transform 2D vector with the matrix
          *
-         * Translation is not involved in the transformation. @f[
+         * Unlike in transformPoint(), translation is not involved in the
+         * transformation. @f[
          *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ 0 \end{pmatrix}
          * @f]
-         * @see transformPoint(), Matrix4::transformVector()
+         * @see Complex::transformVector(), Matrix4::transformVector()
          */
         inline Vector2<T> transformVector(const Vector2<T>& vector) const {
             return ((*this)*Vector3<T>(vector, T(0))).xy();
@@ -224,7 +225,8 @@ template<class T> class Matrix3: public Matrix<3, T> {
         /**
          * @brief Transform 2D point with the matrix
          *
-         * Unlike in transformVector(), translation is also involved. @f[
+         * Unlike in transformVector(), translation is also involved in the
+         * transformation. @f[
          *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ 1 \end{pmatrix}
          * @f]
          * @see Matrix4::transformPoint()

src/Math/Matrix4.h

@@ -359,11 +359,11 @@ template<class T> class Matrix4: public Matrix<4, T> {
         /**
          * @brief Transform 3D vector with the matrix
          *
-         * Translation is not involved in the transformation. @f[
+         * Unlike in transformVector(), translation is not involved in the
+         * transformation. @f[
          *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 0 \end{pmatrix}
          * @f]
-         * @see transformPoint(), Quaternion::transformVector(),
-         *      Matrix3::transformVector()
+         * @see Quaternion::transformVector(), Matrix3::transformVector()
          */
         inline Vector3<T> transformVector(const Vector3<T>& vector) const {
             return ((*this)*Vector4<T>(vector, T(0))).xyz();
@@ -372,7 +372,8 @@ template<class T> class Matrix4: public Matrix<4, T> {
         /**
          * @brief Transform 3D point with the matrix
          *
-         * Unlike in transformVector(), translation is also involved. @f[
+         * Unlike in transformVector(), translation is also involved in the
+         * transformation. @f[
          *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 1 \end{pmatrix}
          * @f]
          * @see DualQuaternion::transformPoint(), Matrix3::transformPoint()

src/Math/Quaternion.h

@@ -408,7 +408,8 @@ template<class T> class Quaternion {
          * quaternions. @f[
          *      v' = qvq^{-1} = q [\boldsymbol v, 0] q^{-1}
          * @f]
-         * @see Quaternion(const Vector3&), Matrix4::transformVector(), DualQuaternion::transformPoint()
+         * @see Quaternion(const Vector3&), vector(), Matrix4::transformVector(),
+         *      DualQuaternion::transformPoint(), Complex::transformVector()
          */
         inline Vector3<T> transformVector(const Vector3<T>& vector) const {
             return ((*this)*Quaternion<T>(vector)*inverted()).vector();
@@ -417,11 +418,13 @@ template<class T> class Quaternion {
         /**
          * @brief Rotate vector with normalized quaternion
          *
-         * Faster alternative to transformVector(), expects that the quaternion is
-         * normalized. @f[
+         * Faster alternative to transformVector(), expects that the quaternion
+         * is normalized. @f[
          *      v' = qvq^{-1} = qvq^* = q [\boldsymbol v, 0] q^*
          * @f]
-         * @see Quaternion(const Vector3&), Matrix4::transformVector(), DualQuaternion::transformPointNormalized()
+         * @see Quaternion(const Vector3&), vector(), Matrix4::transformVector(),
+         *      DualQuaternion::transformPointNormalized(),
+         *      Complex::transformVectorNormalized()
          */
         inline Vector3<T> transformVectorNormalized(const Vector3<T>& vector) const {
             CORRADE_ASSERT(MathTypeTraits<T>::equals(dot(), T(1)),

src/Math/Test/ComplexTest.cpp

@@ -49,6 +49,8 @@ class ComplexTest: public Corrade::TestSuite::Tester {
         void angle();
         void rotation();
         void matrix();
+        void transformVector();
+        void transformVectorNormalized();
 
         void debug();
 };
@@ -78,6 +80,8 @@ ComplexTest::ComplexTest() {
              &ComplexTest::angle,
              &ComplexTest::rotation,
              &ComplexTest::matrix,
+             &ComplexTest::transformVector,
+             &ComplexTest::transformVectorNormalized,
 
              &ComplexTest::debug);
 }
@@ -266,6 +270,32 @@ void ComplexTest::matrix() {
     CORRADE_COMPARE(a.matrix(), m);
 }
 
+void ComplexTest::transformVector() {
+    Complex a = Complex::rotation(Deg(23.0f));
+    Matrix3 m = Matrix3::rotation(Deg(23.0f));
+    Vector2 v(-3.6f, 0.7f);
+
+    Vector2 rotated = a.transformVector(v);
+    CORRADE_COMPARE(rotated, m.transformVector(v));
+    CORRADE_COMPARE(rotated, Vector2(-3.58733f, -0.762279f));
+}
+
+void ComplexTest::transformVectorNormalized() {
+    Complex a = Complex::rotation(Deg(23.0f));
+    Matrix3 m = Matrix3::rotation(Deg(23.0f));
+    Vector2 v(-3.6f, 0.7f);
+
+    std::ostringstream o;
+    Error::setOutput(&o);
+    Vector2 notRotated = (a*2).transformVectorNormalized(v);
+    CORRADE_VERIFY(notRotated != notRotated);
+    CORRADE_COMPARE(o.str(), "Math::Complex::transformVectorNormalized(): complex number must be normalized\n");
+
+    Vector2 rotated = a.transformVectorNormalized(v);
+    CORRADE_COMPARE(rotated, m.transformVector(v));
+    CORRADE_COMPARE(rotated, a.transformVector(v));
+}
+
 void ComplexTest::debug() {
     std::ostringstream o;
 

src/Math/Test/QuaternionTest.cpp

@@ -340,7 +340,7 @@ void QuaternionTest::transformVectorNormalized() {
     Vector3 v(5.0f, -3.6f, 0.7f);
 
     std::ostringstream o;
-    Corrade::Utility::Error::setOutput(&o);
+    Error::setOutput(&o);
     Vector3 notRotated = (a*2).transformVectorNormalized(v);
     CORRADE_VERIFY(notRotated != notRotated);
     CORRADE_COMPARE(o.str(), "Math::Quaternion::transformVectorNormalized(): quaternion must be normalized\n");