Math: translation dual complex number.

src/Math/DualComplex.h

@@ -49,6 +49,20 @@ template<class T> class DualComplex: public Dual<Complex<T>> {
             return {Complex<T>::rotation(angle), {{}, {}}};
         }
 
+        /**
+         * @brief Translation dual complex number
+         * @param vector    Translation vector
+         *
+         * @f[
+         *      \hat c = (0 + i1) + \epsilon (v_x + iv_y)
+         * @f]
+         * @see translation() const, Matrix3::translation(const Vector2&),
+         *      DualQuaternion::translation(), Vector2::xAxis(), Vector2::yAxis()
+         */
+        inline static DualComplex<T> translation(const Vector2<T>& vector) {
+            return {{}, {vector.x(), vector.y()}};
+        }
+
         /**
          * @brief Default constructor
          *
@@ -84,6 +98,18 @@ template<class T> class DualComplex: public Dual<Complex<T>> {
             return this->real().rotationAngle();
         }
 
+        /**
+         * @brief Translation part of dual complex number
+         *
+         * @f[
+         *      \boldsymbol a = (c_\epsilon c_0^*)
+         * @f]
+         * @see translation(const Vector2&)
+         */
+        inline Vector2<T> translation() const {
+            return Vector2<T>(this->dual()*this->real().conjugated());
+        }
+
         /**
          * @brief Complex-conjugated dual complex number
          *

src/Math/DualQuaternion.h

@@ -59,8 +59,9 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * @f[
          *      \hat q = [\boldsymbol 0, 1] + \epsilon [\frac{\boldsymbol v}{2}, 0]
          * @f]
-         * @see translation() const, Matrix3::translation(const Vector2&),
+         * @see translation() const, Matrix4::translation(const Vector3&),
-         *      Vector3::xAxis(), Vector3::yAxis(), Vector3::zAxis()
+         *      DualComplex::translation(), Vector3::xAxis(), Vector3::yAxis(),
+         *      Vector3::zAxis()
          */
         inline static DualQuaternion<T> translation(const Vector3<T>& vector) {
             return {{}, {vector/T(2), T(0)}};

src/Math/Matrix3.h

@@ -38,8 +38,9 @@ template<class T> class Matrix3: public Matrix<3, T> {
          * @brief 2D translation matrix
          * @param vector    Translation vector
          *
-         * @see translation(), Matrix4::translation(const Vector3&),
+         * @see translation(), DualComplex::translation(),
-         *      Vector2::xAxis(), Vector2::yAxis()
+         *      Matrix4::translation(const Vector3&), Vector2::xAxis(),
+         *      Vector2::yAxis()
          */
         inline constexpr static Matrix3<T> translation(const Vector2<T>& vector) {
             return {{      T(1),       T(0), T(0)},

src/Math/Test/DualComplexTest.cpp

@@ -40,6 +40,7 @@ class DualComplexTest: public Corrade::TestSuite::Tester {
         void invertedNormalized();
 
         void rotation();
+        void translation();
 
         void debug();
 };
@@ -49,6 +50,7 @@ typedef Math::Rad<float> Rad;
 typedef Math::Complex<float> Complex;
 typedef Math::Dual<float> Dual;
 typedef Math::DualComplex<float> DualComplex;
+typedef Math::Vector2<float> Vector2;
 
 DualComplexTest::DualComplexTest() {
     addTests(&DualComplexTest::construct,
@@ -67,6 +69,7 @@ DualComplexTest::DualComplexTest() {
              &DualComplexTest::invertedNormalized,
 
              &DualComplexTest::rotation,
+             &DualComplexTest::translation,
 
              &DualComplexTest::debug);
 }
@@ -161,6 +164,13 @@ void DualComplexTest::rotation() {
     CORRADE_COMPARE_AS(a.rotationAngle(), Deg(120.0f), Rad);
 }
 
+void DualComplexTest::translation() {
+    Vector2 vec(1.5f, -3.5f);
+    DualComplex a = DualComplex::translation(vec);
+    CORRADE_COMPARE(a, DualComplex({}, {1.5f, -3.5f}));
+    CORRADE_COMPARE(a.translation(), vec);
+}
+
 void DualComplexTest::debug() {
     std::ostringstream o;