From e7ceddf0fc2dd7fc02aeb31a665c0669bb7656f2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Fri, 22 Feb 2013 17:55:00 +0100
Subject: [PATCH] Math: rotation complex number.

---
 src/Math/Complex.h            | 24 ++++++++++++++++++++++++
 src/Math/Matrix3.h            |  3 ++-
 src/Math/Quaternion.h         |  6 +++---
 src/Math/Test/ComplexTest.cpp | 17 +++++++++++++++++
 4 files changed, 46 insertions(+), 4 deletions(-)

diff --git a/src/Math/Complex.h b/src/Math/Complex.h
index 93122b74b..62053251c 100644
--- a/src/Math/Complex.h
+++ b/src/Math/Complex.h
@@ -66,6 +66,19 @@ template<class T> class Complex {
             return Rad<T>(std::acos(normalizedA._real*normalizedB._real + normalizedA._imaginary*normalizedB._imaginary));
         }
 
+        /**
+         * @brief Rotation complex number
+         * @param angle             Rotation angle (counterclockwise)
+         *
+         * @f[
+         *      c = cos \theta + i sin \theta
+         * @f]
+         * @see rotationAngle(), Matrix3::rotation(), Quaternion::rotation()
+         */
+        inline static Complex<T> rotation(Rad<T> angle) {
+            return {std::cos(T(angle)), std::sin(T(angle))};
+        }
+
         /**
          * @brief Default constructor
          *
@@ -101,6 +114,17 @@ template<class T> class Complex {
         /** @brief Imaginary part */
         inline constexpr T imaginary() const { return _imaginary; }
 
+        /**
+         * @brief Rotation angle of complex number
+         *
+         * @f[
+         *      \theta = atan2(b, a)
+         * @f]
+         */
+        inline Rad<T> rotationAngle() const {
+            return Rad<T>(std::atan2(_imaginary, _real));
+        }
+
         /**
          * @brief Add complex number and assign
          *
diff --git a/src/Math/Matrix3.h b/src/Math/Matrix3.h
index d93050281..87be55128 100644
--- a/src/Math/Matrix3.h
+++ b/src/Math/Matrix3.h
@@ -64,7 +64,8 @@ template<class T> class Matrix3: public Matrix<3, T> {
          * @brief 2D rotation matrix
          * @param angle     Rotation angle (counterclockwise)
          *
-         * @see rotation() const, Matrix4::rotation(Rad, const Vector3&)
+         * @see rotation() const, Complex::rotation(),
+         *      Matrix4::rotation(Rad, const Vector3&)
          */
         static Matrix3<T> rotation(Rad<T> angle) {
             T sine = std::sin(T(angle));
diff --git a/src/Math/Quaternion.h b/src/Math/Quaternion.h
index 5edfee668..6ce8ae078 100644
--- a/src/Math/Quaternion.h
+++ b/src/Math/Quaternion.h
@@ -108,15 +108,15 @@ template<class T> class Quaternion {
 
         /**
          * @brief Rotation quaternion
-         * @param angle             Rotation angle (counterclockwise, in radians)
+         * @param angle             Rotation angle (counterclockwise)
          * @param normalizedAxis    Normalized rotation axis
          *
          * Expects that the rotation axis is normalized. @f[
          *      q = [\boldsymbol a \cdot sin \frac \theta 2, cos \frac \theta 2]
          * @f]
          * @see rotationAngle(), rotationAxis(), DualQuaternion::rotation(),
-         *      Matrix4::rotation(), Vector3::xAxis(), Vector3::yAxis(),
-         *      Vector3::zAxis()
+         *      Matrix4::rotation(), Complex::rotation(), Vector3::xAxis(),
+         *      Vector3::yAxis(), Vector3::zAxis()
          */
         inline static Quaternion<T> rotation(Rad<T> angle, const Vector3<T>& normalizedAxis) {
             CORRADE_ASSERT(MathTypeTraits<T>::equals(normalizedAxis.dot(), T(1)),
diff --git a/src/Math/Test/ComplexTest.cpp b/src/Math/Test/ComplexTest.cpp
index f448f2003..c0a25c62a 100644
--- a/src/Math/Test/ComplexTest.cpp
+++ b/src/Math/Test/ComplexTest.cpp
@@ -46,6 +46,7 @@ class ComplexTest: public Corrade::TestSuite::Tester {
         void invertedNormalized();
 
         void angle();
+        void rotation();
 
         void debug();
 };
@@ -72,10 +73,12 @@ ComplexTest::ComplexTest() {
              &ComplexTest::invertedNormalized,
 
              &ComplexTest::angle,
+             &ComplexTest::rotation,
 
              &ComplexTest::debug);
 }
 
+typedef Math::Deg<float> Deg;
 typedef Math::Rad<float> Rad;
 typedef Math::Complex<float> Complex;
 typedef Math::Vector2<float> Vector2;
@@ -228,6 +231,20 @@ void ComplexTest::angle() {
     CORRADE_COMPARE(angle, Rad(2.933128f));
 }
 
+void ComplexTest::rotation() {
+    Complex a = Complex::rotation(Deg(120.0f));
+    CORRADE_COMPARE(a, Complex(-0.5f, 0.8660254f));
+    CORRADE_COMPARE_AS(a.rotationAngle(), Deg(120.0f), Rad);
+
+    /* Verify negative angle */
+    Complex b = Complex::rotation(Deg(-240.0f));
+    CORRADE_COMPARE(b, Complex(-0.5f, 0.8660254f));
+    CORRADE_COMPARE_AS(b.rotationAngle(), Deg(120.0f), Rad);
+
+    /* Default-constructed complex number has zero angle */
+    CORRADE_COMPARE_AS(Complex().rotationAngle(), Deg(0.0f), Rad);
+}
+
 void ComplexTest::debug() {
     std::ostringstream o;