Math: renamed DualQuaternion::norm() to length(), added lengthSquared().

Hopefully this is properly implemented and properly named. On the other
hand, having length everywhere (vectors, quaternions, complex numbers)
and norm only at one place is inconsistent.

src/Math/DualQuaternion.h

@@ -185,15 +185,27 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
         }
 
         /**
-         * @brief %Dual quaternion norm
+         * @brief %Dual quaternion length squared
          *
-         * @f[
-         *      ||\hat q|| = \sqrt{\hat q^* \hat q} = ||q_0|| + \epsilon \frac{q_0 \cdot q_\epsilon}{||q_0||}
+         * Should be used instead of length() for comparing dual quaternion
+         * length with other values, because it doesn't compute the square root. @f[
+         *      |\hat q|^2 = \sqrt{\hat q^* \hat q}^2 = q_0 \cdot q_0 + \epsilon 2 (q_0 \cdot q_\epsilon)
+         * @f]
+         */
+        inline Dual<T> lengthSquared() const {
+            return {this->real().dot(), T(2)*Quaternion<T>::dot(this->real(), this->dual())};
+        }
+
+        /**
+         * @brief %Dual quaternion length
+         *
+         * See lengthSquared() which is faster for comparing length with other
+         * values. @f[
+         *      |\hat q| = \sqrt{\hat q^* \hat q} = |q_0| + \epsilon \frac{q_0 \cdot q_\epsilon}{|q_0|}
          * @f]
          */
-        inline Dual<T> norm() const {
-            T norm = this->real().length();
-            return {norm, Quaternion<T>::dot(this->real(), this->dual())/norm};
+        inline Dual<T> length() const {
+            return Math::sqrt(lengthSquared());
         }
 
         /**
@@ -205,7 +217,7 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * @f]
          */
         inline DualQuaternion<T> inverted() const {
-            return quaternionConjugated()/Math::pow<2>(norm());
+            return quaternionConjugated()/Math::pow<2>(length());
         }
 
         /**
@@ -217,7 +229,7 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * @f]
          */
         inline DualQuaternion<T> invertedNormalized() const {
-            CORRADE_ASSERT(MathTypeTraits<T>::equals(norm(), T(1)),
+            CORRADE_ASSERT(MathTypeTraits<T>::equals(lengthSquared(), T(1)),
                            "Math::DualQuaternion::invertedNormalized(): dual quaternion must be normalized", {});
             return quaternionConjugated();
         }
@@ -231,7 +243,7 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          * @see DualQuaternion(const Vector3&), Matrix4::transformPoint(), Quaternion::rotateVectorNormalized()
          */
         inline Vector3<T> transformPointNormalized(const Vector3<T>& vector) const {
-            CORRADE_ASSERT(MathTypeTraits<Dual<T>>::equals(norm(), Dual<T>(1)),
+            CORRADE_ASSERT(MathTypeTraits<Dual<T>>::equals(lengthSquared(), Dual<T>(1)),
                            "Math::DualQuaternion::transformPointNormalized(): dual quaternion must be normalized",
                            Vector3<T>(std::numeric_limits<T>::quiet_NaN()));
             return ((*this)*DualQuaternion<T>(vector)*conjugated()).dual().vector();

src/Math/Test/DualQuaternionTest.cpp

@@ -29,7 +29,8 @@ class DualQuaternionTest: public Corrade::TestSuite::Tester {
         void constructDefault();
         void constructFromVector();
 
-        void norm();
+        void lengthSquared();
+        void length();
 
         void quaternionConjugated();
         void dualConjugated();
@@ -57,7 +58,8 @@ DualQuaternionTest::DualQuaternionTest() {
              &DualQuaternionTest::constructDefault,
              &DualQuaternionTest::constructFromVector,
 
-             &DualQuaternionTest::norm,
+             &DualQuaternionTest::lengthSquared,
+             &DualQuaternionTest::length,
 
              &DualQuaternionTest::quaternionConjugated,
              &DualQuaternionTest::dualConjugated,
@@ -87,11 +89,18 @@ void DualQuaternionTest::constructFromVector() {
     CORRADE_COMPARE(DualQuaternion({1.0f, 2.0f, 3.0f}), DualQuaternion({{0.0f, 0.0f, 0.0f}, 1.0f}, {{1.0f, 2.0f, 3.0f}, 0.0f}));
 }
 
-void DualQuaternionTest::norm() {
-    CORRADE_COMPARE(DualQuaternion().norm(), 1.0f);
+void DualQuaternionTest::lengthSquared() {
+    CORRADE_COMPARE(DualQuaternion().lengthSquared(), 1.0f);
 
     DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.0f, 3.0f}, 2.0f});
-    CORRADE_COMPARE(a.norm(), Dual(5.477226f, -0.821584f));
+    CORRADE_COMPARE(a.lengthSquared(), Dual(30.0f, -9.0f));
+}
+
+void DualQuaternionTest::length() {
+    CORRADE_COMPARE(DualQuaternion().length(), 1.0f);
+
+    DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.0f, 3.0f}, 2.0f});
+    CORRADE_COMPARE(a.length(), Dual(5.477226f, -0.821584f));
 }
 
 void DualQuaternionTest::quaternionConjugated() {