Renamed Vector::lengthSquared() to parameterless Vector::dot().

It's now less confusing ("length squared" looks like it's even heavier
than length), but on the other hand it's not so obvious that these two
functions come together.

src/Math/Geometry/Distance.h

@@ -52,7 +52,7 @@ class Distance {
          * values, because it doesn't compute the square root.
          */
         template<class T> static T linePointSquared(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
-            return Vector3<T>::cross(point - a, point - b).lengthSquared()/(b - a).lengthSquared();
+            return Vector3<T>::cross(point - a, point - b).dot()/(b - a).dot();
         }
 
         /**
@@ -97,9 +97,9 @@ class Distance {
         template<class T> static T lineSegmentPointSquared(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
             Vector3<T> pointMinusA = point - a;
             Vector3<T> pointMinusB = point - b;
-            T pointDistanceA = pointMinusA.lengthSquared();
-            T pointDistanceB = pointMinusB.lengthSquared();
-            T bDistanceA = (b - a).lengthSquared();
+            T pointDistanceA = pointMinusA.dot();
+            T pointDistanceB = pointMinusB.dot();
+            T bDistanceA = (b - a).dot();
 
             /* Point is before A */
             if(pointDistanceB > bDistanceA + pointDistanceA)
@@ -110,7 +110,7 @@ class Distance {
                 return pointDistanceB;
 
             /* Between A and B */
-            return Vector3<T>::cross(pointMinusA, pointMinusB).lengthSquared()/bDistanceA;
+            return Vector3<T>::cross(pointMinusA, pointMinusB).dot()/bDistanceA;
         }
 };
 

src/Math/Test/VectorTest.cpp

@@ -37,8 +37,8 @@ VectorTest::VectorTest() {
              &VectorTest::dot,
              &VectorTest::multiplyDivide,
              &VectorTest::addSubstract,
+             &VectorTest::dotSelf,
              &VectorTest::length,
-             &VectorTest::lengthSquared,
              &VectorTest::normalized,
              &VectorTest::sum,
              &VectorTest::product,
@@ -110,12 +110,12 @@ void VectorTest::addSubstract() {
     CORRADE_COMPARE(expected - b, a);
 }
 
-void VectorTest::length() {
-    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).length(), 5.4772256f);
+void VectorTest::dotSelf() {
+    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).dot(), 30.0f);
 }
 
-void VectorTest::lengthSquared() {
-    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).lengthSquared(), 30.0f);
+void VectorTest::length() {
+    CORRADE_COMPARE(Vector4(1.0f, 2.0f, 3.0f, 4.0f).length(), 5.4772256f);
 }
 
 void VectorTest::normalized() {

src/Math/Test/VectorTest.h

@@ -29,8 +29,8 @@ class VectorTest: public Corrade::TestSuite::Tester<VectorTest> {
         void dot();
         void multiplyDivide();
         void addSubstract();
+        void dotSelf();
         void length();
-        void lengthSquared();
         void normalized();
         void sum();
         void product();

src/Math/Vector.h

@@ -70,6 +70,7 @@ template<size_t size, class T> class Vector {
          * @f[
          * a \cdot b = \sum_{i=0}^{n-1} a_ib_i
          * @f]
+         * @see dot() const
          */
         static T dot(const Vector<size, T>& a, const Vector<size, T>& b) {
             T out(0);
@@ -243,24 +244,26 @@ template<size_t size, class T> class Vector {
         }
 
         /**
-         * @brief %Vector length
+         * @brief Dot product of the vector
          *
-         * @see lengthSquared()
+         * Should be used instead of length() for comparing vector length with
+         * other values, because it doesn't compute the square root, just the
+         * dot product: @f$ a \cdot a < length \cdot length @f$ is faster
+         * than @f$ \sqrt{a \cdot a} < length @f$.
+         *
+         * @see dot(const Vector<size, T>&, const Vector<size, T>&)
          */
-        inline T length() const {
-            return std::sqrt(dot(*this, *this));
+        inline T dot() const {
+            return dot(*this, *this);
         }
 
         /**
-         * @brief %Vector length squared
+         * @brief %Vector length
          *
-         * More efficient than length() for comparing vector length with
-         * other values, because it doesn't compute the square root, just the
-         * dot product: @f$ a \cdot a < length \cdot length @f$ is faster
-         * than @f$ \sqrt{a \cdot a} < length @f$.
+         * @see dot() const
          */
-        inline T lengthSquared() const {
-            return dot(*this, *this);
+        inline T length() const {
+            return std::sqrt(dot());
         }
 
         /** @brief Normalized vector (of length 1) */

src/Physics/Sphere.cpp

@@ -41,7 +41,7 @@ bool Sphere::collides(const AbstractShape* other) const {
 }
 
 bool Sphere::operator%(const Point& other) const {
-    return (other.transformedPosition()-transformedPosition()).lengthSquared() <
+    return (other.transformedPosition()-transformedPosition()).dot() <
         Math::pow<2>(transformedRadius());
 }
 
@@ -56,7 +56,7 @@ bool Sphere::operator%(const LineSegment& other) const {
 }
 
 bool Sphere::operator%(const Sphere& other) const {
-    return (other.transformedPosition()-transformedPosition()).lengthSquared() <
+    return (other.transformedPosition()-transformedPosition()).dot() <
         Math::pow<2>(transformedRadius()+other.transformedRadius());
 }