Add of some mathematical functions

Plane: Getters and classic planes
Sphere: Getter
Vector2: Angle between two vectors
Vector3: Same in 3D

Former-commit-id: 07e6421def813743e5fd8248fe2e9503cebbb8a8

include/Nazara/Math/Plane.hpp

@@ -1,4 +1,4 @@
-// Copyright (C) 2014 Jérôme Leclercq
+// Copyright (C) 2014 Jérôme Leclercq
 // This file is part of the "Nazara Engine - Mathematics module"
 // For conditions of distribution and use, see copyright notice in Config.hpp
 
@@ -27,6 +27,9 @@ class NzPlane
 		T Distance(const NzVector3<T>& point) const;
 		T Distance(T x, T y, T z) const;
 
+		NzVector3 GetNormal() const;
+		T GetDistance() const;
+
 		NzPlane& Set(T normalX, T normalY, T normalZ, T Distance);
 		NzPlane& Set(const T plane[4]);
 		NzPlane& Set(const NzPlane& plane);
@@ -38,6 +41,9 @@ class NzPlane
 		NzString ToString() const;
 
 		static NzPlane Lerp(const NzPlane& from, const NzPlane& to, T interpolation);
+		static NzPlane XY();
+		static NzPlane XZ();
+		static NzPlane YZ();
 
 		NzVector3<T> normal;
 		T distance;

include/Nazara/Math/Plane.inl

@@ -58,6 +58,18 @@ T NzPlane<T>::Distance(T x, T y, T z) const
 	return Distance(NzVector3<T>(x, y, z));
 }
 
+template<typename T>
+NzVector3 NzPlane<T>::GetNormal() const
+{
+    return normal;
+}
+
+template<typename T>
+T NzPlane<T>::GetDistance() const
+{
+    return distance;
+}
+
 template<typename T>
 NzPlane<T>& NzPlane<T>::Set(T normalX, T normalY, T normalZ, T D)
 {
@@ -152,6 +164,24 @@ NzPlane<T> NzPlane<T>::Lerp(const NzPlane& from, const NzPlane& to, T interpolat
 	return plane;
 }
 
+template<typename T>
+NzPlane<T> NzPlane<T>::XY()
+{
+    return NzPlane<T>(F(0.0), F(0.0), F(1.0), F(0.0));
+}
+
+template<typename T>
+NzPlane<T> NzPlane<T>::XZ()
+{
+    return NzPlane<T>(F(0.0), F(1.0), F(0.0), F(0.0));
+}
+
+template<typename T>
+NzPlane<T> NzPlane<T>::YZ()
+{
+    return NzPlane<T>(F(1.0), F(0.0), F(0.0), F(0.0));
+}
+
 template<typename T>
 std::ostream& operator<<(std::ostream& out, const NzPlane<T>& plane)
 {

include/Nazara/Math/Sphere.hpp

@@ -39,6 +39,7 @@ class NzSphere
 		NzVector3<T> GetNegativeVertex(const NzVector3<T>& normal) const;
 		NzVector3<T> GetPosition() const;
 		NzVector3<T> GetPositiveVertex(const NzVector3<T>& normal) const;
+		T GetRadius() const;
 
 		bool Intersect(const NzBox<T>& box) const;
 		bool Intersect(const NzSphere& sphere) const;

include/Nazara/Math/Sphere.inl

@@ -117,6 +117,13 @@ NzVector3<T> NzSphere<T>::GetPositiveVertex(const NzVector3<T>& normal) const
 
 	return pos;
 }
+
+template<typename T>
+T NzSphere<T>::GetRadius() const
+{
+    return radius;
+}
+
 template<typename T>
 bool NzSphere<T>::Intersect(const NzBox<T>& box) const
 {

include/Nazara/Math/Vector2.hpp

@@ -23,6 +23,8 @@ class NzVector2
 
 		T AbsDotProduct(const NzVector2& vec) const;
 
+		T AngleBetween(const NzVector2& vec, bool toDegree = true) const;
+
 		T Distance(const NzVector2& vec) const;
 		float Distancef(const NzVector2& vec) const;
 

include/Nazara/Math/Vector2.inl

@@ -54,6 +54,15 @@ inline unsigned int NzVector2<unsigned int>::AbsDotProduct(const NzVector2<unsig
 	return std::labs(x * vec.x) + std::labs(y * vec.y);
 }
 
+template<typename T>
+T NzVector2<T>::AngleBetween(const NzVector2& vec, bool toDegree) const
+{
+    if (toDegree)
+        return NzRadianToDegree(std::atan2(vec.y, vec.x) - std::atan2(y, x));
+    else
+        return std::atan2(vec.y, vec.x) - std::atan2(y, x);
+}
+
 template<typename T>
 T NzVector2<T>::Distance(const NzVector2& vec) const
 {

include/Nazara/Math/Vector3.hpp

@@ -24,6 +24,8 @@ template<typename T> class NzVector3
 
 		T AbsDotProduct(const NzVector3& vec) const;
 
+		T AngleBetween(const NzVector3& vec, bool toDegree = true) const;
+
 		NzVector3 CrossProduct(const NzVector3& vec) const;
 
 		T Distance(const NzVector3& vec) const;

include/Nazara/Math/Vector3.inl

@@ -60,6 +60,30 @@ inline unsigned int NzVector3<unsigned int>::AbsDotProduct(const NzVector3<unsig
 	return std::labs(x * vec.x) + std::labs(y * vec.y) + std::labs(z * vec.z);
 }
 
+template<typename T>
+T NzVector3<T>::AngleBetween(const NzVector3& vec, bool toDegree) const
+{
+    T alpha = DotProduct(vec);
+    T divisor = (GetLength() * vec.GetLength());
+
+    #if NAZARA_MATH_SAFE
+	if (NzNumberEquals(divisor, F(0.0)))
+	{
+		NzString error("Division by zero");
+
+		NazaraError(error);
+		throw std::domain_error(error);
+	}
+	#endif
+
+	alpha /= divisor;
+
+	if (toDegree)
+        return NzRadianToDegree(std::acos(NzClamp(alpha, F(-1.0), F(1.0))));
+    else
+        return std::acos(NzClamp(alpha, F(-1.0), F(1.0)));
+}
+
 template<typename T>
 NzVector3<T> NzVector3<T>::CrossProduct(const NzVector3& vec) const
 {