/**
 * \defgroup Math3DAPI Math3D library
 * @{
 */

/**
\brief Vector constructor from components
    \param x \p float x component
	\param y \p float y component
	\param z \p float z component
	\return \p vector resulting vector
	@code
		Print( Vector(1, 2, 3) );

		>> <1,2,3>
	@endcode
*/
proto native vector Vector(float x, float y, float z);

enum ECurveType
{
	CatmullRom,
	NaturalCubic,
	UniformCubic
};

class Math3D
{
	private void Math3D() {}
	private void ~Math3D() {}
	
	//-----------------------------------------------------------------
	proto static vector ClipLine(vector start, vector end, vector norm, float d);

	/**
	\brief Tests whether ray is intersecting sphere.
		\param raybase \p vector Start of ray
		\param raycos \p vector End of ray
		\param center \p vector Center of sphere
		\param radius \p float Radius of sphere
		\return \p float -1 when not intersecting, else the fraction of ray
	*/
	proto static float IntersectRaySphere(vector raybase, vector raycos, vector center, float radius);
	
	/**
	\brief Tests whether ray is intersecting axis aligned box.
		\param start \p vector Start of ray
		\param end \p vector End of ray
		\param mins \p vector Minimums of bound box
		\param maxs \p vector Maximums of bound box
		\return \p float -1 when not intersecting, else the fraction of ray
	*/
	proto static float IntersectRayBox(vector start, vector end, vector mins, vector maxs);
	
	/**
	\brief Tests whether sphere is intersecting axis aligned box.
		\param origin \p vector Origin of sphere
		\param radius \p float Radius of sphere
		\param mins \p vector Minimums of bound box
		\param maxs \p vector Maximums of bound box
		\return \p bool True when intersects
	*/
	proto static bool IntersectSphereBox(vector origin, float radius, vector mins, vector maxs);
	
	/**
	\brief Tests whether sphere is intersecting cone.
		\param origin \p vector Origin of sphere
		\param radius \p float Radius of sphere
		\param conepos \p vector Position of top of cone
		\param axis \p vector Orientation of cone in direction from top to bottom
		\param angle \p float Angle of cone in radians
		\return \p bool True when sphere is intersecting cone
	*/
	proto static bool IntersectSphereCone(vector origin, float radius, vector conepos, vector axis, float angle);
	
	/**
	\brief Tests whether sphere is fully inside cone.
		\param origin \p vector Origin of sphere
		\param radius \p float Radius of sphere
		\param conepos \p vector Position of top of cone
		\param axis \p vector Orientation of cone in direction from top to bottom
		\param angle \p float Angle of cone in radians
		\return \p bool True when sphere is fully inside cone
	*/
	proto static bool IntersectWholeSphereCone(vector origin, float radius, vector conepos, vector axis, float angle);
	
	/**
	\brief Tests whether cylinder is intersecting oriented box.
		\param mins \p vector Minimums of bound box
		\param maxs \p vector Maximums of bound box
		\param obbMat \p vector Transform of box
		\param cylMat \p vector Transform of cylinder
		\param cylinderRadius \p float Radius of cylinder
		\param cylinderHeight \p float Height of cylinder
		\return \p bool True when cylinder is intersecting oriented box
	*/
	proto static bool IntersectCylinderOBB(vector mins, vector maxs, vector obbMat[4], vector cylMat[4], float cylinderRadius, float cylinderHeight);
	
	/**
	\brief Tests whether ray is intersecting cylinder.
		\param rayStart \p vector Start of ray
		\param rayEnd \p vector End of ray
		\param center \p vector Center of cylinder
		\param radius \p float Radius of cylinder
		\param height \p float Height of cylinder
		\return \p bool True when ray is intersecting cylinder
	*/
	proto static bool IntersectRayCylinder(vector rayStart, vector rayEnd, vector center, float radius, float height);
	
	/**
	\brief Tests whether ray is intersecting plane.
		\param rayStart \p vector Start of ray
		\param rayEnd \p vector End of ray
		\param planeNormal \p vector Normal of the plane
		\param planeDist \p float Length of the plane
		\param intersection \p vector Intersection point of the plane, only valid when return is 3
		\return \p int 1 when behind, 2 when in front and 3 when intersecting the plane
	*/
	proto static int IntersectRayPlane(vector rayStart, vector rayEnd, vector planeNormal, float planeDist, out vector intersection);
	
	/**
	\brief Creates rotation matrix from angles
		\param ang \p vector which contains angles
		\param[out] mat \p vector created rotation matrix
		@code
			vector mat[3];
			YawPitchRollMatrix( "70 15 45", mat );
			Print( mat );

			>> <0.330366,0.0885213,-0.939693>,<0.458809,0.854988,0.241845>,<0.824835,-0.511037,0.241845>
		@endcode
	*/
	proto static void YawPitchRollMatrix(vector ang, out vector mat[3]);

	/**
	\brief Creates rotation matrix from direction and up vector
		\param dir \p vector direction vector
		\param up \p vector up vector
		\param[out] mat \p vector[4] created rotation matrix
		@code
			vector mat[4];
			vector dir = "1 0 1";
			vector up = "0 1 0";
			DirectionAndUpMatrix( dir, up, mat );
			Print( mat );

			>> <0.707107,0,-0.707107>,<0,1,0>,<0.707107,0,0.707107>,<0,0,0>
		@endcode
	*/
	proto static void DirectionAndUpMatrix(vector dir, vector up, out vector mat[4]);

	/**
	\brief Transforms matrix
		\param mat0 \p vector[4] first matrix
		\param mat1 \p vector[4] second matrix
		\param[out] res \p vector[4] result of first and second matrix multiplication
		@code
			vector mat0[4] = { "2 0 0 0", "0 3 0 0", "0 1 0 0", "0 0 0 1" }; // scale matrix
			vector mat1[4] = { "1 0 0 0", "0 1 0 0", "0 1 0 0", "2 4 1 3" }; // translation matrix
			vector res[4];
			Math3D.MatrixMultiply4(mat0, mat1, res)
			Print( res );

			>> <2,0,0>,<0,3,0>,<0,3,0>,<4,13,0>
		@endcode
	*/
	proto static void MatrixMultiply4(vector mat0[4], vector mat1[4], out vector res[4]);

	/**
	\brief Transforms rotation matrix
		\param mat0 \p vector[3] first matrix
		\param mat1 \p vector[3] second matrix
		\param[out] res \p vector[3] result of first and second matrix multiplication
		@code
			vector mat0[3] = { "1.5 2.5 0", "0.1 1.3 0", "0 0 1" }; // rotation matrix
			vector mat1[3] = { "1 0.4 0", "0 1 0", "0 1.3 2.7" }; // rotation matrix
			vector res[3];
			Math3D.MatrixMultiply3(mat0, mat1, res)
			Print( res );

			>> <1.54,3.02,0>,<0.1,1.3,0>,<0.13,1.69,2.7>
		@endcode
	*/
	proto static void MatrixMultiply3(vector mat0[3], vector mat1[3], out vector res[3]);

	/**
	\brief Invert-transforms matrix
		\param mat0 \p vector[4] first matrix
		\param mat1 \p vector[4] second matrix
		\param[out] res \p vector[4] inverse result of first and second matrix multiplication
		@code
			vector mat0[4] = { "2 0 0", "0 3 0", "0 0 1", "0 0 0" }; // scale matrix
			vector mat1[4] = { "1 0 0", "0 1 0", "0 0 1", "2 4 1" }; // translation matrix
			vector res[4];
			Math3D.MatrixInvMultiply4(mat0, mat1, res)
			Print( res );

			>> <2,0,0>,<0,3,1>,<0,3,1>,<4,12,4>
		@endcode
	*/
	proto static void MatrixInvMultiply4(vector mat0[4], vector mat1[4], out vector res[4]);

	/**
	\brief Invert-transforms rotation matrix
		\param mat0 \p vector[3] first matrix
		\param mat1 \p vector[3] second matrix
		\param[out] res \p vector[3] result of first and second matrix multiplication
		@code
			vector mat0[3] = { "1.5 2.5 0", "0.1 1.3 0", "0 0 1" }; // rotation matrix
			vector mat1[3] = { "1 0.4 0", "0 1 0", "0 1.3 2.7" }; // rotation matrix
			vector res[3];
			Math3D.MatrixInvMultiply3(mat0, mat1, res)
			Print( res );

			>> <2.5,0.62,0>,<2.5,1.3,0>,<3.25,1.69,2.7>
		@endcode
	*/
	proto static void MatrixInvMultiply3(vector mat0[3], vector mat1[3], out vector res[3]);

	/**
	\brief Inverses a matrix
	    \param[it] mat \p matrix which should be inversed
	*/
	proto static void MatrixInverse4(vector mat[4]);
	
	/**
	\brief Inverses a matrix
	    \param[it] mat \p matrix which should be inversed
	*/
	proto static void MatrixInverse3(vector mat[3]);

	/**
	\brief Orthogonalizes matrix
	    \param[it] mat \p matrix which should be orthogonalized
	*/
	proto static void MatrixOrthogonalize4(vector mat[4]);
	
	/**
	\brief Orthogonalizes matrix
	    \param[it] mat \p matrix which should be orthogonalized
	*/
	proto static void MatrixOrthogonalize3(vector mat[3]);
	
	/**
	\brief Creates identity matrix
	    \param[out] mat \p created identity matrix
		@code
	        vector mat[4];
	    	Math3D.MatrixIdentity4( mat );
	    	Print( mat );

			>> <1,0,0>,<0,1,0>,<0,0,1>,<0,0,0>
		@endcode
	*/
	
	static void MatrixIdentity4(out vector mat[4])
	{
		mat[0] = "1 0 0";
		mat[1] = "0 1 0";
		mat[2] = "0 0 1";
		mat[3] = vector.Zero;
	}
	
	/**
	\brief Creates identity matrix
	    \param[out] mat \p created identity matrix
		@code
	        vector mat[3];
	    	Math3D.MatrixIdentity3( mat );
	    	Print( mat );

			>> <1,0,0>,<0,1,0>,<0,0,1>
		@endcode
	*/
	static void MatrixIdentity3(out vector mat[3])
	{
		mat[0] = "1 0 0";
		mat[1] = "0 1 0";
		mat[2] = "0 0 1";
	}

	/**
	\brief Creates scale matrix
	    \param scale \p scale coeficient
	    \param[out] mat \p created scale matrix
		@code
	        vector mat[3];
	    	Math3D.ScaleMatrix( 2.5, mat );
	    	Print( mat );

			>> <2.5,0,0>,<0,2.5,0>,<0,0,2.5>
		@endcode
	*/
	static void ScaleMatrix(float scale, out vector mat[3])
	{
		vector v0, v1, v2;
		v0[0] = scale;
		v1[1] = scale;
		v2[2] = scale;
		mat[0] = v0;
		mat[1] = v1;
		mat[2] = v2;
	}

	/**
	\brief Creates identity quaternion
		\param[out] q \p float[4] created identity quaternion
		@code
			float q[4];
			Math3D.QuatIdentity( q );
			Print( q );

			>> {0,0,0,1}
		@endcode
	*/
	static void QuatIdentity(out float q[4])
	{
		q[0] = 0;
		q[1] = 0;
		q[2] = 0;
		q[3] = 1;
	}

	/**
	\brief Copies quaternion
	    \param s \p float[4] quaternion to copy
		\param[out] d \p float[4] created quaternion copy
		@code
			float s[4] = { 2, 3, 4, 1 };
			float d[4];
			Math3D.QuatCopy( s, d );
			Print( d );

			>> {2,3,4,1}
		@endcode
	*/
	static void QuatCopy(float s[4], out float d[4])
	{
		d[0] = s[0];
		d[1] = s[1];
		d[2] = s[2];
		d[3] = s[3];
	}

	/**
	\brief Converts rotation matrix to quaternion
	    \param mat \p vector[3] rotation matrix
		\param[out] d \p float[4] created quaternion copy
		@code
			vector mat[3];
			vector rot = "70 15 45";
			rot.RotationMatrixFromAngles( mat );
			float d[4];
			Math3D.MatrixToQuat( mat, d );
			Print( d );

			>> {0.241626,0.566299,-0.118838,0.778973}
		@endcode
	*/
	proto static void MatrixToQuat(vector mat[3], out float d[4]);

	
	//! Converts quaternion to rotation matrix
	proto static void QuatToMatrix(float q[4], out vector mat[3]);

	/**
	\brief Returns angles of rotation matrix
		\param mat \p vector[3] rotation matrix
		\return \p vector roll, pitch, yaw angles
		@code
			vector mat[3];
			Math3D.RollPitchYawMatrix( "70 15 45", mat );
			vector ang = Math3D.MatrixToAngles( mat );
			Print( ang );

			>> <70,15,-45>
		@endcode
	*/
	proto static vector MatrixToAngles(vector mat[3]);
	
	/**
	\brief Linear interpolation between q1 and q2 with weight 'frac' (0...1)
	    \param[out] qout \p float[4] result quaternion
		\param q1 \p float[4] first quaternion
		\param q2 \p float[4] second quaternion
		\param frac \p float interpolation weight
		@code
			float q1[4] = { 1, 1, 1, 1 };
			float q2[4] = { 2, 2, 2, 1 };
			float qout[4];
			Math3D.QuatLerp( qout, q1, q2, 0.5 );
			Print( qout );

			>> {1.5,1.5,1.5,1}
		@endcode
	*/
	proto static void QuatLerp(out float qout[4], float q1[4], float q2[4], float frac);

	/**
	\brief Multiplies quaternions
	    \param[out] qout \p float[4] result quaternion
		\param q1 \p float[4] first quaternion
		\param q2 \p float[4] second quaternion
		@code
			float q1[4] = { 1, 2, 3, 1 };
			float q2[4] = { 2, 2, 2, 1 };
			float qout[4];
			Math3D.QuatMultiply( qout, q1, q2 );
			Print( qout );

			>> {2,4,6,1}
		@endcode
	*/
	proto static void QuatMultiply(out float qout[4], float q1[4], float q2[4]);

	//! Returns Angles vector from quaternion
	proto static vector QuatToAngles(float q[4]);
	
	/**
	\brief Returns 1, when bounding boxes intersects
	    \param mins1 \p vector minimum point of first bounding box
		\param maxs1 \p vector maximum point of first bounding box
		\param mins2 \p vector minimum point of second bounding box
		\param maxs2 \p vector maximum point of second bounding box
		\return \p int 1 if boundig boxes intersects, otherwise 0
		@code
			vector mins1 = "1 1 1";
			vector maxs1 = "3 3 3";
			vector mins2 = "2 2 2";
			vector maxs2 = "4 4 4";
			Print( Math3D.CheckBoundBox(mins1, maxs1, mins2, maxs2) );

			>> 1
		@endcode
	*/
	proto static int CheckBoundBox(vector mins1, vector maxs1, vector mins2, vector maxs2);
	
	/**
	\brief Returns randon normalized direction
	    \return \p vector 
		@code
			Print( Math3D.GetRandomDir() );

			>>vector ret =  0x0000000007c1a1c0 {<0.422565,0,-0.906333>}
		@endcode
	*/
	static vector GetRandomDir()
	{
		float x = Math.RandomFloatInclusive(-1, 1);
		float y = Math.RandomFloatInclusive(-1, 1);
		float z = Math.RandomFloatInclusive(-1, 1);
			
		return Vector(x, y, z).Normalized();
	}
	
	
	/**
	\brief Computes curve
		\return \p vector 
		@code
			auto points = new array<vector>();
			points.Insert( Vector( 0, 0, 0) );
	    	points.Insert( Vector( 5, 0, 0) );
	    	points.Insert( Vector( 8, 3, 0) );
	    	points.Insert( Vector( 6, 1, 0) );
		
			float t = 0.5;
			vector result = Math3D.Curve(ECurveType.CatmullRom, t, points);
		@endcode
	*/
	proto static native vector Curve(ECurveType type, float param, notnull array<vector> points);
	
	
	/**
	\brief Point on line beg .. end nearest to pos
		\return \p vector
	*/
	proto static vector NearestPoint(vector beg, vector end, vector pos);
	
	/**
	\brief Angle that a target is from the direction of an origin
		\return \p float Angle in radians
	*/
	proto static float AngleFromPosition(vector origin, vector originDir, vector target);
	
	/**
	\brief Calculates the points of a right 2D cone in 3D space
		\param origin \p vector Origin of cone
		\param length \p float Length of the cone
		\param halfAngle \p float Half of the angle of the cone in radians
		\param angleOffset \p float Angle offset of the cone in radians (handy for rotating it along with something in the world)
		\param[out] leftPoint \p vector Left point of the cone
		\param[out] rightPoint \p vector Right point of the cone
	*/
	proto static void ConePoints(vector origin, float length, float halfAngle, float angleOffset, out vector leftPoint, out vector rightPoint);
};
//@}