/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
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* for more details.                                                         *
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Revision 1.2  2004/04/28 11:37:15  pietroni
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Revision 1.1  2004/04/22 13:19:12  ganovelli
first version

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Revision 1.1  2004/04/08 01:13:31  pietroni
Initial commit


****************************************************************************/
#ifndef __VCG_TETRA3
#define __VCG_TETRA3

namespace vcg {

/** \addtogroup space */
/*@{*/
/** 
		Templated class for storing a generic tetrahedron in a 3D space.
    Note the relation with the Face class of TetraMesh complex, both classes provide the P(i) access functions to their points and therefore they share the algorithms on it (e.g. area, normal etc...)
 */
template <class SCALAR_TETRA_TYPE> class Tetra3
{
public:
  typedef SCALAR_TETRA_TYPE ScalarType;
	typedef Point3< ScalarType > CoordType;

/*********************************************
  
**/

protected:
	/// Vector of the 4 points that defines the tetrahedron
	Point3<ScalarType> _v[4];

public:
///constructor with 4 points
  Tetra3(CoordType p0,CoordType p1,CoordType p2,CoordType p3)
  {
    _v[0]=p0;
    _v[1]=p1;
    _v[2]=p2;
    _v[3]=p3;
  }

/// compute and return the volume of a tetrahedron
  	ScalarType ComputeVolume(){
				return (( _v[2]-_v[0])^(_v[1]-_v[0] ))*(_v[3]-_v[0])/6.0;
		}

/// compute and return the solid angle on a vertex
	double SolidAngle(int vind)
	{	
		double da0=DiedralAngle(EofV(vind,0));
		double da1=DiedralAngle(EofV(vind,1));
		double da2=DiedralAngle(EofV(vind,2));
		return((da0 + da1 + da2)- M_PI);
	}

/// compute and return the diadedral angle on an edge
	double DiedralAngle(int edgeind)
	{
		int f1=FofE(edgeind,0);
		int f2=FofE(edgeind,1);
		Point3d p0=_v[FofV(f1,0)];
		Point3d p1=_v[FofV(f1,1)];
		Point3d p2=_v[FofV(f1,2)];
		Point3d norm1=((p1-p0)^(p2-p0));
		p0=_v[FofV(f2,0)];
		p1=_v[FofV(f2,1)];
		p2=_v[FofV(f2,2)];
		Point3d norm2=((p1-p0)^(p2-p0));
		norm1.Normalize();
		norm2.Normalize();
		return (M_PI-acos(double(norm1*norm2)));
	}

/// compute and return the aspect ratio of the tetrahedron 
ScalarType ComputeAspectRatio()
	{	
		double a0=SolidAngle(0);
		double a1=SolidAngle(1);
		double a2=SolidAngle(2);
		double a3=SolidAngle(3);
		return (min(a0,min(a1,min(a2,a3))));
	}

//Tatrahedron Functions to retrieve information about relation between faces of tetrahedron(faces,adges,vertices).

  static int VofE(const int &indexE,const int &indexV)
  {	assert ((indexE<6)&&(indexV<2));
   static int edgevert[4][3] ={{0,1},
					{0,2},
					{0,3},
					{1,2},
					{1,3},
					{2,3}};
   return (edgevert[indexE][indexV]);
  }

	static int VofF(const int &indexF,const int &indexV)
	{	assert ((indexF<4)&&(indexV<3));
    static int facevert[4][3]={{0,1,2},
					{0,3,1},
					{0,2,3},
					{1,3,2}};
		return (facevert[indexF][indexV]);
	}

  static int EofV(const int &indexV,const int &indexE) 
	{	
    assert ((indexE<3)&&(indexV<4));
		static int vertedge[4][3]={{0,1,2},
											{0,3,4},
											{5,1,3},
											{4,5,2}};
		return vertedge[indexV][indexE];
	}

 static int EofF(const int &indexF,const int &indexE) 
	{	assert ((indexF<4)&&(faceindexEdge<3));
    static int faceedge[4][3]={{0,3,1},
					{2,4,0},
					{1,5,2},
					{4,5,3}
					};
		return faceedge [indexF][faceindexEdge];
	}

	static int FofV(const int &indexV,const int &indexF)
	{	
    assert ((indexV<4)&&(indexF<3));
    static int vertface[4][3]={{0,1,2},
					{0,3,1},
					{0,2,3},
					{1,3,2}};
		return vertface[indexV][indexF];
	}
  
  static int FofE(const int &indexE,const int &indexSide) 
	{	assert ((indexE<6)&&(indexSide<2));
    static int edgeface[6][2]={{0,1},
					{0,2},
					{1,2},
					{0,3},
					{1,3},
					{2,3}};
		return edgeface [indexE][indexSide];
	}

static int VofEE(const int &indexE0,const int &indexE1)
{
  assert ((indexE0<6)&&(indexE0>=0));
  assert ((indexE1<6)&&(indexE1>=0));
  static int edgesvert[6][6]={{-1,0,0,1,1,-1},
  {0,-1,0,2,-1,2},
  {0,0,-1,-1,3,3},
  {1,2,-1,-1,1,2},
  {1,-1,3,1,-1,3},
  {-1,2,3,2,3,-1}};
return (edgesvert[indexE0][indexE1]);
}

static int VofFFF(const int &indexF0,const int &indexF1,const int &indexF2)
{
  assert ((indexF0<4)&&(indexF0>=0));
  assert ((indexF1<4)&&(indexF1>=0));
  assert ((indexF2<4)&&(indexF2>=0));
  static int facesvert[4][4][4]={
		{//0
			{-1,-1,-1,-1},{-1,-1,0,1},{-1,0,-1,2},{-1,1,2,-1}
		},
		{//1
			{-1,-1,0,1},{-1,-1,-1,-1},{0,-1,-1,3},{1,-1,3,-1}
		},
		{//2
			{-1,0,-1,2},{0,-1,-1,3},{-1,-1,-1,-1},{2,3,-1,-1}
		},
		{//3
			{-1,1,2,-1},{1,-1,3,-1},{2,3,-1,-1},{-1,-1,-1,-1}
		}
	};
  return facesvert[indexF0][indexF1][indexF2];
}

static int EofFF(const int &indexF0,const int &indexF1)
{
  assert ((indexF0<4)&&(indexF0>=0));
  assert ((indexF1<4)&&(indexF1>=0));
  static	int facesedge[4][4]={{-1,  0,  1,  3},
						  { 0, -1,  2,  4},
						  { 1,  2, -1,  5},
						  { 3,  4,  5, -1}};
  return (facesedge[indexF0][indexF1]);
}

static int EofVV(const int &indexV0,const int &indexV1) 
{
      assert ((indexV0<4)&&(indexV0>=0));
      assert ((indexV1<4)&&(indexV1>=0));
      static	int verticesedge[4][4]={{-1,  0,  1,  2},
						  { 0, -1,  3,  4},
						  { 1,  3, -1,  5},
						  { 2,  4,  5, -1}};
			
			return verticesedge[indexV0][indexV1];
}

static FofVVV(const int &indexV0,const int &indexV1,const int &indexV2)
{

assert ((indexV0<4)&&(indexV0>=0));
assert ((indexV1<4)&&(indexV1>=0));
assert ((indexV2<4)&&(indexV2>=0));

static int verticesface[4][4][4]={
		{//0
			{-1,-1,-1,-1},{-1,-1,0,1},{-1,0,-1,2},{-1,1,2,-1}
		},
		{//1
			{-1,-1,0,1},{-1,-1,-1,-1},{0,-1,-1,3},{1,-1,3,-1}
		},
		{//2
			{-1,0,-1,2},{0,-1,-1,3},{-1,-1,-1,-1},{2,3,-1,-1}
		},
		{//3
			{-1,1,2,-1},{1,-1,3,-1},{2,3,-1,-1},{-1,-1,-1,-1}
		}
	};
return verticesface[indexV0][indexV1][indexV2];
}

static int FofEE(const int &indexE0,const int &indexE1)
{
  assert ((indexE0<6)&&(indexE0>=0));
  assert ((indexE1<6)&&(indexE1>=0));
  static	int edgesface[6][6]={{-1,0,1,0,1,-1},
    {0,-1,2,0,-1,2},
    {1,2,-1,-1,1,2},
    {0,0,-1,-1,3,3},
    {1,-1,1,3,-1,3},
    {-1,2,2,3,3,-1}};
						  
			return edgesface[indexE0][indexE1];
}

}; //end Class


}	 // end namespace


#endif