vcglib/vcg/math/quadric5.h

/****************************************************************************
* MeshLab                                                           o o     *
* A versatile mesh processing toolbox                             o     o   *
*                                                                _   O  _   *
* Copyright(C) 2005                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
*                                                                    \      *
* All rights reserved.                                                      *
*                                                                           *
* This program is free software; you can redistribute it and/or modify      *   
* it under the terms of the GNU General Public License as published by      *
* the Free Software Foundation; either version 2 of the License, or         *
* (at your option) any later version.                                       *
*                                                                           *
* This program is distributed in the hope that it will be useful,           *
* but WITHOUT ANY WARRANTY; without even the implied warranty of            *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
*                                                                           *
****************************************************************************/
/****************************************************************************
  History
$Log$
Revision 1.7  2008/04/26 13:45:48  pirosu
improved loss of precision minimization

Revision 1.6  2008/04/26 12:50:32  pirosu
commented assert

Revision 1.5  2008/04/04 10:03:51  cignoni
Solved namespace ambiguities caused by the removal of a silly 'using namespace' in meshmodel.h

Revision 1.4  2008/03/02 15:15:50  pirosu
loss of precision management

Revision 1.3  2008/02/29 20:37:27  pirosu
fixed zero area faces management

Revision 1.2  2007/03/20 15:51:15  cignoni
Update to the new texture syntax

Revision 1.1  2007/02/08 13:39:59  pirosu
Added Quadric Simplification(with textures) Filter


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

#ifndef __VCGLIB_QUADRIC5
#define __VCGLIB_QUADRIC5

#include <vcg/math/quadric.h>

namespace vcg
{
namespace math {

  typedef double ScalarType;

  // r = a-b
  void inline sub_vec5(const ScalarType a[5], const ScalarType b[5], ScalarType r[5])
  {
    r[0] = a[0] - b[0];
    r[1] = a[1] - b[1];
    r[2] = a[2] - b[2];
    r[3] = a[3] - b[3];
    r[4] = a[4] - b[4];
  }

  // returns the in-product a*b
  ScalarType inline inproduct5(const ScalarType a[5], const ScalarType b[5])
  {
    return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]+a[3]*b[3]+a[4]*b[4];
  }

  // r = out-product of a*b
  void inline outproduct5(const ScalarType a[5], const ScalarType b[5], ScalarType r[5][5])
  {
    for(int i = 0; i < 5; i++)
      for(int j = 0; j < 5; j++)
        r[i][j] = a[i]*b[j];
  }

  // r = m*v
  void inline prod_matvec5(ScalarType m[5][5], ScalarType v[5], ScalarType r[5])
  {
    r[0] = inproduct5(m[0],v);
    r[1] = inproduct5(m[1],v);
    r[2] = inproduct5(m[2],v);
    r[3] = inproduct5(m[3],v);
    r[4] = inproduct5(m[4],v);
  }

  // r = (v transposed)*m
  void inline prod_vecmat5(ScalarType v[5],ScalarType m[5][5], ScalarType r[5])
  {
    for(int i = 0; i < 5; i++)
      for(int j = 0; j < 5; j++)
        r[j] = v[j]*m[j][i];
  }

  void inline normalize_vec5(ScalarType v[5])
  {
    ScalarType norma = sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]+v[3]*v[3]+v[4]*v[4]);

    v[0]/=norma;
    v[1]/=norma;
    v[2]/=norma;
    v[3]/=norma;
    v[4]/=norma;
  }

  void inline normalize_vec3(ScalarType v[3])
  {
    ScalarType norma = sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);

    v[0]/=norma;
    v[1]/=norma;
    v[2]/=norma;

  }

  // dest -= m

  void inline sub_mat5(ScalarType dest[5][5],ScalarType m[5][5])
  {
    for(int i = 0; i < 5; i++)
      for(int j = 0; j < 5; j++)
        dest[i][j] -= m[i][j];
  }

  /* computes the symmetric matrix v*v */
  void inline symprod_vvt5(ScalarType dest[15],ScalarType v[5])
  {
    dest[0] = v[0]*v[0];
    dest[1] = v[0]*v[1];
    dest[2] = v[0]*v[2];
    dest[3] = v[0]*v[3];
    dest[4] = v[0]*v[4];
    dest[5] = v[1]*v[1];
    dest[6] = v[1]*v[2];
    dest[7] = v[1]*v[3];
    dest[8] = v[1]*v[4];
    dest[9] = v[2]*v[2];
    dest[10] = v[2]*v[3];
    dest[11] = v[2]*v[4];
    dest[12] = v[3]*v[3];
    dest[13] = v[3]*v[4];
    dest[14] = v[4]*v[4];

  }

  /* subtracts symmetric matrix */
  void inline sub_symmat5(ScalarType dest[15],ScalarType m[15])
  {
    for(int i = 0; i < 15; i++)
      dest[i] -= m[i];
  }

}
template<typename  Scalar>
class Quadric5
{
public:
    typedef Scalar ScalarType;
//	typedef  CMeshO::VertexType::FaceType FaceType;
	
	// the real quadric
	ScalarType a[15];
	ScalarType b[5];
	ScalarType c;
	
	inline Quadric5() { c = -1;}

	// Necessari se si utilizza stl microsoft
	// inline bool operator <  ( const Quadric & q ) const { return false; }
	// inline bool operator == ( const Quadric & q ) const { return true; }

	bool IsValid() const { return (c>=0); }
	void SetInvalid() { c = -1.0; }

	void Zero()																// Azzera le quadriche
	{
		a[0] = 0;
		a[1] = 0;
		a[2] = 0;
		a[3] = 0;
		a[4] = 0;
		a[5] = 0;
		a[6] = 0;
		a[7] = 0;
		a[8] = 0;
		a[9] = 0;
		a[10] = 0;
		a[11] = 0;
		a[12] = 0;
		a[13] = 0;
		a[14] = 0;

		b[0] = 0;
		b[1] = 0;
		b[2] = 0;
		b[3] = 0;
		b[4] = 0;

		c    = 0;
	}

	void swapv(ScalarType *vv, ScalarType *ww)
	{
		ScalarType tmp;
		for(int i = 0; i < 5; i++)
		{
			tmp = vv[i];
			vv[i] = ww[i];
			ww[i] = tmp;
		}
	}
	
	// Add the right subset of the current 5D quadric to a given 3D quadric.
  void AddtoQ3(math::Quadric<double> &q3) const
	{
		q3.a[0] += a[0];
		q3.a[1] += a[1];
		q3.a[2] += a[2];
		q3.a[3] += a[5];
		q3.a[4] += a[6];

		q3.a[5] += a[9];

		q3.b[0] += b[0];
		q3.b[1] += b[1];
		q3.b[2] += b[2];

		q3.c += c;
		
		assert(q3.IsValid());
	}
	
	
	// computes the real quadric and the geometric quadric using the face
	// The geometric quadric is added to the parameter qgeo
  template <class FaceType>
  void byFace(FaceType &f, math::Quadric<double> &q1, math::Quadric<double> &q2, math::Quadric<double> &q3,bool QualityQuadric)
	{
		double q = QualityFace(f);
		
		// if quality==0 then the geometrical quadric has just zeroes
		if(q)
		{
			byFace(f,true);			// computes the geometrical quadric
			AddtoQ3(q1);
			AddtoQ3(q2);
			AddtoQ3(q3);			
			byFace(f,false);		// computes the real quadric
			for(int j=0;j<3;++j)
			{
				if( f.IsB(j) || QualityQuadric )
				{
					Quadric5<double> temp;
					TexCoord2f newtex;
					Point3f newpoint = (f.P0(j)+f.P1(j))/2.0 + (f.N()/f.N().Norm())*Distance(f.P0(j),f.P1(j));
					newtex.u() = (f.WT( (j+0)%3 ).u()+f.WT( (j+1)%3 ).u())/2.0;
					newtex.v() = (f.WT( (j+0)%3 ).v()+f.WT( (j+1)%3 ).v())/2.0;
					Point3f oldpoint = f.P2(j);
					TexCoord2f oldtex = f.WT((j+2)%3); 
					
					f.P2(j)=newpoint;
					f.WT((j+2)%3).u()=newtex.u();
					f.WT((j+2)%3).v()=newtex.v();
					
					temp.byFace(f,false);			// computes the full quadric
					if(! f.IsB(j) ) temp.Scale(0.05);
					*this+=temp;
					
					f.P2(j)=oldpoint;
					f.WT((j+2)%3).u()=oldtex.u();
					f.WT((j+2)%3).v()=oldtex.v();
				}	
			}

		}
		else if(
			(f.WT(1).u()-f.WT(0).u()) * (f.WT(2).v()-f.WT(0).v()) -
			(f.WT(2).u()-f.WT(0).u()) * (f.WT(1).v()-f.WT(0).v())
			)
			byFace(f,false); // computes the real quadric
		else // the area is zero also in the texture space
		{
			a[0]=a[1]=a[2]=a[3]=a[4]=a[5]=a[6]=a[7]=a[8]=a[9]=a[10]=a[11]=a[12]=a[13]=a[14]=0;
			b[0]=b[1]=b[2]=b[3]=b[4]=0;
			c=0;
		}
	}
	
		
	// Computes the geometrical quadric if onlygeo == true and the real quadric if onlygeo == false
  template<class FaceType>
  void byFace(FaceType &fi, bool onlygeo)
	{
	  //assert(onlygeo==false);
		ScalarType p[5]; 
		ScalarType q[5];
		ScalarType r[5];
//		ScalarType A[5][5];
		ScalarType e1[5];
		ScalarType e2[5];

		// computes p
		p[0] = fi.P(0).X();
		p[1] = fi.P(0).Y();
		p[2] = fi.P(0).Z();
		p[3] = fi.WT(0).u();
		p[4] = fi.WT(0).v();

		//  computes q
		q[0] = fi.P(1).X();
		q[1] = fi.P(1).Y();
		q[2] = fi.P(1).Z();
		q[3] = fi.WT(1).u();
		q[4] = fi.WT(1).v();

		//  computes r
		r[0] = fi.P(2).X();
		r[1] = fi.P(2).Y();
		r[2] = fi.P(2).Z();
		r[3] = fi.WT(2).u();
		r[4] = fi.WT(2).v();

		if(onlygeo)		{
			p[3] = 0; q[3] = 0;	r[3] = 0;
			p[4] = 0; q[4] = 0;	r[4] = 0;
		}

		ComputeE1E2(p,q,r,e1,e2);
		ComputeQuadricFromE1E2(e1,e2,p);
		
		if(IsValid())	return;
//		qDebug("Warning: failed to find a good 5D quadric try to permute stuff.");
		
		/*
		When c is very close to 0, loss of precision causes it to be computed as a negative number,
		which is invalid for a quadric. Vertex switches are performed in order to try to obtain a smaller
		loss of precision. The one with the smallest error is chosen.
		*/
		double minerror = std::numeric_limits<double>::max();
		int minerror_index = 0;
		for(int i = 0; i < 7; i++) // tries the 6! configurations and chooses the one with the smallest error
		{
			switch(i)
			{
			case 0:
				break;
			case 1:
			case 3:
			case 5:
				swapv(q,r);
				break;
			case 2:
			case 4:
				swapv(p,r);
				break;
			case 6: // every swap has loss of precision
				swapv(p,r);
				for(int j = 0; j <= minerror_index; j++)
				{
					switch(j)
					{
					case 0:
						break;
					case 1:
					case 3:
					case 5:
						swapv(q,r);
						break;
					case 2:
					case 4:
						swapv(p,r);
						break;
					default:
						assert(0);
					}
				}
				minerror_index = -1;
				break;
			default:
				assert(0);
			}
			
      ComputeE1E2(p,q,r,e1,e2);
			ComputeQuadricFromE1E2(e1,e2,p);
			
			if(IsValid())
				return;
			else if (minerror_index == -1) // the one with the smallest error has been computed
				break;
			else if(-c < minerror)
			{
				minerror = -c;
				minerror_index = i;
			}
		}
		// failed to find a valid vertex switch

		// assert(-c <= 1e-8); // small error

		c = 0; // rounds up to zero
	}

// Given three 5D points it compute an orthonormal basis e1 e2
void ComputeE1E2 (const ScalarType p[5],	const	ScalarType q[5],	const	ScalarType r[5], ScalarType e1[5], ScalarType e2[5]) const
{
		ScalarType diffe[5];
		ScalarType tmpmat[5][5];  
		ScalarType tmpvec[5];  
//  computes e1
		math::sub_vec5(q,p,e1);
		math::normalize_vec5(e1);
		
		//  computes e2
		math::sub_vec5(r,p,diffe);
		math::outproduct5(e1,diffe,tmpmat);
		math::prod_matvec5(tmpmat,e1,tmpvec);
		math::sub_vec5(diffe,tmpvec,e2);
		math::normalize_vec5(e2);
}

// Given two orthonormal 5D vectors lying on the plane and one of the three points of the triangle compute the quadric.
// Note it uses the same notation of the original garland 98 paper. 
void ComputeQuadricFromE1E2(ScalarType e1[5], ScalarType e2[5], ScalarType p[5] )
{
	// computes A
	a[0] = 1;
	a[1] = 0;
	a[2] = 0;
	a[3] = 0;
	a[4] = 0;
	a[5] = 1;
	a[6] = 0;
	a[7] = 0;
	a[8] = 0;
	a[9] = 1;
	a[10] = 0;
	a[11] = 0;
	a[12] = 1;
	a[13] = 0;
	a[14] = 1;

		ScalarType tmpsymmat[15];  // a compactly stored 5x5 symmetric matrix. 
	math::symprod_vvt5(tmpsymmat,e1);
	math::sub_symmat5(a,tmpsymmat);
	math::symprod_vvt5(tmpsymmat,e2);
	math::sub_symmat5(a,tmpsymmat);

		ScalarType pe1;
		ScalarType pe2;

	pe1 = math::inproduct5(p,e1);
	pe2 = math::inproduct5(p,e2);
	
	//  computes b
		ScalarType tmpvec[5];  

	tmpvec[0] = pe1*e1[0] + pe2*e2[0]; 
	tmpvec[1] = pe1*e1[1] + pe2*e2[1]; 
	tmpvec[2] = pe1*e1[2] + pe2*e2[2]; 
	tmpvec[3] = pe1*e1[3] + pe2*e2[3]; 
	tmpvec[4] = pe1*e1[4] + pe2*e2[4];

	math::sub_vec5(tmpvec,p,b);

	//  computes c
	c = math::inproduct5(p,p)-pe1*pe1-pe2*pe2;
}
			
	bool Gauss55( ScalarType x[], ScalarType C[5][5+1] )
	{
		const ScalarType keps = (ScalarType)1e-6;
		int i,j,k;

		ScalarType eps;					// Determina valore cond.
			eps = math::Abs(C[0][0]);
		for(i=1;i<5;++i)
		{
			ScalarType t = math::Abs(C[i][i]);
			if( eps<t ) eps = t;
		}
		eps *= keps;

		for (i = 0; i < 5 - 1; ++i)    		// Ciclo di riduzione
		{
			int ma = i;				// Ricerca massimo pivot
			ScalarType vma = math::Abs( C[i][i] );
			for (k = i + 1; k < 5; k++)
			{
				ScalarType t = math::Abs( C[k][i] );
				if (t > vma)
				{
					vma = t;
					ma  = k;
				}
			}
			if (vma<eps)
				return false;        			// Matrice singolare
			if(i!=ma)				// Swap del massimo pivot
				for(k=0;k<=5;k++)
				{
					ScalarType t = C[i][k];
					C[i][k] = C[ma][k];
					C[ma][k] = t;
				}

			for (k = i + 1; k < 5; k++)        	//  Riduzione
			{
				ScalarType s;
				s = C[k][i] / C[i][i];
				for (j = i+1; j <= 5; j++)
					C[k][j] -= C[i][j] * s;
				C[k][i] = 0.0;
			}
		}

			// Controllo finale singolarita'
		if( math::Abs(C[5-1][5- 1])<eps)
			return false;

		for (i=5-1; i>=0; i--)			// Sostituzione
		{
			ScalarType t;
			for (t = 0.0, j = i + 1; j < 5; j++)
				t += C[i][j] * x[j];
			x[i] = (C[i][5] - t) / C[i][i];
		}

		return true;
	}

	
	// computes the minimum of the quadric, imposing the geometrical constraint (geo[3] and geo[4] are obviosly ignored)
	bool MinimumWithGeoContraints(ScalarType x[5],ScalarType geo[5])
	{	
		x[0] = geo[0];
		x[1] = geo[1];
		x[2] = geo[2];

		ScalarType C3 = -(b[3]+geo[0]*a[3]+geo[1]*a[7]+geo[2]*a[10]);
		ScalarType C4 = -(b[4]+geo[0]*a[4]+geo[1]*a[8]+geo[2]*a[11]);

		if(a[12] != 0)
		{
			double tmp = (a[14]-a[13]*a[13]/a[12]);

			if(tmp == 0)
				return false;

			x[4] = (C4 - a[13]*C3/a[12])/ tmp;
			x[3] = (C3 - a[13]*x[4])/a[12];
		}
		else
		{
			if(a[13] == 0)
				return false;

			x[4] = C3/a[13];
			x[3] = (C4 - a[14]*x[4])/a[13];
		}

		return true;
	}

	// computes the minimum of the quadric
	bool Minimum(ScalarType x[5])
	{	
			ScalarType C[5][6];

			C[0][0] = a[0];
			C[0][1] = a[1];
			C[0][2] = a[2];
			C[0][3] = a[3];
			C[0][4] = a[4];
			C[1][0] = a[1];
			C[1][1] = a[5];
			C[1][2] = a[6];
			C[1][3] = a[7];
			C[1][4] = a[8];
			C[2][0] = a[2];
			C[2][1] = a[6];
			C[2][2] = a[9];
			C[2][3] = a[10];
			C[2][4] = a[11];
			C[3][0] = a[3];
			C[3][1] = a[7];
			C[3][2] = a[10];
			C[3][3] = a[12];
			C[3][4] = a[13];
			C[4][0] = a[4];
			C[4][1] = a[8];
			C[4][2] = a[11];
			C[4][3] = a[13];
			C[4][4] = a[14];

			C[0][5]=-b[0];
			C[1][5]=-b[1];
			C[2][5]=-b[2];
			C[3][5]=-b[3];
			C[4][5]=-b[4];
			
			return Gauss55(&(x[0]),C);
	}

	void operator = ( const Quadric5<double> & q )			// Assegna una quadrica
	{
		//assert( IsValid() );
		assert( q.IsValid() );

		a[0] = q.a[0];
		a[1] = q.a[1];
		a[2] = q.a[2];
		a[3] = q.a[3];
		a[4] = q.a[4];
		a[5] = q.a[5];
		a[6] = q.a[6];
		a[7] = q.a[7];
		a[8] = q.a[8];
		a[9] = q.a[9];
		a[10] = q.a[10];
		a[11] = q.a[11];
		a[12] = q.a[12];
		a[13] = q.a[13];
		a[14] = q.a[14];

		b[0] = q.b[0];
		b[1] = q.b[1];
		b[2] = q.b[2];
		b[3] = q.b[3];
		b[4] = q.b[4];

		c    = q.c;
	}

	// sums the geometrical and the real quadrics
	void operator += ( const Quadric5<double> & q )			
	{
		//assert( IsValid() );
		assert( q.IsValid() );

		a[0] += q.a[0];
		a[1] += q.a[1];
		a[2] += q.a[2];
		a[3] += q.a[3];
		a[4] += q.a[4];
		a[5] += q.a[5];
		a[6] += q.a[6];
		a[7] += q.a[7];
		a[8] += q.a[8];
		a[9] += q.a[9];
		a[10] += q.a[10];
		a[11] += q.a[11];
		a[12] += q.a[12];
		a[13] += q.a[13];
		a[14] += q.a[14];

		b[0] += q.b[0];
		b[1] += q.b[1];
		b[2] += q.b[2];
		b[3] += q.b[3];
		b[4] += q.b[4];

		c    += q.c;

	}

/*
it sums the real quadric of the class with a quadric obtained by the geometrical quadric of the vertex.
This quadric is obtained extending to five dimensions the geometrical quadric and simulating that it has been
obtained by sums of 5-dimension quadrics which were computed using vertexes and faces with always the same values 
in the fourth and fifth dimensions (respectly the function parameter u and the function parameter v).
this allows to simulate the inexistant continuity in vertexes with multiple texture coords
however this continuity is still inexistant, so even if the algorithm makes a good collapse with this expedient,it obviously
computes bad the priority......this should be adjusted with the extra weight user parameter through.....

*/
	void inline Sum3 (const math::Quadric<double> & q3, float u, float v)
  {
		assert( q3.IsValid() );

		a[0] += q3.a[0];
		a[1] += q3.a[1];
		a[2] += q3.a[2];

		a[5] += q3.a[3];
		a[6] += q3.a[4];

		a[9] += q3.a[5];
	
		a[12] += 1;
		a[14] += 1;

		b[0] += q3.b[0];
		b[1] += q3.b[1];
		b[2] += q3.b[2];

		b[3] -= u;
		b[4] -= v;

		c    += q3.c + u*u + v*v;

	}
	
	void Scale(ScalarType val)	
	{
	 for(int i=0;i<15;++i)
		 a[i]*=val;
	 for(int i=0;i<5;++i)
		 b[i]*=val;
	 c*=val;
	}

  // returns the quadric value in v
  	ScalarType Apply(ScalarType v[5])
	{

		assert( IsValid() );

		ScalarType tmpmat[5][5];  
		ScalarType tmpvec[5];  

		tmpmat[0][0] = a[0]; 
		tmpmat[0][1] = tmpmat[1][0] = a[1]; 
		tmpmat[0][2] = tmpmat[2][0] = a[2]; 
		tmpmat[0][3] = tmpmat[3][0] = a[3]; 
		tmpmat[0][4] = tmpmat[4][0] = a[4]; 
		
		tmpmat[1][1] = a[5]; 
		tmpmat[1][2] = tmpmat[2][1] = a[6]; 
		tmpmat[1][3] = tmpmat[3][1] = a[7]; 
		tmpmat[1][4] = tmpmat[4][1] = a[8]; 

		tmpmat[2][2] = a[9]; 
		tmpmat[2][3] = tmpmat[3][2] = a[10]; 
		tmpmat[2][4] = tmpmat[4][2] = a[11]; 

		tmpmat[3][3] = a[12]; 
		tmpmat[3][4] = tmpmat[4][3] = a[13]; 

		tmpmat[4][4] = a[14];

		math::prod_matvec5(tmpmat,v,tmpvec);

		return  math::inproduct5(v,tmpvec) + 2*math::inproduct5(b,v) + c;

	}
};

} // end namespace vcg;
#endif