295 lines
8.2 KiB
C++
295 lines
8.2 KiB
C++
/****************************************************************************
|
|
* VCGLib o o *
|
|
* Visual and Computer Graphics Library o o *
|
|
* _ O _ *
|
|
* Copyright(C) 2004 \/)\/ *
|
|
* 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: not supported by cvs2svn $
|
|
|
|
****************************************************************************/
|
|
#ifndef __VCGLIB_QUADRIC
|
|
#define __VCGLIB_QUADRIC
|
|
|
|
#include <vcg/space/point3.h>
|
|
#include <vcg/space/plane3.h>
|
|
|
|
namespace vcg {
|
|
namespace math {
|
|
|
|
|
|
template<typename PlaneType>
|
|
class Quadric
|
|
{
|
|
public:
|
|
typedef typename PlaneType::ScalarType ScalarType;
|
|
ScalarType a[6]; // Matrice 3x3 simmetrica: a11 a12 a13 a22 a23 a33
|
|
ScalarType b[3]; // Vettore r3
|
|
ScalarType c; // Fattore scalare (se -1 quadrica nulla)
|
|
|
|
inline Quadric() { 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 ByPlane( const PlaneType & p ) // Init dato un piano
|
|
{
|
|
a[0] = p.Direction()[0]*p.Direction()[0]; // a11
|
|
a[1] = p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
|
|
a[2] = p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
|
|
a[3] = p.Direction()[1]*p.Direction()[1]; // a22
|
|
a[4] = p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
|
|
a[5] = p.Direction()[2]*p.Direction()[2]; // a33
|
|
b[0] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[0];
|
|
b[1] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[1];
|
|
b[2] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[2];
|
|
c = p.Offset()*p.Offset();
|
|
}
|
|
|
|
void Zero() // Azzera la quadrica
|
|
{
|
|
a[0] = 0;
|
|
a[1] = 0;
|
|
a[2] = 0;
|
|
a[3] = 0;
|
|
a[4] = 0;
|
|
a[5] = 0;
|
|
b[0] = 0;
|
|
b[1] = 0;
|
|
b[2] = 0;
|
|
c = 0;
|
|
}
|
|
|
|
void operator = ( const Quadric & 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];
|
|
b[0] = q.b[0];
|
|
b[1] = q.b[1];
|
|
b[2] = q.b[2];
|
|
c = q.c;
|
|
}
|
|
|
|
void operator += ( const Quadric & q ) // Somma 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];
|
|
b[0] += q.b[0];
|
|
b[1] += q.b[1];
|
|
b[2] += q.b[2];
|
|
c += q.c;
|
|
}
|
|
|
|
ScalarType Apply( const Point3<ScalarType> & p ) const // Applica la quadrica al punto p
|
|
{
|
|
assert( IsValid() );
|
|
|
|
// Versione Lenta
|
|
/*
|
|
Point3d t;
|
|
t[0] = p[0]*a[0] + p[1]*a[1] + p[2]*a[2];
|
|
t[1] = p[0]*a[1] + p[1]*a[3] + p[2]*a[4];
|
|
t[2] = p[0]*a[2] + p[1]*a[4] + p[2]*a[5];
|
|
double k = b[0]*p[0] + b[1]*p[1] + b[2]*p[2];
|
|
double tp =t*p;
|
|
return tp + k + c;
|
|
|
|
*/
|
|
/* Versione veloce */
|
|
|
|
return p[0]*p[0]*a[0] + 2*p[0]*p[1]*a[1] + 2*p[0]*p[2]*a[2] + p[0]*b[0]
|
|
+ p[1]*p[1]*a[3] + 2*p[1]*p[2]*a[4] + p[1]*b[1]
|
|
+ p[2]*p[2]*a[5] + p[2]*b[2] + c;
|
|
}
|
|
|
|
// spostare..risolve un sistema 3x3
|
|
template<class FLTYPE>
|
|
bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
|
|
{
|
|
const FLTYPE keps = (FLTYPE)1e-6;
|
|
int i,j,k;
|
|
|
|
FLTYPE eps; // Determina valore cond.
|
|
eps = math::Abs(C[0][0]);
|
|
for(i=1;i<3;++i)
|
|
{
|
|
FLTYPE t = math::Abs(C[i][i]);
|
|
if( eps<t ) eps = t;
|
|
}
|
|
eps *= keps;
|
|
|
|
for (i = 0; i < 3 - 1; ++i) // Ciclo di riduzione
|
|
{
|
|
int ma = i; // Ricerca massimo pivot
|
|
FLTYPE vma = math::Abs( C[i][i] );
|
|
for (k = i + 1; k < 3; k++)
|
|
{
|
|
FLTYPE 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<=3;k++)
|
|
{
|
|
FLTYPE t = C[i][k];
|
|
C[i][k] = C[ma][k];
|
|
C[ma][k] = t;
|
|
}
|
|
for (k = i + 1; k < 3; k++) // Riduzione
|
|
{
|
|
FLTYPE s;
|
|
s = C[k][i] / C[i][i];
|
|
for (j = i+1; j <= 3; j++)
|
|
C[k][j] -= C[i][j] * s;
|
|
C[k][i] = 0.0;
|
|
}
|
|
}
|
|
|
|
// Controllo finale singolarita'
|
|
if( math::Abs(C[3-1][3- 1])<eps)
|
|
return false;
|
|
|
|
for (i=3-1; i>=0; i--) // Sostituzione
|
|
{
|
|
FLTYPE t;
|
|
for (t = 0.0, j = i + 1; j < 3; j++)
|
|
t += C[i][j] * x[j];
|
|
x[i] = (C[i][3] - t) / C[i][i];
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
// determina il punto di errore minimo
|
|
bool Minimum(Point3<ScalarType> &x)
|
|
{
|
|
ScalarType C[3][4];
|
|
C[0][0]=a[0]; C[0][1]=a[1]; C[0][2]=a[2];
|
|
C[1][0]=a[1]; C[1][1]=a[3]; C[1][2]=a[4];
|
|
C[2][0]=a[2]; C[2][1]=a[4]; C[2][2]=a[5];
|
|
|
|
C[0][3]=-b[0]/2;
|
|
C[1][3]=-b[1]/2;
|
|
C[2][3]=-b[2]/2;
|
|
return Gauss33(&(x[0]),C);
|
|
}
|
|
|
|
// determina il punto di errore minimo vincolato nel segmento (a,b)
|
|
bool Minimum(Point3<ScalarType> &x,Point3<ScalarType> &pa,Point3<ScalarType> &pb){
|
|
ScalarType t1,t2, t4, t5, t8, t9,
|
|
t11,t12,t14,t15,t17,t18,t25,t26,t30,t34,t35,
|
|
t41,t42,t44,t45,t50,t52,t54,
|
|
t56,t21,t23,t37,t64,lambda;
|
|
|
|
t1 = a[4]*pb.z();
|
|
t2 = t1*pa.y();
|
|
t4 = a[1]*pb.y();
|
|
t5 = t4*pa.x();
|
|
t8 = a[1]*pa.y();
|
|
t9 = t8*pa.x();
|
|
t11 = a[4]*pa.z();
|
|
t12 = t11*pa.y();
|
|
t14 = pa.z()*pa.z();
|
|
t15 = a[5]*t14;
|
|
t17 = a[2]*pa.z();
|
|
t18 = t17*pa.x();
|
|
t21 = 2.0*t11*pb.y();
|
|
t23 = a[5]*pb.z()*pa.z();
|
|
t25 = a[2]*pb.z();
|
|
t26 = t25*pa.x();
|
|
t30 = a[0]*pb.x()*pa.x();
|
|
t34 = 2.0*a[3]*pb.y()*pa.y();
|
|
t35 = t17*pb.x();
|
|
t37 = t8*pb.x();
|
|
t41 = pa.x()*pa.x();
|
|
t42 = a[0]*t41;
|
|
t44 = pa.y()*pa.y();
|
|
t45 = a[3]*t44;
|
|
t50 = 2.0*t30+t34+2.0*t35+2.0*t37-(-b[2]/2)*pa.z()-(-b[0]/2)*pa.x()-2.0*t42-2.0*t45+(-b[1]/2)*pb.y()
|
|
+(-b[0]/2)*pb.x()-(-b[1]/2)*pa.y();
|
|
t52 = pb.y()*pb.y();
|
|
t54 = pb.z()*pb.z();
|
|
t56 = pb.x()*pb.x();
|
|
t64 = t5+t37-t9+t30-t18+t35+t26-t25*pb.x()+t2-t1*pb.y()+t23;
|
|
lambda = (2.0*t2+2.0*t5+(-b[2]/2)*pb.z()-4.0*t9-4.0*t12-2.0*t15-4.0*t18+t21+2.0*t23+
|
|
2.0*t26+t50)/(-t45-a[3]*t52-a[5]*t54-a[0]*t56-t15-t42+t34-2.0*t12+t21-2.0*t4*pb.x()+
|
|
2.0*t64)/2.0;
|
|
|
|
if(lambda<0) lambda=0; else if(lambda>1) lambda = 1;
|
|
|
|
x = pa*(1.0-lambda)+pb*lambda;
|
|
return true;
|
|
}
|
|
|
|
void operator *= ( const ScalarType & w ) // Amplifica una quadirca
|
|
{
|
|
assert( IsValid() );
|
|
|
|
a[0] *= w;
|
|
a[1] *= w;
|
|
a[2] *= w;
|
|
a[3] *= w;
|
|
a[4] *= w;
|
|
a[5] *= w;
|
|
b[0] *= w;
|
|
b[1] *= w;
|
|
b[2] *= w;
|
|
c *= w;
|
|
}
|
|
|
|
|
|
};
|
|
|
|
typedef Quadric<short> Quadrics;
|
|
typedef Quadric<int> Quadrici;
|
|
typedef Quadric<float> Quadricf;
|
|
typedef Quadric<double> Quadricd;
|
|
|
|
|
|
|
|
} // end namespace math
|
|
} // end namespace vcg
|
|
|
|
#endif
|