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vcglib/vcg/space/quadric.h

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/****************************************************************************
* 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 $
Revision 1.1 2004/07/12 23:46:03 cignoni
Initial Commit
****************************************************************************/
#ifndef __VCGLIB_QUADRIC
#define __VCGLIB_QUADRIC
#ifndef __VCGLIB_POINT3
#include <vcg/space/point3.h>
#endif
#ifndef __VCGLIB_PLANE3
#include <vcg/space/plane3.h>
#endif
namespace vcg {
template<class T>
class Quadric
{
public:
T a[6]; // Matrice 3x3 simmetrica: a11 a12 a13 a22 a23 a33
T b[3]; // Vettore r3
T c; // Fattore scalare (se -1 quadrica nulla)
inline Quadric() { c = -1; }
bool IsValid() const { return c>=0; }
void SetInvalid() { c = -1.0; }
void ByPlane( const Plane3<T> & p ) // Init dato un piano
{
a[0] = p.n[0]*p.n[0]; // a11
a[1] = p.n[1]*p.n[0]; // a12 (=a21)
a[2] = p.n[2]*p.n[0]; // a13 (=a31)
a[3] = p.n[1]*p.n[1]; // a22
a[4] = p.n[2]*p.n[1]; // a23 (=a32)
a[5] = p.n[2]*p.n[2]; // a33
b[0] = (T)(-2.0)*p.d*p.n[0];
b[1] = (T)(-2.0)*p.d*p.n[1];
b[2] = (T)(-2.0)*p.d*p.n[2];
c = p.d*p.d;
}
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;
}
T Apply( const Point3<T> & 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;
}
/// Draft version. It should be done in a more correctly way by using LRU decomposition.
bool Minimum(Point3<T> &x)
{
//T 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);
Matrix33<T> mm;
mm[0][0]=a[0]; mm[0][1]=a[1]; mm[0][2]=a[2];
mm[1][0]=a[1]; mm[1][1]=a[3]; mm[1][2]=a[4];
mm[2][0]=a[2]; mm[2][1]=a[4]; mm[2][2]=a[5];
mm.Invert();
x=mm*Point3<t>(-b[0]/2,-b[1]/2,-b[2]/2);
return true;
}
// determina il punto di errore minimo vincolato nel segmento (a,b)
bool Minimum(Point3<T> &x,Point3<T> &pa,Point3<T> &pb){
T 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 T & 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
#endif
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