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Switched to eigen to find the optimal position for quadric. Removed old unused funcitons. Commented.

This commit is contained in:
Paolo Cignoni 2016-03-24 14:15:55 +00:00
parent 0aec75be39
commit a58040cf9c
1 changed files with 168 additions and 203 deletions
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195
vcg/math/quadric.h
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@ -19,30 +19,6 @@
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
Revision 1.7 2006/11/13 12:53:40 ponchio
just added an #include <matrix33>
Revision 1.6 2006/10/09 20:23:00 cignoni
Added a minimum method that uses SVD. Unfortunately it is much much slower.
Revision 1.5 2004/12/10 01:31:59 cignoni
added an alternative QuadricMinimization (we should use LRU decomposition!!)
Revision 1.3 2004/10/25 16:23:51 ponchio
typedef ScalarType ScalarType; was a problem on g++
Revision 1.2 2004/10/25 16:15:59 ganovelli
template changed
Revision 1.1 2004/09/14 19:48:27 ganovelli
created
****************************************************************************/
#ifndef __VCGLIB_QUADRIC
#define __VCGLIB_QUADRIC
@ -50,31 +26,33 @@ created
#include <vcg/space/point3.h>
#include <vcg/space/plane3.h>
#include <vcg/math/matrix33.h>
#include <eigenlib/Eigen/Core>
namespace vcg {
namespace math {
template<typename Scalar>
/*
* This class encode a quadric function
* f(x) = xAx +bx + c
* where A is a symmetric 3x3 matrix, b a vector and c a scalar constant.
*/
template<typename _ScalarType>
class Quadric
{
public:
typedef Scalar 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)
typedef _ScalarType ScalarType;
ScalarType a[6]; // Symmetric Matrix 3x3 : a11 a12 a13 a22 a23 a33
ScalarType b[3]; // Vector r3
ScalarType c; // Scalar (-1 means null/un-initialized quadric)
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; }
template< class PlaneType >
void ByPlane( const PlaneType & p ) // Init dato un piano
// Initialize the quadric to keep the squared distance from a given Plane
template< class PlaneType >
void ByPlane( const PlaneType & p )
{
a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11
a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
@ -88,9 +66,10 @@ template< class PlaneType >
c = (ScalarType)p.Offset()*p.Offset();
}
/* Initializes the quadric as the squared distance from a given line.
Notice that this code also works for a vcg::Ray<T>, even though the (squared) distance
from a ray is different "before" its origin.
/*
* Initializes the quadric as the squared distance from a given line.
* Note that this code also works for a vcg::Ray<T>, even though the (squared) distance
* from a ray is different "before" its origin.
*/
template< class LineType >
void ByLine( const LineType & r ) // Init dato un raggio
@ -108,7 +87,7 @@ template< class PlaneType >
c = -K*K + (ScalarType)(r.Origin()*r.Origin());
}
void SetZero() // Azzera la quadrica
void SetZero()
{
a[0] = 0;
a[1] = 0;
@ -122,9 +101,8 @@ template< class PlaneType >
c = 0;
}
void operator = ( const Quadric & q ) // Assegna una quadrica
void operator = ( const Quadric & q )
{
//assert( IsValid() );
assert( q.IsValid() );
a[0] = q.a[0];
@ -139,7 +117,7 @@ void operator = ( const Quadric & q ) // Assegna una quadrica
c = q.c;
}
void operator += ( const Quadric & q ) // Somma una quadrica
void operator += ( const Quadric & q )
{
assert( IsValid() );
assert( q.IsValid() );
@ -156,31 +134,72 @@ void operator = ( const Quadric & q ) // Assegna una quadrica
c += q.c;
}
template <class ResultScalarType>
ResultScalarType Apply( const Point3<ResultScalarType> & p ) const // Applica la quadrica al punto p
void operator *= ( const ScalarType & w ) // Amplifica una quadirca
{
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 ;
assert(tp+k+c >= 0);
return tp + k + c;
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;
}
/* Evaluate a quadric over a point p.
*/
/* Versione veloce */
template <class ResultScalarType>
ResultScalarType Apply( const Point3<ResultScalarType> & p ) const
{
assert( IsValid() );
return ResultScalarType (
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);
}
static double &RelativeErrorThr()
{
static double _err = 0.000001;
return _err;
}
// Find the point minimizing the quadric xAx + bx + c
// by solving the first derivative 2 Ax + b = 0
// return true if the found solution fits the system.
template <class ReturnScalarType>
bool Minimum(Point3<ReturnScalarType> &x)
{
Eigen::Matrix3d A;
Eigen::Vector3d be;
A << a[0], a[1], a[2],
a[1], a[3], a[4],
a[2], a[4], a[5];
be << -b[0]/2, -b[1]/2, -b[2]/2;
// Eigen::Vector3d xe = A.colPivHouseholderQr().solve(bv);
// Eigen::Vector3d xe = A.partialPivLu().solve(bv);
Eigen::Vector3d xe = A.fullPivLu().solve(be);
double relative_error = (A*xe - be).norm() / be.norm();
if(relative_error> Quadric<ScalarType>::RelativeErrorThr() )
return false;
x.FromEigenVector(xe);
return true;
}
// spostare..risolve un sistema 3x3
template<class FLTYPE>
bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
@ -244,9 +263,10 @@ bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
return true;
}
// determina il punto di errore minimo
template <class ReturnScalarType>
bool Minimum(Point3<ReturnScalarType> &x)
bool MinimumOld(Point3<ReturnScalarType> &x)
{
ReturnScalarType C[3][4];
C[0][0]=a[0]; C[0][1]=a[1]; C[0][2]=a[2];
@ -259,44 +279,6 @@ bool Minimum(Point3<ReturnScalarType> &x)
return Gauss33(&(x[0]),C);
}
// determina il punto di errore minimo usando le fun di inversione di matrice che usano svd
// Molto + lento
template <class ReturnScalarType>
bool MinimumSVD(Point3<ReturnScalarType> &x)
{
Matrix33<ReturnScalarType> C;
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];
Invert(C);
C[0][3]=-b[0]/2;
C[1][3]=-b[1]/2;
C[2][3]=-b[2]/2;
x = C * Point3<ReturnScalarType>(-b[0]/2,-b[1]/2,-b[2]/2) ;
return true;
}
bool MinimumNew(Point3<ScalarType> &x) const
{
ScalarType c0=-b[0]/2;
ScalarType c1=-b[1]/2;
ScalarType c2=-b[2]/2;
ScalarType t125 = a[4]*a[1];
ScalarType t124 = a[4]*a[4]-a[3]*a[5];
ScalarType t123 = -a[1]*a[5]+a[4]*a[2];
ScalarType t122 = a[2]*a[3]-t125;
ScalarType t121 = -a[2]*a[1]+a[0]*a[4];
ScalarType t120 = a[2]*a[2];
ScalarType t119 = a[1]*a[1];
ScalarType t117 = 1.0/(-a[3]*t120+2*a[2]*t125-t119*a[5]-t124*a[0]);
x[0] = -(t124*c0+t122*c2-t123*c1)*t117;
x[1] = (t123*c0-t121*c2+(-t120+a[0]*a[5])*c1)*t117;
x[2] = -(t122*c0+(t119-a[0]*a[3])*c2+t121*c1)*t117;
return true;
}
// 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,
@ -344,23 +326,6 @@ ScalarType t1,t2, t4, t5, t8, t9,
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;