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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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vcg/math/quadric.h
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@ -19,30 +19,6 @@
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) * * GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. * * 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 #ifndef __VCGLIB_QUADRIC
#define __VCGLIB_QUADRIC #define __VCGLIB_QUADRIC
@ -50,137 +26,180 @@ created
#include <vcg/space/point3.h> #include <vcg/space/point3.h>
#include <vcg/space/plane3.h> #include <vcg/space/plane3.h>
#include <vcg/math/matrix33.h> #include <vcg/math/matrix33.h>
#include <eigenlib/Eigen/Core>
namespace vcg { namespace vcg {
namespace math { 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 class Quadric
{ {
public: public:
typedef Scalar ScalarType; typedef _ScalarType ScalarType;
ScalarType a[6]; // Matrice 3x3 simmetrica: a11 a12 a13 a22 a23 a33 ScalarType a[6]; // Symmetric Matrix 3x3 : a11 a12 a13 a22 a23 a33
ScalarType b[3]; // Vettore r3 ScalarType b[3]; // Vector r3
ScalarType c; // Fattore scalare (se -1 quadrica nulla) ScalarType c; // Scalar (-1 means null/un-initialized quadric)
inline Quadric() { c = -1; } inline Quadric() { c = -1; }
// Necessari se si utilizza stl microsoft bool IsValid() const { return c>=0; }
// inline bool operator < ( const Quadric & q ) const { return false; } void SetInvalid() { c = -1.0; }
// inline bool operator == ( const Quadric & q ) const { return true; }
// Initialize the quadric to keep the squared distance from a given Plane
bool IsValid() const { return c>=0; } template< class PlaneType >
void SetInvalid() { c = -1.0; } void ByPlane( const PlaneType & p )
{
template< class PlaneType > a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11
void ByPlane( const PlaneType & p ) // Init dato un piano a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
{ a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11 a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22
a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21) a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31) a[5] = (ScalarType)p.Direction()[2]*p.Direction()[2]; // a33
a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22 b[0] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[0];
a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32) b[1] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[1];
a[5] = (ScalarType)p.Direction()[2]*p.Direction()[2]; // a33 b[2] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[2];
b[0] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[0]; c = (ScalarType)p.Offset()*p.Offset();
b[1] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[1]; }
b[2] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[2];
c = (ScalarType)p.Offset()*p.Offset(); /*
} * 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
/* Initializes the quadric as the squared distance from a given line. * from a ray is different "before" its origin.
Notice 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
template< class LineType > {
void ByLine( const LineType & r ) // Init dato un raggio ScalarType K = (ScalarType)(r.Origin()*r.Direction());
{ a[0] = (ScalarType)1.0-r.Direction()[0]*r.Direction()[0]; // a11
ScalarType K = (ScalarType)(r.Origin()*r.Direction()); a[1] = (ScalarType)-r.Direction()[0]*r.Direction()[1]; // a12 (=a21)
a[0] = (ScalarType)1.0-r.Direction()[0]*r.Direction()[0]; // a11 a[2] = (ScalarType)-r.Direction()[0]*r.Direction()[2]; // a13 (=a31)
a[1] = (ScalarType)-r.Direction()[0]*r.Direction()[1]; // a12 (=a21) a[3] = (ScalarType)1.0-r.Direction()[1]*r.Direction()[1]; // a22
a[2] = (ScalarType)-r.Direction()[0]*r.Direction()[2]; // a13 (=a31) a[4] = (ScalarType)-r.Direction()[1]*r.Direction()[2]; // a23 (=a32)
a[3] = (ScalarType)1.0-r.Direction()[1]*r.Direction()[1]; // a22 a[5] = (ScalarType)1.0-r.Direction()[2]*r.Direction()[2]; // a33
a[4] = (ScalarType)-r.Direction()[1]*r.Direction()[2]; // a23 (=a32) b[0] = (ScalarType)2.0*(r.Direction()[0]*K - r.Origin()[0]);
a[5] = (ScalarType)1.0-r.Direction()[2]*r.Direction()[2]; // a33 b[1] = (ScalarType)2.0*(r.Direction()[1]*K - r.Origin()[1]);
b[0] = (ScalarType)2.0*(r.Direction()[0]*K - r.Origin()[0]); b[2] = (ScalarType)2.0*(r.Direction()[2]*K - r.Origin()[2]);
b[1] = (ScalarType)2.0*(r.Direction()[1]*K - r.Origin()[1]); c = -K*K + (ScalarType)(r.Origin()*r.Origin());
b[2] = (ScalarType)2.0*(r.Direction()[2]*K - r.Origin()[2]);
c = -K*K + (ScalarType)(r.Origin()*r.Origin());
} }
void SetZero() // Azzera la quadrica void SetZero()
{ {
a[0] = 0; a[0] = 0;
a[1] = 0; a[1] = 0;
a[2] = 0; a[2] = 0;
a[3] = 0; a[3] = 0;
a[4] = 0; a[4] = 0;
a[5] = 0; a[5] = 0;
b[0] = 0; b[0] = 0;
b[1] = 0; b[1] = 0;
b[2] = 0; b[2] = 0;
c = 0; c = 0;
} }
void operator = ( const Quadric & q ) // Assegna una quadrica void operator = ( const Quadric & q )
{ {
//assert( IsValid() ); assert( q.IsValid() );
assert( q.IsValid() );
a[0] = q.a[0];
a[0] = q.a[0]; a[1] = q.a[1];
a[1] = q.a[1]; a[2] = q.a[2];
a[2] = q.a[2]; a[3] = q.a[3];
a[3] = q.a[3]; a[4] = q.a[4];
a[4] = q.a[4]; a[5] = q.a[5];
a[5] = q.a[5]; b[0] = q.b[0];
b[0] = q.b[0]; b[1] = q.b[1];
b[1] = q.b[1]; b[2] = q.b[2];
b[2] = q.b[2]; c = q.c;
c = q.c; }
}
void operator += ( const Quadric & q )
void operator += ( const Quadric & q ) // Somma una quadrica {
{ assert( IsValid() );
assert( IsValid() ); assert( q.IsValid() );
assert( q.IsValid() );
a[0] += q.a[0];
a[0] += q.a[0]; a[1] += q.a[1];
a[1] += q.a[1]; a[2] += q.a[2];
a[2] += q.a[2]; a[3] += q.a[3];
a[3] += q.a[3]; a[4] += q.a[4];
a[4] += q.a[4]; a[5] += q.a[5];
a[5] += q.a[5]; b[0] += q.b[0];
b[0] += q.b[0]; b[1] += q.b[1];
b[1] += q.b[1]; b[2] += q.b[2];
b[2] += q.b[2]; c += q.c;
c += q.c; }
}
void operator *= ( const ScalarType & w ) // Amplifica una quadirca
template <class ResultScalarType> {
ResultScalarType Apply( const Point3<ResultScalarType> & p ) const // Applica la quadrica al punto p assert( IsValid() );
{
assert( IsValid() ); a[0] *= w;
/* a[1] *= w;
// Versione Lenta a[2] *= w;
a[3] *= w;
Point3d t; a[4] *= w;
t[0] = p[0]*a[0] + p[1]*a[1] + p[2]*a[2]; a[5] *= w;
t[1] = p[0]*a[1] + p[1]*a[3] + p[2]*a[4]; b[0] *= w;
t[2] = p[0]*a[2] + p[1]*a[4] + p[2]*a[5]; b[1] *= w;
double k = b[0]*p[0] + b[1]*p[1] + b[2]*p[2]; b[2] *= w;
double tp = t*p ; c *= w;
assert(tp+k+c >= 0); }
return tp + k + c;
*/
/* Versione veloce */ /* Evaluate a quadric over a point p.
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] template <class ResultScalarType>
+ p[1]*p[1]*a[3] + 2*p[1]*p[2]*a[4] + p[1]*b[1] ResultScalarType Apply( const Point3<ResultScalarType> & p ) const
+ p[2]*p[2]*a[5] + p[2]*b[2] + c); {
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 // spostare..risolve un sistema 3x3
template<class FLTYPE> template<class FLTYPE>
bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] ) bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
@ -244,9 +263,10 @@ bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
return true; return true;
} }
// determina il punto di errore minimo
template <class ReturnScalarType> template <class ReturnScalarType>
bool Minimum(Point3<ReturnScalarType> &x) bool MinimumOld(Point3<ReturnScalarType> &x)
{ {
ReturnScalarType C[3][4]; ReturnScalarType C[3][4];
C[0][0]=a[0]; C[0][1]=a[1]; C[0][2]=a[2]; 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); 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) // determina il punto di errore minimo vincolato nel segmento (a,b)
bool Minimum(Point3<ScalarType> &x,Point3<ScalarType> &pa,Point3<ScalarType> &pb){ bool Minimum(Point3<ScalarType> &x,Point3<ScalarType> &pa,Point3<ScalarType> &pb){
ScalarType t1,t2, t4, t5, t8, t9, ScalarType t1,t2, t4, t5, t8, t9,
@ -344,23 +326,6 @@ ScalarType t1,t2, t4, t5, t8, t9,
return true; 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<short> Quadrics;