Switched to eigen to find the optimal position for quadric. Removed old unused funcitons. Commented.
This commit is contained in:
parent
0aec75be39
commit
a58040cf9c
|
|
@ -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
|
||||
|
|
@ -50,49 +26,52 @@ 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; }
|
||||
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; }
|
||||
|
||||
bool IsValid() const { return c>=0; }
|
||||
void SetInvalid() { c = -1.0; }
|
||||
// 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)
|
||||
a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
|
||||
a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22
|
||||
a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
|
||||
a[5] = (ScalarType)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 = (ScalarType)p.Offset()*p.Offset();
|
||||
}
|
||||
|
||||
template< class PlaneType >
|
||||
void ByPlane( const PlaneType & p ) // Init dato un piano
|
||||
{
|
||||
a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11
|
||||
a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
|
||||
a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
|
||||
a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22
|
||||
a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
|
||||
a[5] = (ScalarType)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 = (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.
|
||||
*/
|
||||
template< class LineType >
|
||||
/*
|
||||
* 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
|
||||
{
|
||||
ScalarType K = (ScalarType)(r.Origin()*r.Direction());
|
||||
|
|
@ -108,78 +87,118 @@ template< class PlaneType >
|
|||
c = -K*K + (ScalarType)(r.Origin()*r.Origin());
|
||||
}
|
||||
|
||||
void SetZero() // 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 SetZero()
|
||||
{
|
||||
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() );
|
||||
void operator = ( const Quadric & q )
|
||||
{
|
||||
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;
|
||||
}
|
||||
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() );
|
||||
void operator += ( const Quadric & 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];
|
||||
b[0] += q.b[0];
|
||||
b[1] += q.b[1];
|
||||
b[2] += q.b[2];
|
||||
c += q.c;
|
||||
}
|
||||
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 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;
|
||||
}
|
||||
|
||||
|
||||
|
||||
/* Evaluate a quadric over a point p.
|
||||
*/
|
||||
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;
|
||||
}
|
||||
|
||||
template <class ResultScalarType>
|
||||
ResultScalarType Apply( const Point3<ResultScalarType> & 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 ;
|
||||
assert(tp+k+c >= 0);
|
||||
return tp + k + c;
|
||||
*/
|
||||
|
||||
/* Versione veloce */
|
||||
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);
|
||||
|
||||
}
|
||||
|
||||
// spostare..risolve un sistema 3x3
|
||||
template<class FLTYPE>
|
||||
|
|
@ -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;
|
||||
|
|
|
|||
Loading…
Reference in New Issue