Switched to eigen to find the optimal position for quadric. Removed old unused funcitons. Commented.
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0aec75be39
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@ -19,30 +19,6 @@
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: not supported by cvs2svn $
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Revision 1.7 2006/11/13 12:53:40 ponchio
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just added an #include <matrix33>
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Revision 1.6 2006/10/09 20:23:00 cignoni
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Added a minimum method that uses SVD. Unfortunately it is much much slower.
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Revision 1.5 2004/12/10 01:31:59 cignoni
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added an alternative QuadricMinimization (we should use LRU decomposition!!)
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Revision 1.3 2004/10/25 16:23:51 ponchio
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typedef ScalarType ScalarType; was a problem on g++
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Revision 1.2 2004/10/25 16:15:59 ganovelli
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template changed
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Revision 1.1 2004/09/14 19:48:27 ganovelli
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created
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****************************************************************************/
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#ifndef __VCGLIB_QUADRIC
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#define __VCGLIB_QUADRIC
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@ -50,137 +26,180 @@ created
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#include <vcg/space/point3.h>
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#include <vcg/space/plane3.h>
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#include <vcg/math/matrix33.h>
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#include <eigenlib/Eigen/Core>
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namespace vcg {
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namespace math {
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template<typename Scalar>
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/*
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* This class encode a quadric function
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* f(x) = xAx +bx + c
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* where A is a symmetric 3x3 matrix, b a vector and c a scalar constant.
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*/
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template<typename _ScalarType>
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class Quadric
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{
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public:
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typedef Scalar ScalarType;
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ScalarType a[6]; // Matrice 3x3 simmetrica: a11 a12 a13 a22 a23 a33
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ScalarType b[3]; // Vettore r3
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ScalarType c; // Fattore scalare (se -1 quadrica nulla)
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inline Quadric() { c = -1; }
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// Necessari se si utilizza stl microsoft
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// inline bool operator < ( const Quadric & q ) const { return false; }
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// inline bool operator == ( const Quadric & q ) const { return true; }
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bool IsValid() const { return c>=0; }
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void SetInvalid() { c = -1.0; }
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template< class PlaneType >
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void ByPlane( const PlaneType & p ) // Init dato un piano
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{
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a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11
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a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
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a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
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a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22
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a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
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a[5] = (ScalarType)p.Direction()[2]*p.Direction()[2]; // a33
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b[0] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[0];
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b[1] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[1];
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b[2] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[2];
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c = (ScalarType)p.Offset()*p.Offset();
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}
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/* Initializes the quadric as the squared distance from a given line.
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Notice that this code also works for a vcg::Ray<T>, even though the (squared) distance
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from a ray is different "before" its origin.
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*/
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template< class LineType >
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void ByLine( const LineType & r ) // Init dato un raggio
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{
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ScalarType K = (ScalarType)(r.Origin()*r.Direction());
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a[0] = (ScalarType)1.0-r.Direction()[0]*r.Direction()[0]; // a11
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a[1] = (ScalarType)-r.Direction()[0]*r.Direction()[1]; // a12 (=a21)
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a[2] = (ScalarType)-r.Direction()[0]*r.Direction()[2]; // a13 (=a31)
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a[3] = (ScalarType)1.0-r.Direction()[1]*r.Direction()[1]; // a22
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a[4] = (ScalarType)-r.Direction()[1]*r.Direction()[2]; // a23 (=a32)
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a[5] = (ScalarType)1.0-r.Direction()[2]*r.Direction()[2]; // a33
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b[0] = (ScalarType)2.0*(r.Direction()[0]*K - r.Origin()[0]);
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b[1] = (ScalarType)2.0*(r.Direction()[1]*K - r.Origin()[1]);
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b[2] = (ScalarType)2.0*(r.Direction()[2]*K - r.Origin()[2]);
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c = -K*K + (ScalarType)(r.Origin()*r.Origin());
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typedef _ScalarType ScalarType;
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ScalarType a[6]; // Symmetric Matrix 3x3 : a11 a12 a13 a22 a23 a33
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ScalarType b[3]; // Vector r3
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ScalarType c; // Scalar (-1 means null/un-initialized quadric)
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inline Quadric() { c = -1; }
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bool IsValid() const { return c>=0; }
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void SetInvalid() { c = -1.0; }
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// Initialize the quadric to keep the squared distance from a given Plane
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template< class PlaneType >
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void ByPlane( const PlaneType & p )
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{
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a[0] = (ScalarType)p.Direction()[0]*p.Direction()[0]; // a11
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a[1] = (ScalarType)p.Direction()[1]*p.Direction()[0]; // a12 (=a21)
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a[2] = (ScalarType)p.Direction()[2]*p.Direction()[0]; // a13 (=a31)
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a[3] = (ScalarType)p.Direction()[1]*p.Direction()[1]; // a22
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a[4] = (ScalarType)p.Direction()[2]*p.Direction()[1]; // a23 (=a32)
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a[5] = (ScalarType)p.Direction()[2]*p.Direction()[2]; // a33
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b[0] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[0];
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b[1] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[1];
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b[2] = (ScalarType)(-2.0)*p.Offset()*p.Direction()[2];
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c = (ScalarType)p.Offset()*p.Offset();
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}
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/*
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* Initializes the quadric as the squared distance from a given line.
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* Note that this code also works for a vcg::Ray<T>, even though the (squared) distance
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* from a ray is different "before" its origin.
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*/
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template< class LineType >
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void ByLine( const LineType & r ) // Init dato un raggio
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{
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ScalarType K = (ScalarType)(r.Origin()*r.Direction());
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a[0] = (ScalarType)1.0-r.Direction()[0]*r.Direction()[0]; // a11
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a[1] = (ScalarType)-r.Direction()[0]*r.Direction()[1]; // a12 (=a21)
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a[2] = (ScalarType)-r.Direction()[0]*r.Direction()[2]; // a13 (=a31)
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a[3] = (ScalarType)1.0-r.Direction()[1]*r.Direction()[1]; // a22
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a[4] = (ScalarType)-r.Direction()[1]*r.Direction()[2]; // a23 (=a32)
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a[5] = (ScalarType)1.0-r.Direction()[2]*r.Direction()[2]; // a33
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b[0] = (ScalarType)2.0*(r.Direction()[0]*K - r.Origin()[0]);
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b[1] = (ScalarType)2.0*(r.Direction()[1]*K - r.Origin()[1]);
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b[2] = (ScalarType)2.0*(r.Direction()[2]*K - r.Origin()[2]);
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c = -K*K + (ScalarType)(r.Origin()*r.Origin());
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}
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void SetZero() // Azzera la quadrica
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{
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a[0] = 0;
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a[1] = 0;
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a[2] = 0;
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a[3] = 0;
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a[4] = 0;
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a[5] = 0;
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b[0] = 0;
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b[1] = 0;
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b[2] = 0;
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c = 0;
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}
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void operator = ( const Quadric & q ) // Assegna una quadrica
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{
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//assert( IsValid() );
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assert( q.IsValid() );
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a[0] = q.a[0];
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a[1] = q.a[1];
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a[2] = q.a[2];
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a[3] = q.a[3];
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a[4] = q.a[4];
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a[5] = q.a[5];
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b[0] = q.b[0];
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b[1] = q.b[1];
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b[2] = q.b[2];
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c = q.c;
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}
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void operator += ( const Quadric & q ) // Somma una quadrica
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{
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assert( IsValid() );
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assert( q.IsValid() );
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a[0] += q.a[0];
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a[1] += q.a[1];
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a[2] += q.a[2];
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a[3] += q.a[3];
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a[4] += q.a[4];
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a[5] += q.a[5];
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b[0] += q.b[0];
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b[1] += q.b[1];
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b[2] += q.b[2];
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c += q.c;
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}
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template <class ResultScalarType>
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ResultScalarType Apply( const Point3<ResultScalarType> & p ) const // Applica la quadrica al punto p
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{
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assert( IsValid() );
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/*
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// Versione Lenta
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Point3d t;
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t[0] = p[0]*a[0] + p[1]*a[1] + p[2]*a[2];
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t[1] = p[0]*a[1] + p[1]*a[3] + p[2]*a[4];
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t[2] = p[0]*a[2] + p[1]*a[4] + p[2]*a[5];
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double k = b[0]*p[0] + b[1]*p[1] + b[2]*p[2];
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double tp = t*p ;
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assert(tp+k+c >= 0);
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return tp + k + c;
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*/
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/* Versione veloce */
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return ResultScalarType (
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p[0]*p[0]*a[0] + 2*p[0]*p[1]*a[1] + 2*p[0]*p[2]*a[2] + p[0]*b[0]
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+ p[1]*p[1]*a[3] + 2*p[1]*p[2]*a[4] + p[1]*b[1]
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+ p[2]*p[2]*a[5] + p[2]*b[2] + c);
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}
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void SetZero()
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{
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a[0] = 0;
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a[1] = 0;
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a[2] = 0;
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a[3] = 0;
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a[4] = 0;
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a[5] = 0;
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b[0] = 0;
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b[1] = 0;
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b[2] = 0;
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c = 0;
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}
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void operator = ( const Quadric & q )
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{
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assert( q.IsValid() );
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a[0] = q.a[0];
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a[1] = q.a[1];
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a[2] = q.a[2];
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a[3] = q.a[3];
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a[4] = q.a[4];
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a[5] = q.a[5];
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b[0] = q.b[0];
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b[1] = q.b[1];
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b[2] = q.b[2];
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c = q.c;
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}
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void operator += ( const Quadric & q )
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{
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assert( IsValid() );
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assert( q.IsValid() );
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a[0] += q.a[0];
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a[1] += q.a[1];
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a[2] += q.a[2];
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a[3] += q.a[3];
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a[4] += q.a[4];
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a[5] += q.a[5];
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b[0] += q.b[0];
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b[1] += q.b[1];
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b[2] += q.b[2];
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c += q.c;
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}
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void operator *= ( const ScalarType & w ) // Amplifica una quadirca
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{
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assert( IsValid() );
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a[0] *= w;
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a[1] *= w;
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a[2] *= w;
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a[3] *= w;
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a[4] *= w;
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a[5] *= w;
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b[0] *= w;
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b[1] *= w;
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b[2] *= w;
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c *= w;
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}
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/* Evaluate a quadric over a point p.
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*/
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template <class ResultScalarType>
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ResultScalarType Apply( const Point3<ResultScalarType> & p ) const
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{
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assert( IsValid() );
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return ResultScalarType (
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p[0]*p[0]*a[0] + 2*p[0]*p[1]*a[1] + 2*p[0]*p[2]*a[2] + p[0]*b[0]
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+ p[1]*p[1]*a[3] + 2*p[1]*p[2]*a[4] + p[1]*b[1]
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+ p[2]*p[2]*a[5] + p[2]*b[2] + c);
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}
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static double &RelativeErrorThr()
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{
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static double _err = 0.000001;
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return _err;
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}
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// Find the point minimizing the quadric xAx + bx + c
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// by solving the first derivative 2 Ax + b = 0
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// return true if the found solution fits the system.
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template <class ReturnScalarType>
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bool Minimum(Point3<ReturnScalarType> &x)
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{
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Eigen::Matrix3d A;
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Eigen::Vector3d be;
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A << a[0], a[1], a[2],
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a[1], a[3], a[4],
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a[2], a[4], a[5];
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be << -b[0]/2, -b[1]/2, -b[2]/2;
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// Eigen::Vector3d xe = A.colPivHouseholderQr().solve(bv);
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// Eigen::Vector3d xe = A.partialPivLu().solve(bv);
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Eigen::Vector3d xe = A.fullPivLu().solve(be);
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double relative_error = (A*xe - be).norm() / be.norm();
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if(relative_error> Quadric<ScalarType>::RelativeErrorThr() )
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return false;
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x.FromEigenVector(xe);
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return true;
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}
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// spostare..risolve un sistema 3x3
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template<class FLTYPE>
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bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
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@ -244,9 +263,10 @@ bool Gauss33( FLTYPE x[], FLTYPE C[3][3+1] )
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return true;
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}
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// determina il punto di errore minimo
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template <class ReturnScalarType>
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bool Minimum(Point3<ReturnScalarType> &x)
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bool MinimumOld(Point3<ReturnScalarType> &x)
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{
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ReturnScalarType C[3][4];
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C[0][0]=a[0]; C[0][1]=a[1]; C[0][2]=a[2];
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@ -259,44 +279,6 @@ bool Minimum(Point3<ReturnScalarType> &x)
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return Gauss33(&(x[0]),C);
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}
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// determina il punto di errore minimo usando le fun di inversione di matrice che usano svd
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// Molto + lento
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template <class ReturnScalarType>
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bool MinimumSVD(Point3<ReturnScalarType> &x)
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{
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Matrix33<ReturnScalarType> C;
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C[0][0]=a[0]; C[0][1]=a[1]; C[0][2]=a[2];
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C[1][0]=a[1]; C[1][1]=a[3]; C[1][2]=a[4];
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C[2][0]=a[2]; C[2][1]=a[4]; C[2][2]=a[5];
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Invert(C);
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C[0][3]=-b[0]/2;
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C[1][3]=-b[1]/2;
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C[2][3]=-b[2]/2;
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x = C * Point3<ReturnScalarType>(-b[0]/2,-b[1]/2,-b[2]/2) ;
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return true;
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}
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bool MinimumNew(Point3<ScalarType> &x) const
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{
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ScalarType c0=-b[0]/2;
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ScalarType c1=-b[1]/2;
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ScalarType c2=-b[2]/2;
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ScalarType t125 = a[4]*a[1];
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ScalarType t124 = a[4]*a[4]-a[3]*a[5];
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ScalarType t123 = -a[1]*a[5]+a[4]*a[2];
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ScalarType t122 = a[2]*a[3]-t125;
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ScalarType t121 = -a[2]*a[1]+a[0]*a[4];
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ScalarType t120 = a[2]*a[2];
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ScalarType t119 = a[1]*a[1];
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ScalarType t117 = 1.0/(-a[3]*t120+2*a[2]*t125-t119*a[5]-t124*a[0]);
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x[0] = -(t124*c0+t122*c2-t123*c1)*t117;
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x[1] = (t123*c0-t121*c2+(-t120+a[0]*a[5])*c1)*t117;
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x[2] = -(t122*c0+(t119-a[0]*a[3])*c2+t121*c1)*t117;
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return true;
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}
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// determina il punto di errore minimo vincolato nel segmento (a,b)
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bool Minimum(Point3<ScalarType> &x,Point3<ScalarType> &pa,Point3<ScalarType> &pb){
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ScalarType t1,t2, t4, t5, t8, t9,
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@ -344,23 +326,6 @@ ScalarType t1,t2, t4, t5, t8, t9,
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return true;
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}
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void operator *= ( const ScalarType & w ) // Amplifica una quadirca
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{
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assert( IsValid() );
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a[0] *= w;
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a[1] *= w;
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a[2] *= w;
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a[3] *= w;
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a[4] *= w;
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a[5] *= w;
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b[0] *= w;
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b[1] *= w;
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b[2] *= w;
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c *= w;
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}
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};
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typedef Quadric<short> Quadrics;
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