diff --git a/vcg/space/quadric.h b/vcg/space/quadric.h new file mode 100644 index 00000000..66f9d1b8 --- /dev/null +++ b/vcg/space/quadric.h @@ -0,0 +1,238 @@ +/**************************************************************************** +* 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 $ + +****************************************************************************/ + +#ifndef __VCGLIB_QUADRIC +#define __VCGLIB_QUADRIC + +#ifndef __VCGLIB_POINT3 +#include +#endif +#ifndef __VCGLIB_PLANE3 +#include +#endif + +namespace vcg { + +template +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 & 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 & 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 &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 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(-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 &x,Point3 &pa,Point3 &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 Quadrics; +typedef Quadric Quadrici; +typedef Quadric Quadricf; +typedef Quadric Quadricd; + + + +} // end namespace + +#endif