/**************************************************************************** * 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 $ Revision 1.1 2004/07/12 23:46:03 cignoni Initial Commit ****************************************************************************/ #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