303 lines
9.8 KiB
C++
303 lines
9.8 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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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 1.10 2004/08/09 09:48:43 pietroni
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correcter .dir to .Direction and .ori in .Origin()
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Revision 1.9 2004/08/04 20:55:02 pietroni
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added rey triangle intersections funtions
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Revision 1.8 2004/07/11 22:08:04 cignoni
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Added a cast to remove a warning
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Revision 1.7 2004/05/14 03:14:29 ponchio
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Fixed some minor bugs
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Revision 1.6 2004/05/13 23:43:54 ponchio
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minor bug
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Revision 1.5 2004/05/05 08:21:55 cignoni
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syntax errors in inersection plane line.
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Revision 1.4 2004/05/04 02:37:58 ganovelli
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Triangle3<T> replaced by TRIANGLE
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Segment<T> replaced by EDGETYPE
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Revision 1.3 2004/04/29 10:48:44 ganovelli
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error in plane segment corrected
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Revision 1.2 2004/04/26 12:34:50 ganovelli
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plane line
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plane segment
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triangle triangle added
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Revision 1.1 2004/04/21 14:22:27 cignoni
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Initial Commit
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****************************************************************************/
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#ifndef __VCGLIB_INTERSECTION_3
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#define __VCGLIB_INTERSECTION_3
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#include <vcg/space/point3.h>
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#include <vcg/space/line3.h>
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#include <vcg/space/plane3.h>
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#include <vcg/space/segment3.h>
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#include <vcg/space/sphere3.h>
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#include <vcg/space/triangle3.h>
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#include <vcg/space/intersection/triangle_triangle3.h>
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/** \addtogroup space */
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/*@{*/
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/**
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Function computing the intersection between couple of geometric primitives in
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3 dimension
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*/
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namespace vcg {
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/// interseciton between sphere and line
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template<class T>
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inline bool Intersection( const Sphere3<T> & sp, const Line3<T> & li, Point3<T> & p0,Point3<T> & p1 ){
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// Per prima cosa si sposta il sistema di riferimento
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// fino a portare il centro della sfera nell'origine
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Point3<T> neworig=li.Origin()-sp.Center();
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// poi si risolve il sistema di secondo grado (con maple...)
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T t1 = li.Direction().X()*li.Direction().X();
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T t2 = li.Direction().Y()*li.Direction().Y();
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T t3 = li.Direction().Z()*li.Direction().Z();
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T t6 = neworig.Y()*li.Direction().Y();
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T t7 = neworig.X()*li.Direction().X();
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T t8 = neworig.Z()*li.Direction().Z();
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T t15 = sp.Radius()*sp.Radius();
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T t17 = neworig.Z()*neworig.Z();
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T t19 = neworig.Y()*neworig.Y();
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T t21 = neworig.X()*neworig.X();
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T t28 = T(2.0*t7*t6+2.0*t6*t8+2.0*t7*t8+t1*t15-t1*t17-t1*t19-t2*t21+t2*t15-t2*t17-t3*t21+t3*t15-t3*t19);
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if(t28<0) return false;
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T t29 = sqrt(t28);
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T val0 = 1/(t1+t2+t3)*(-t6-t7-t8+t29);
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T val1 = 1/(t1+t2+t3)*(-t6-t7-t8-t29);
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p0=li.P(val0);
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p1=li.P(val1);
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return true;
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}
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/// intersection between line and plane
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template<class T>
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inline bool Intersection( const Plane3<T> & pl, const Line3<T> & li, Point3<T> & po){
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const T epsilon = T(1e-8);
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T k = pl.Direction() * li.Direction(); // Compute 'k' factor
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if( (k > -epsilon) && (k < epsilon))
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return false;
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T r = (pl.Offset() - pl.Direction()*li.Origin())/k; // Compute ray distance
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po = li.Origin() + li.Direction()*r;
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return true;
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}
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/// intersection between segment and plane
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template<typename SEGMENTTYPE>
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inline bool Intersection( const Plane3<typename SEGMENTTYPE::ScalarType> & pl,
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const SEGMENTTYPE & sg,
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Point3<typename SEGMENTTYPE::ScalarType> & po){
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typedef typename SEGMENTTYPE::ScalarType T;
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const T epsilon = T(1e-8);
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T k = pl.Direction() * (sg.P1()-sg.P0());
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if( (k > -epsilon) && (k < epsilon))
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return false;
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T r = (pl.Offset() - pl.Direction()*sg.P0())/k; // Compute ray distance
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if( (r<0) || (r > 1.0))
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return false;
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po = sg.P0()*(1-r)+sg.P1() * r;
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return true;
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}
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/// intersection between plane and triangle
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// not optimal: uses plane-segment intersection (and the fact the two or none edges can be intersected)
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template<typename TRIANGLETYPE>
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inline bool Intersection( const Plane3<typename TRIANGLETYPE::ScalarType> & pl,
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const TRIANGLETYPE & tr,
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Segment3<typename TRIANGLETYPE::ScalarType> & sg){
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typedef typename TRIANGLETYPE::ScalarType T;
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if(Intersection(pl,Segment3<T>(tr.P(0),tr.P(1)),sg.P0())){
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if(Intersection(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1()))
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return true;
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else
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{
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Intersection(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P1());
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return true;
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}
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}else
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{
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if(Intersection(pl,Segment3<T>(tr.P(1),tr.P(2)),sg.P0()))
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{
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Intersection(pl,Segment3<T>(tr.P(0),tr.P(2)),sg.P1());
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return true;
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}
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}
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return false;
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}
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/// intersection between two triangles
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template<typename TRIANGLETYPE>
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inline bool Intersection(const TRIANGLETYPE & t0,const TRIANGLETYPE & t1){
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return NoDivTriTriIsect(t0.P0(0),t0.P0(1),t0.P0(2),
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t1.P0(0),t1.P0(1),t1.P0(2));
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}
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template<class T>
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inline bool Intersection(Point3<T> V0,Point3<T> V1,Point3<T> V2,
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Point3<T> U0,Point3<T> U1,Point3<T> U2){
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return NoDivTriTriIsect(V0,V1,V2,U0,U1,U2);
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}
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template<class T>
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inline bool Intersection(Point3<T> V0,Point3<T> V1,Point3<T> V2,
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Point3<T> U0,Point3<T> U1,Point3<T> U2,int *coplanar,
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Point3<T> &isectpt1,Point3<T> &isectpt2){
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return tri_tri_intersect_with_isectline(V0,V1,V2,U0,U1,U2,
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coplanar,isectpt1,isectpt2);
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}
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template<typename TRIANGLETYPE,typename SEGMENTTYPE >
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inline bool Intersection(const TRIANGLETYPE & t0,const TRIANGLETYPE & t1,bool &coplanar,
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SEGMENTTYPE & sg){
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Point3<typename SEGMENTTYPE::PointType> ip0,ip1;
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return tri_tri_intersect_with_isectline(t0.P0(0),t0.P0(1),t0.P0(2),
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t1.P0(0),t1.P0(1),t1.P0(2),
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coplanar,sg.P0(),sg.P1()
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);
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}
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// ray-triangle, gives barycentric coords of intersection and distance along ray
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template<class T>
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bool Intersection( const Line3<T> & ray, const Point3<T> & vert0,
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const Point3<T> & vert1, const Point3<T> & vert2,
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T & a ,T & b, T & dist)
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{
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// small (hum) borders around triangle
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const T EPSILON2= T(1e-8);
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const T EPSILON = T(1e-8);
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Point3<T> edge1 = vert1 - vert0;
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Point3<T> edge2 = vert2 - vert0;
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// determinant
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Point3<T> pvec = ray.Direction() ^ edge2;
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T det = edge1*pvec;
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// if determinant is near zero, ray lies in plane of triangle
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if (fabs(det) < EPSILON) return false;
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// calculate distance from vert0 to ray origin
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Point3<T> tvec = ray.Origin()- vert0;
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// calculate A parameter and test bounds
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a = tvec * pvec;
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if (a < -EPSILON2*det || a > det+det*EPSILON2) return false;
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// prepare to test V parameter
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Point3<T> qvec = tvec ^ edge1;
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// calculate B parameter and test bounds
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b = ray.Direction() * qvec ;
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if (b < -EPSILON2*det || b + a > det+det*EPSILON2) return false;
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// calculate t, scale parameters, ray intersects triangle
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dist = edge2 * qvec;
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if (dist<0) return false;
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T inv_det = 1.0 / det;
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dist *= inv_det;
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a *= inv_det;
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b *= inv_det;
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return true;
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}
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// ray-triangle, gives intersection 3d point and distance along ray
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template<class T>
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bool Intersection( const Line3<T> & ray, const Point3<T> & vert0,
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const Point3<T> & vert1, const Point3<T> & vert2,
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Point3<T> & inte)
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{
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// small (hum) borders around triangle
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const T EPSILON2= T(1e-8);
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const T EPSILON = T(1e-8);
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Point3<T> edge1 = vert1 - vert0;
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Point3<T> edge2 = vert2 - vert0;
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// determinant
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Point3<T> pvec = ray.Direction() ^ edge2;
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T det = edge1*pvec;
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// if determinant is near zero, ray lies in plane of triangle
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if (fabs(det) < EPSILON) return false;
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// calculate distance from vert0 to ray origin
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Point3<T> tvec = ray.Origin() - vert0;
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// calculate A parameter and test bounds
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T a = tvec * pvec;
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if (a < -EPSILON2*det || a > det+det*EPSILON2) return false;
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// prepare to test V parameter
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Point3<T> qvec = tvec ^ edge1;
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// calculate B parameter and test bounds
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T b = ray.Direction() * qvec ;
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if (b < -EPSILON2*det || b + a > det+det*EPSILON2) return false;
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// calculate t, scale parameters, ray intersects triangle
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double dist = edge2 * qvec;
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//if (dist<0) return false;
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T inv_det = 1.0 / det;
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dist *= inv_det;
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a *= inv_det;
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b *= inv_det;
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inte = vert0 + edge1*a + edge2*b;
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return true;
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}
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} // end namespace
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#endif
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