626 lines
20 KiB
C++
626 lines
20 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) 2004-2016 \/)\/ *
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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 1.2 2005/10/24 09:19:33 ponchio
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Added newline at end of file (tired of stupid warnings...)
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Revision 1.1 2004/04/26 12:33:59 ganovelli
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first version
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****************************************************************************/
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#ifndef __VCGLIB_INTERSECTIONTRITRI3
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#define __VCGLIB_INTERSECTIONTRITRI3
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#include <vcg/space/point3.h>
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#include <math.h>
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namespace vcg {
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/** \addtogroup space */
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/*@{*/
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/**
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Triangle/triangle intersection ,based on the algorithm presented in "A Fast Triangle-Triangle Intersection Test",
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Journal of Graphics Tools, 2(2), 1997
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*/
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#ifndef FABS
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#define FABS(x) (T(fabs(x)))
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#endif
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#define USE_EPSILON_TEST
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#define TRI_TRI_INT_EPSILON 0.000001
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#define CROSS(dest,v1,v2){ \
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dest[0]=v1[1]*v2[2]-v1[2]*v2[1]; \
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dest[1]=v1[2]*v2[0]-v1[0]*v2[2]; \
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dest[2]=v1[0]*v2[1]-v1[1]*v2[0];}
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#define DOT(v1,v2) (v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])
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#define SUB(dest,v1,v2){ \
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dest[0]=v1[0]-v2[0]; \
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dest[1]=v1[1]-v2[1]; \
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dest[2]=v1[2]-v2[2];}
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#define SORT(a,b) \
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if(a>b) \
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{ \
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T c; \
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c=a; \
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a=b; \
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b=c; \
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}
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#define EDGE_EDGE_TEST(V0,U0,U1) \
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Bx=U0[i0]-U1[i0]; \
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By=U0[i1]-U1[i1]; \
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Cx=V0[i0]-U0[i0]; \
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Cy=V0[i1]-U0[i1]; \
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f=Ay*Bx-Ax*By; \
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d=By*Cx-Bx*Cy; \
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if((f>0 && d>=0 && d<=f) || (f<0 && d<=0 && d>=f)) \
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{ \
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e=Ax*Cy-Ay*Cx; \
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if(f>0) \
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{ \
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if(e>=0 && e<=f) return 1; \
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} \
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else \
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{ \
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if(e<=0 && e>=f) return 1; \
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} \
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}
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#define EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2) \
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{ \
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T Ax,Ay,Bx,By,Cx,Cy,e,d,f; \
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Ax=V1[i0]-V0[i0]; \
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Ay=V1[i1]-V0[i1]; \
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/* test edge U0,U1 against V0,V1 */ \
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EDGE_EDGE_TEST(V0,U0,U1); \
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/* test edge U1,U2 against V0,V1 */ \
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EDGE_EDGE_TEST(V0,U1,U2); \
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/* test edge U2,U1 against V0,V1 */ \
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EDGE_EDGE_TEST(V0,U2,U0); \
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}
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#define POINT_IN_TRI(V0,U0,U1,U2) \
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{ \
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T a,b,c,d0,d1,d2; \
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/* is T1 completly inside T2? */ \
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/* check if V0 is inside tri(U0,U1,U2) */ \
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a=U1[i1]-U0[i1]; \
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b=-(U1[i0]-U0[i0]); \
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c=-a*U0[i0]-b*U0[i1]; \
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d0=a*V0[i0]+b*V0[i1]+c; \
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\
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a=U2[i1]-U1[i1]; \
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b=-(U2[i0]-U1[i0]); \
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c=-a*U1[i0]-b*U1[i1]; \
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d1=a*V0[i0]+b*V0[i1]+c; \
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\
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a=U0[i1]-U2[i1]; \
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b=-(U0[i0]-U2[i0]); \
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c=-a*U2[i0]-b*U2[i1]; \
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d2=a*V0[i0]+b*V0[i1]+c; \
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if(d0*d1>0.0) \
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{ \
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if(d0*d2>0.0) return 1; \
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} \
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}
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template<class T>
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/** CHeck two triangles for coplanarity
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@param N
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@param V0 A vertex of the first triangle
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@param V1 A vertex of the first triangle
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@param V2 A vertex of the first triangle
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@param U0 A vertex of the second triangle
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@param U1 A vertex of the second triangle
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@param U2 A vertex of the second triangle
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@return true se due triangoli sono cooplanari, false altrimenti
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*/
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bool coplanar_tri_tri(const Point3<T> N, const Point3<T> V0, const Point3<T> V1,const Point3<T> V2,
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const Point3<T> U0, const Point3<T> U1,const Point3<T> U2)
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{
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T A[3];
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short i0,i1;
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/* first project onto an axis-aligned plane, that maximizes the area */
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/* of the triangles, compute indices: i0,i1. */
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A[0]=FABS(N[0]);
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A[1]=FABS(N[1]);
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A[2]=FABS(N[2]);
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if(A[0]>A[1])
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{
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if(A[0]>A[2])
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{
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i0=1; /* A[0] is greatest */
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i1=2;
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}
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else
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{
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i0=0; /* A[2] is greatest */
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i1=1;
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}
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}
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else /* A[0]<=A[1] */
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{
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if(A[2]>A[1])
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{
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i0=0; /* A[2] is greatest */
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i1=1;
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}
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else
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{
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i0=0; /* A[1] is greatest */
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i1=2;
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}
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}
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/* test all edges of triangle 1 against the edges of triangle 2 */
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EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2);
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EDGE_AGAINST_TRI_EDGES(V1,V2,U0,U1,U2);
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EDGE_AGAINST_TRI_EDGES(V2,V0,U0,U1,U2);
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/* finally, test if tri1 is totally contained in tri2 or vice versa */
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POINT_IN_TRI(V0,U0,U1,U2);
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POINT_IN_TRI(U0,V0,V1,V2);
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return 0;
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}
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#define NEWCOMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,A,B,C,X0,X1) \
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{ \
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if(D0D1>0.0f) \
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{ \
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/* here we know that D0D2<=0.0 */ \
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/* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
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A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
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} \
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else if(D0D2>0.0f)\
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{ \
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/* here we know that d0d1<=0.0 */ \
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A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
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} \
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else if(D1*D2>0.0f || D0!=0.0f) \
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{ \
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/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
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A=VV0; B=(VV1-VV0)*D0; C=(VV2-VV0)*D0; X0=D0-D1; X1=D0-D2; \
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} \
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else if(D1!=0.0f) \
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{ \
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A=VV1; B=(VV0-VV1)*D1; C=(VV2-VV1)*D1; X0=D1-D0; X1=D1-D2; \
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} \
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else if(D2!=0.0f) \
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{ \
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A=VV2; B=(VV0-VV2)*D2; C=(VV1-VV2)*D2; X0=D2-D0; X1=D2-D1; \
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} \
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else \
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{ \
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/* triangles are coplanar */ \
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return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
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} \
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}
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template<class T>
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/*
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@param V0 A vertex of the first triangle
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@param V1 A vertex of the first triangle
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@param V2 A vertex of the first triangle
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@param U0 A vertex of the second triangle
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@param U1 A vertex of the second triangle
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@param U2 A vertex of the second triangle
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@return true if the two triangles interesect
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*/
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bool NoDivTriTriIsect(const Point3<T> V0,const Point3<T> V1,const Point3<T> V2,
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const Point3<T> U0,const Point3<T> U1,const Point3<T> U2)
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{
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Point3<T> E1,E2;
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Point3<T> N1,N2;
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T d1,d2;
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T du0,du1,du2,dv0,dv1,dv2;
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Point3<T> D;
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T isect1[2], isect2[2];
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T du0du1,du0du2,dv0dv1,dv0dv2;
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short index;
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T vp0,vp1,vp2;
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T up0,up1,up2;
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T bb,cc,max;
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/* compute plane equation of triangle(V0,V1,V2) */
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SUB(E1,V1,V0);
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SUB(E2,V2,V0);
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CROSS(N1,E1,E2);
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N1.Normalize(); // aggiunto rispetto al codice orig.
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d1=-DOT(N1,V0);
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/* plane equation 1: N1.X+d1=0 */
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/* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
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du0=DOT(N1,U0)+d1;
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du1=DOT(N1,U1)+d1;
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du2=DOT(N1,U2)+d1;
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/* coplanarity robustness check */
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#ifdef USE_TRI_TRI_INT_EPSILON_TEST
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if(FABS(du0)<TRI_TRI_INT_EPSILON) du0=0.0;
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if(FABS(du1)<TRI_TRI_INT_EPSILON) du1=0.0;
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if(FABS(du2)<TRI_TRI_INT_EPSILON) du2=0.0;
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#endif
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du0du1=du0*du1;
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du0du2=du0*du2;
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if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
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return 0; /* no intersection occurs */
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/* compute plane of triangle (U0,U1,U2) */
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SUB(E1,U1,U0);
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SUB(E2,U2,U0);
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CROSS(N2,E1,E2);
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d2=-DOT(N2,U0);
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/* plane equation 2: N2.X+d2=0 */
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/* put V0,V1,V2 into plane equation 2 */
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dv0=DOT(N2,V0)+d2;
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dv1=DOT(N2,V1)+d2;
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dv2=DOT(N2,V2)+d2;
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#ifdef USE_TRI_TRI_INT_EPSILON_TEST
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if(FABS(dv0)<TRI_TRI_INT_EPSILON) dv0=0.0;
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if(FABS(dv1)<TRI_TRI_INT_EPSILON) dv1=0.0;
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if(FABS(dv2)<TRI_TRI_INT_EPSILON) dv2=0.0;
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#endif
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dv0dv1=dv0*dv1;
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dv0dv2=dv0*dv2;
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if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
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return 0; /* no intersection occurs */
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/* compute direction of intersection line */
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CROSS(D,N1,N2);
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/* compute and index to the largest component of D */
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max=(T)FABS(D[0]);
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index=0;
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bb=(T)FABS(D[1]);
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cc=(T)FABS(D[2]);
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if(bb>max) max=bb,index=1;
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if(cc>max) max=cc,index=2;
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/* this is the simplified projection onto L*/
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vp0=V0[index];
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vp1=V1[index];
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vp2=V2[index];
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up0=U0[index];
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up1=U1[index];
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up2=U2[index];
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/* compute interval for triangle 1 */
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T a,b,c,x0,x1;
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NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);
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/* compute interval for triangle 2 */
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T d,e,f,y0,y1;
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NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);
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T xx,yy,xxyy,tmp;
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xx=x0*x1;
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yy=y0*y1;
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xxyy=xx*yy;
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tmp=a*xxyy;
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isect1[0]=tmp+b*x1*yy;
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isect1[1]=tmp+c*x0*yy;
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tmp=d*xxyy;
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isect2[0]=tmp+e*xx*y1;
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isect2[1]=tmp+f*xx*y0;
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SORT(isect1[0],isect1[1]);
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SORT(isect2[0],isect2[1]);
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if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
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return 1;
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}
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#define DOT(v1,v2) (v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])
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#define ADD(dest,v1,v2) dest[0]=v1[0]+v2[0]; dest[1]=v1[1]+v2[1]; dest[2]=v1[2]+v2[2];
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#define MULT(dest,v,factor) dest[0]=factor*v[0]; dest[1]=factor*v[1]; dest[2]=factor*v[2];
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#define SET(dest,src) dest[0]=src[0]; dest[1]=src[1]; dest[2]=src[2];
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/* sort so that a<=b */
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#define SORT2(a,b,smallest) \
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if(a>b) \
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{ \
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float c; \
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c=a; \
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a=b; \
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b=c; \
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smallest=1; \
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} \
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else smallest=0;
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template <class T>
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inline void isect2(Point3<T> VTX0,Point3<T> VTX1,Point3<T> VTX2,float VV0,float VV1,float VV2,
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float D0,float D1,float D2,float *isect0,float *isect1,Point3<T> &isectpoint0,Point3<T> &isectpoint1)
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{
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float tmp=D0/(D0-D1);
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float diff[3];
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*isect0=VV0+(VV1-VV0)*tmp;
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SUB(diff,VTX1,VTX0);
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MULT(diff,diff,tmp);
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ADD(isectpoint0,diff,VTX0);
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tmp=D0/(D0-D2);
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*isect1=VV0+(VV2-VV0)*tmp;
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SUB(diff,VTX2,VTX0);
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MULT(diff,diff,tmp);
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ADD(isectpoint1,VTX0,diff);
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}
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template <class T>
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inline int compute_intervals_isectline(Point3<T> VERT0,Point3<T> VERT1,Point3<T> VERT2,
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float VV0,float VV1,float VV2,float D0,float D1,float D2,
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float D0D1,float D0D2,float *isect0,float *isect1,
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Point3<T> & isectpoint0, Point3<T> & isectpoint1)
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{
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if(D0D1>0.0f)
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{
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/* here we know that D0D2<=0.0 */
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/* that is D0, D1 are on the same side, D2 on the other or on the plane */
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isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,isect0,isect1,isectpoint0,isectpoint1);
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}
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else if(D0D2>0.0f)
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{
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/* here we know that d0d1<=0.0 */
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isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,isect0,isect1,isectpoint0,isectpoint1);
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}
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else if(D1*D2>0.0f || D0!=0.0f)
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{
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/* here we know that d0d1<=0.0 or that D0!=0.0 */
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isect2(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,isect0,isect1,isectpoint0,isectpoint1);
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}
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else if(D1!=0.0f)
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{
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isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,isect0,isect1,isectpoint0,isectpoint1);
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}
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else if(D2!=0.0f)
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{
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isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,isect0,isect1,isectpoint0,isectpoint1);
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}
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else
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{
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/* triangles are coplanar */
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return 1;
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}
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return 0;
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}
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#define COMPUTE_INTERVALS_ISECTLINE(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,isect0,isect1,isectpoint0,isectpoint1) \
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if(D0D1>0.0f) \
|
|
{ \
|
|
/* here we know that D0D2<=0.0 */ \
|
|
/* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
|
|
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,&isect0,&isect1,isectpoint0,isectpoint1); \
|
|
}
|
|
#if 0
|
|
else if(D0D2>0.0f) \
|
|
{ \
|
|
/* here we know that d0d1<=0.0 */ \
|
|
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
|
|
} \
|
|
else if(D1*D2>0.0f || D0!=0.0f) \
|
|
{ \
|
|
/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
|
|
isect2(VERT0,VERT1,VERT2,VV0,VV1,VV2,D0,D1,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
|
|
} \
|
|
else if(D1!=0.0f) \
|
|
{ \
|
|
isect2(VERT1,VERT0,VERT2,VV1,VV0,VV2,D1,D0,D2,&isect0,&isect1,isectpoint0,isectpoint1); \
|
|
} \
|
|
else if(D2!=0.0f) \
|
|
{ \
|
|
isect2(VERT2,VERT0,VERT1,VV2,VV0,VV1,D2,D0,D1,&isect0,&isect1,isectpoint0,isectpoint1); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* triangles are coplanar */ \
|
|
coplanar=1; \
|
|
return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2); \
|
|
}
|
|
#endif
|
|
|
|
template <class T>
|
|
bool tri_tri_intersect_with_isectline( Point3<T> V0,Point3<T> V1,Point3<T> V2,
|
|
Point3<T> U0,Point3<T> U1,Point3<T> U2,bool &coplanar,
|
|
Point3<T> &isectpt1,Point3<T> &isectpt2)
|
|
{
|
|
Point3<T> E1,E2;
|
|
Point3<T> N1,N2;
|
|
T d1,d2;
|
|
float du0,du1,du2,dv0,dv1,dv2;
|
|
Point3<T> D;
|
|
float isect1[2], isect2[2];
|
|
Point3<T> isectpointA1,isectpointA2;
|
|
Point3<T> isectpointB1,isectpointB2;
|
|
float du0du1,du0du2,dv0dv1,dv0dv2;
|
|
short index;
|
|
float vp0,vp1,vp2;
|
|
float up0,up1,up2;
|
|
float b,c,max;
|
|
|
|
Point3<T> diff;
|
|
int smallest1,smallest2;
|
|
|
|
/* compute plane equation of triangle(V0,V1,V2) */
|
|
SUB(E1,V1,V0);
|
|
SUB(E2,V2,V0);
|
|
CROSS(N1,E1,E2);
|
|
d1=-DOT(N1,V0);
|
|
/* plane equation 1: N1.X+d1=0 */
|
|
|
|
/* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
|
|
du0=DOT(N1,U0)+d1;
|
|
du1=DOT(N1,U1)+d1;
|
|
du2=DOT(N1,U2)+d1;
|
|
|
|
/* coplanarity robustness check */
|
|
#ifdef USE_EPSILON_TEST
|
|
if(fabs(du0)<TRI_TRI_INT_EPSILON) du0=0.0;
|
|
if(fabs(du1)<TRI_TRI_INT_EPSILON) du1=0.0;
|
|
if(fabs(du2)<TRI_TRI_INT_EPSILON) du2=0.0;
|
|
#endif
|
|
du0du1=du0*du1;
|
|
du0du2=du0*du2;
|
|
|
|
if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
|
|
return 0; /* no intersection occurs */
|
|
|
|
/* compute plane of triangle (U0,U1,U2) */
|
|
SUB(E1,U1,U0);
|
|
SUB(E2,U2,U0);
|
|
CROSS(N2,E1,E2);
|
|
d2=-DOT(N2,U0);
|
|
/* plane equation 2: N2.X+d2=0 */
|
|
|
|
/* put V0,V1,V2 into plane equation 2 */
|
|
dv0=DOT(N2,V0)+d2;
|
|
dv1=DOT(N2,V1)+d2;
|
|
dv2=DOT(N2,V2)+d2;
|
|
|
|
#ifdef USE_EPSILON_TEST
|
|
if(fabs(dv0)<TRI_TRI_INT_EPSILON) dv0=0.0;
|
|
if(fabs(dv1)<TRI_TRI_INT_EPSILON) dv1=0.0;
|
|
if(fabs(dv2)<TRI_TRI_INT_EPSILON) dv2=0.0;
|
|
#endif
|
|
|
|
dv0dv1=dv0*dv1;
|
|
dv0dv2=dv0*dv2;
|
|
|
|
if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
|
|
return 0; /* no intersection occurs */
|
|
|
|
/* compute direction of intersection line */
|
|
CROSS(D,N1,N2);
|
|
|
|
/* compute and index to the largest component of D */
|
|
max=fabs(D[0]);
|
|
index=0;
|
|
b=fabs(D[1]);
|
|
c=fabs(D[2]);
|
|
if(b>max) max=b,index=1;
|
|
if(c>max) max=c,index=2;
|
|
|
|
/* this is the simplified projection onto L*/
|
|
vp0=V0[index];
|
|
vp1=V1[index];
|
|
vp2=V2[index];
|
|
|
|
up0=U0[index];
|
|
up1=U1[index];
|
|
up2=U2[index];
|
|
|
|
/* compute interval for triangle 1 */
|
|
coplanar=compute_intervals_isectline(V0,V1,V2,vp0,vp1,vp2,dv0,dv1,dv2,
|
|
dv0dv1,dv0dv2,&isect1[0],&isect1[1],isectpointA1,isectpointA2);
|
|
if(coplanar) return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2);
|
|
|
|
|
|
/* compute interval for triangle 2 */
|
|
compute_intervals_isectline(U0,U1,U2,up0,up1,up2,du0,du1,du2,
|
|
du0du1,du0du2,&isect2[0],&isect2[1],isectpointB1,isectpointB2);
|
|
|
|
SORT2(isect1[0],isect1[1],smallest1);
|
|
SORT2(isect2[0],isect2[1],smallest2);
|
|
|
|
if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return 0;
|
|
|
|
/* at this point, we know that the triangles intersect */
|
|
|
|
if(isect2[0]<isect1[0])
|
|
{
|
|
if(smallest1==0) { SET(isectpt1,isectpointA1); }
|
|
else { SET(isectpt1,isectpointA2); }
|
|
|
|
if(isect2[1]<isect1[1])
|
|
{
|
|
if(smallest2==0) { SET(isectpt2,isectpointB2); }
|
|
else { SET(isectpt2,isectpointB1); }
|
|
}
|
|
else
|
|
{
|
|
if(smallest1==0) { SET(isectpt2,isectpointA2); }
|
|
else { SET(isectpt2,isectpointA1); }
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(smallest2==0) { SET(isectpt1,isectpointB1); }
|
|
else { SET(isectpt1,isectpointB2); }
|
|
|
|
if(isect2[1]>isect1[1])
|
|
{
|
|
if(smallest1==0) { SET(isectpt2,isectpointA2); }
|
|
else { SET(isectpt2,isectpointA1); }
|
|
}
|
|
else
|
|
{
|
|
if(smallest2==0) { SET(isectpt2,isectpointB2); }
|
|
else { SET(isectpt2,isectpointB1); }
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
|
|
} // end namespace
|
|
|
|
#undef FABS
|
|
#undef USE_EPSILON_TEST
|
|
#undef TRI_TRI_INT_EPSILON
|
|
#undef CROSS
|
|
#undef DOT
|
|
#undef SUB
|
|
#undef SORT
|
|
#undef SORT2
|
|
#undef ADD
|
|
#undef MULT
|
|
#undef SET
|
|
#undef EDGE_EDGE_TEST
|
|
#undef EDGE_AGAINST_TRI_EDGE
|
|
#undef POINT_IN_TRI
|
|
#undef COMPUTE_INTERVALS_ISECTLINE
|
|
#undef NEWCOMPUTE_INTERVALS
|
|
#endif
|