575 lines
16 KiB
C
575 lines
16 KiB
C
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/*
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*
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* Triangle-Triangle Overlap Test Routines
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* July, 2002
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* Updated December 2003
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*
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* This file contains C implementation of algorithms for
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* performing two and three-dimensional triangle-triangle intersection test
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* The algorithms and underlying theory are described in
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*
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* "Fast and Robust Triangle-Triangle Overlap Test
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* Using Orientation Predicates" P. Guigue - O. Devillers
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*
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* Journal of Graphics Tools, 8(1), 2003
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*
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* Several geometric predicates are defined. Their parameters are all
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* points. Each point is an array of two or three double precision
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* floating point numbers. The geometric predicates implemented in
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* this file are:
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*
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* int tri_tri_overlap_test_3d(p1,q1,r1,p2,q2,r2)
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* int tri_tri_overlap_test_2d(p1,q1,r1,p2,q2,r2)
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*
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* int tri_tri_intersection_test_3d(p1,q1,r1,p2,q2,r2,
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* coplanar,source,target)
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*
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* is a version that computes the segment of intersection when
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* the triangles overlap (and are not coplanar)
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*
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* each function returns 1 if the triangles (including their
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* boundary) intersect, otherwise 0
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*
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*
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* Other information are available from the Web page
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* http://www.acm.org/jgt/papers/GuigueDevillers03/
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*
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*/
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/* function prototype */
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// Three-dimensional Triangle-Triangle Overlap Test
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int tri_tri_overlap_test_3d(double p1[3], double q1[3], double r1[3],
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double p2[3], double q2[3], double r2[3]);
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// Three-dimensional Triangle-Triangle Overlap Test
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// additionaly computes the segment of intersection of the two triangles if it exists.
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// coplanar returns whether the triangles are coplanar,
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// source and target are the endpoints of the line segment of intersection
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int tri_tri_intersection_test_3d(double p1[3], double q1[3], double r1[3],
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double p2[3], double q2[3], double r2[3],
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int * coplanar,
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double source[3],double target[3]);
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int coplanar_tri_tri3d(double p1[3], double q1[3], double r1[3],
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double p2[3], double q2[3], double r2[3],
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double N1[3], double N2[3]);
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// Two dimensional Triangle-Triangle Overlap Test
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int tri_tri_overlap_test_2d(double p1[2], double q1[2], double r1[2],
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double p2[2], double q2[2], double r2[2]);
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/* some 3D macros */
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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) 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 SCALAR(dest,alpha,v) dest[0] = alpha * v[0]; \
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dest[1] = alpha * v[1]; \
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dest[2] = alpha * v[2];
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#define CHECK_MIN_MAX(p1,q1,r1,p2,q2,r2) {\
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SUB(v1,p2,q1)\
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SUB(v2,p1,q1)\
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CROSS(N1,v1,v2)\
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SUB(v1,q2,q1)\
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if (DOT(v1,N1) > 0.0f) return 0;\
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SUB(v1,p2,p1)\
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SUB(v2,r1,p1)\
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CROSS(N1,v1,v2)\
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SUB(v1,r2,p1) \
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if (DOT(v1,N1) > 0.0f) return 0;\
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else return 1; }
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/* Permutation in a canonical form of T2's vertices */
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#define TRI_TRI_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2) { \
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if (dp2 > 0.0f) { \
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if (dq2 > 0.0f) CHECK_MIN_MAX(p1,r1,q1,r2,p2,q2) \
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else if (dr2 > 0.0f) CHECK_MIN_MAX(p1,r1,q1,q2,r2,p2)\
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else CHECK_MIN_MAX(p1,q1,r1,p2,q2,r2) }\
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else if (dp2 < 0.0f) { \
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if (dq2 < 0.0f) CHECK_MIN_MAX(p1,q1,r1,r2,p2,q2)\
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else if (dr2 < 0.0f) CHECK_MIN_MAX(p1,q1,r1,q2,r2,p2)\
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else CHECK_MIN_MAX(p1,r1,q1,p2,q2,r2)\
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} else { \
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if (dq2 < 0.0f) { \
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if (dr2 >= 0.0f) CHECK_MIN_MAX(p1,r1,q1,q2,r2,p2)\
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else CHECK_MIN_MAX(p1,q1,r1,p2,q2,r2)\
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} \
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else if (dq2 > 0.0f) { \
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if (dr2 > 0.0f) CHECK_MIN_MAX(p1,r1,q1,p2,q2,r2)\
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else CHECK_MIN_MAX(p1,q1,r1,q2,r2,p2)\
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} \
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else { \
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if (dr2 > 0.0f) CHECK_MIN_MAX(p1,q1,r1,r2,p2,q2)\
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else if (dr2 < 0.0f) CHECK_MIN_MAX(p1,r1,q1,r2,p2,q2)\
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else return coplanar_tri_tri3d(p1,q1,r1,p2,q2,r2,N1,N2);\
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}}}
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/*
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*
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* Three-dimensional Triangle-Triangle Overlap Test
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*
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*/
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int tri_tri_overlap_test_3d(double p1[3], double q1[3], double r1[3],
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double p2[3], double q2[3], double r2[3])
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{
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double dp1, dq1, dr1, dp2, dq2, dr2;
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double v1[3], v2[3];
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double N1[3], N2[3];
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/* Compute distance signs of p1, q1 and r1 to the plane of
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triangle(p2,q2,r2) */
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SUB(v1,p2,r2)
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SUB(v2,q2,r2)
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CROSS(N2,v1,v2)
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SUB(v1,p1,r2)
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dp1 = DOT(v1,N2);
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SUB(v1,q1,r2)
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dq1 = DOT(v1,N2);
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SUB(v1,r1,r2)
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dr1 = DOT(v1,N2);
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if (((dp1 * dq1) > 0.0f) && ((dp1 * dr1) > 0.0f)) return 0;
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/* Compute distance signs of p2, q2 and r2 to the plane of
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triangle(p1,q1,r1) */
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SUB(v1,q1,p1)
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SUB(v2,r1,p1)
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CROSS(N1,v1,v2)
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SUB(v1,p2,r1)
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dp2 = DOT(v1,N1);
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SUB(v1,q2,r1)
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dq2 = DOT(v1,N1);
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SUB(v1,r2,r1)
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dr2 = DOT(v1,N1);
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if (((dp2 * dq2) > 0.0f) && ((dp2 * dr2) > 0.0f)) return 0;
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/* Permutation in a canonical form of T1's vertices */
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if (dp1 > 0.0f) {
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if (dq1 > 0.0f) TRI_TRI_3D(r1,p1,q1,p2,r2,q2,dp2,dr2,dq2)
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else if (dr1 > 0.0f) TRI_TRI_3D(q1,r1,p1,p2,r2,q2,dp2,dr2,dq2)
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else TRI_TRI_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2)
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} else if (dp1 < 0.0f) {
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if (dq1 < 0.0f) TRI_TRI_3D(r1,p1,q1,p2,q2,r2,dp2,dq2,dr2)
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else if (dr1 < 0.0f) TRI_TRI_3D(q1,r1,p1,p2,q2,r2,dp2,dq2,dr2)
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else TRI_TRI_3D(p1,q1,r1,p2,r2,q2,dp2,dr2,dq2)
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} else {
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if (dq1 < 0.0f) {
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if (dr1 >= 0.0f) TRI_TRI_3D(q1,r1,p1,p2,r2,q2,dp2,dr2,dq2)
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else TRI_TRI_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2)
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}
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else if (dq1 > 0.0f) {
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if (dr1 > 0.0f) TRI_TRI_3D(p1,q1,r1,p2,r2,q2,dp2,dr2,dq2)
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else TRI_TRI_3D(q1,r1,p1,p2,q2,r2,dp2,dq2,dr2)
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}
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else {
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if (dr1 > 0.0f) TRI_TRI_3D(r1,p1,q1,p2,q2,r2,dp2,dq2,dr2)
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else if (dr1 < 0.0f) TRI_TRI_3D(r1,p1,q1,p2,r2,q2,dp2,dr2,dq2)
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else return coplanar_tri_tri3d(p1,q1,r1,p2,q2,r2,N1,N2);
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}
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}
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};
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int coplanar_tri_tri3d(double p1[3], double q1[3], double r1[3],
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double p2[3], double q2[3], double r2[3],
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double normal_1[3], double normal_2[3]){
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double P1[2],Q1[2],R1[2];
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double P2[2],Q2[2],R2[2];
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double n_x, n_y, n_z;
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n_x = ((normal_1[0]<0)?-normal_1[0]:normal_1[0]);
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n_y = ((normal_1[1]<0)?-normal_1[1]:normal_1[1]);
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n_z = ((normal_1[2]<0)?-normal_1[2]:normal_1[2]);
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/* Projection of the triangles in 3D onto 2D such that the area of
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the projection is maximized. */
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if (( n_x > n_z ) && ( n_x >= n_y )) {
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// Project onto plane YZ
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P1[0] = q1[2]; P1[1] = q1[1];
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Q1[0] = p1[2]; Q1[1] = p1[1];
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R1[0] = r1[2]; R1[1] = r1[1];
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P2[0] = q2[2]; P2[1] = q2[1];
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Q2[0] = p2[2]; Q2[1] = p2[1];
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R2[0] = r2[2]; R2[1] = r2[1];
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} else if (( n_y > n_z ) && ( n_y >= n_x )) {
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// Project onto plane XZ
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P1[0] = q1[0]; P1[1] = q1[2];
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Q1[0] = p1[0]; Q1[1] = p1[2];
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R1[0] = r1[0]; R1[1] = r1[2];
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P2[0] = q2[0]; P2[1] = q2[2];
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Q2[0] = p2[0]; Q2[1] = p2[2];
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R2[0] = r2[0]; R2[1] = r2[2];
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} else {
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// Project onto plane XY
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P1[0] = p1[0]; P1[1] = p1[1];
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Q1[0] = q1[0]; Q1[1] = q1[1];
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R1[0] = r1[0]; R1[1] = r1[1];
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P2[0] = p2[0]; P2[1] = p2[1];
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Q2[0] = q2[0]; Q2[1] = q2[1];
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R2[0] = r2[0]; R2[1] = r2[1];
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}
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return tri_tri_overlap_test_2d(P1,Q1,R1,P2,Q2,R2);
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};
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/*
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*
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* Three-dimensional Triangle-Triangle Intersection
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*
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*/
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/*
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This macro is called when the triangles surely intersect
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It constructs the segment of intersection of the two triangles
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if they are not coplanar.
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*/
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#define CONSTRUCT_INTERSECTION(p1,q1,r1,p2,q2,r2) { \
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SUB(v1,q1,p1) \
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SUB(v2,r2,p1) \
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CROSS(N,v1,v2) \
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SUB(v,p2,p1) \
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if (DOT(v,N) > 0.0f) {\
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SUB(v1,r1,p1) \
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CROSS(N,v1,v2) \
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if (DOT(v,N) <= 0.0f) { \
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SUB(v2,q2,p1) \
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CROSS(N,v1,v2) \
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if (DOT(v,N) > 0.0f) { \
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SUB(v1,p1,p2) \
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SUB(v2,p1,r1) \
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alpha = DOT(v1,N2) / DOT(v2,N2); \
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SCALAR(v1,alpha,v2) \
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SUB(source,p1,v1) \
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SUB(v1,p2,p1) \
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SUB(v2,p2,r2) \
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alpha = DOT(v1,N1) / DOT(v2,N1); \
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SCALAR(v1,alpha,v2) \
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SUB(target,p2,v1) \
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return 1; \
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} else { \
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SUB(v1,p2,p1) \
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SUB(v2,p2,q2) \
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alpha = DOT(v1,N1) / DOT(v2,N1); \
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SCALAR(v1,alpha,v2) \
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SUB(source,p2,v1) \
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SUB(v1,p2,p1) \
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SUB(v2,p2,r2) \
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alpha = DOT(v1,N1) / DOT(v2,N1); \
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SCALAR(v1,alpha,v2) \
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SUB(target,p2,v1) \
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return 1; \
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} \
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} else { \
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return 0; \
|
||
|
|
} \
|
||
|
|
} else { \
|
||
|
|
SUB(v2,q2,p1) \
|
||
|
|
CROSS(N,v1,v2) \
|
||
|
|
if (DOT(v,N) < 0.0f) { \
|
||
|
|
return 0; \
|
||
|
|
} else { \
|
||
|
|
SUB(v1,r1,p1) \
|
||
|
|
CROSS(N,v1,v2) \
|
||
|
|
if (DOT(v,N) >= 0.0f) { \
|
||
|
|
SUB(v1,p1,p2) \
|
||
|
|
SUB(v2,p1,r1) \
|
||
|
|
alpha = DOT(v1,N2) / DOT(v2,N2); \
|
||
|
|
SCALAR(v1,alpha,v2) \
|
||
|
|
SUB(source,p1,v1) \
|
||
|
|
SUB(v1,p1,p2) \
|
||
|
|
SUB(v2,p1,q1) \
|
||
|
|
alpha = DOT(v1,N2) / DOT(v2,N2); \
|
||
|
|
SCALAR(v1,alpha,v2) \
|
||
|
|
SUB(target,p1,v1) \
|
||
|
|
return 1; \
|
||
|
|
} else { \
|
||
|
|
SUB(v1,p2,p1) \
|
||
|
|
SUB(v2,p2,q2) \
|
||
|
|
alpha = DOT(v1,N1) / DOT(v2,N1); \
|
||
|
|
SCALAR(v1,alpha,v2) \
|
||
|
|
SUB(source,p2,v1) \
|
||
|
|
SUB(v1,p1,p2) \
|
||
|
|
SUB(v2,p1,q1) \
|
||
|
|
alpha = DOT(v1,N2) / DOT(v2,N2); \
|
||
|
|
SCALAR(v1,alpha,v2) \
|
||
|
|
SUB(target,p1,v1) \
|
||
|
|
return 1; \
|
||
|
|
}}}}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
#define TRI_TRI_INTER_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2) { \
|
||
|
|
if (dp2 > 0.0f) { \
|
||
|
|
if (dq2 > 0.0f) CONSTRUCT_INTERSECTION(p1,r1,q1,r2,p2,q2) \
|
||
|
|
else if (dr2 > 0.0f) CONSTRUCT_INTERSECTION(p1,r1,q1,q2,r2,p2)\
|
||
|
|
else CONSTRUCT_INTERSECTION(p1,q1,r1,p2,q2,r2) }\
|
||
|
|
else if (dp2 < 0.0f) { \
|
||
|
|
if (dq2 < 0.0f) CONSTRUCT_INTERSECTION(p1,q1,r1,r2,p2,q2)\
|
||
|
|
else if (dr2 < 0.0f) CONSTRUCT_INTERSECTION(p1,q1,r1,q2,r2,p2)\
|
||
|
|
else CONSTRUCT_INTERSECTION(p1,r1,q1,p2,q2,r2)\
|
||
|
|
} else { \
|
||
|
|
if (dq2 < 0.0f) { \
|
||
|
|
if (dr2 >= 0.0f) CONSTRUCT_INTERSECTION(p1,r1,q1,q2,r2,p2)\
|
||
|
|
else CONSTRUCT_INTERSECTION(p1,q1,r1,p2,q2,r2)\
|
||
|
|
} \
|
||
|
|
else if (dq2 > 0.0f) { \
|
||
|
|
if (dr2 > 0.0f) CONSTRUCT_INTERSECTION(p1,r1,q1,p2,q2,r2)\
|
||
|
|
else CONSTRUCT_INTERSECTION(p1,q1,r1,q2,r2,p2)\
|
||
|
|
} \
|
||
|
|
else { \
|
||
|
|
if (dr2 > 0.0f) CONSTRUCT_INTERSECTION(p1,q1,r1,r2,p2,q2)\
|
||
|
|
else if (dr2 < 0.0f) CONSTRUCT_INTERSECTION(p1,r1,q1,r2,p2,q2)\
|
||
|
|
else { \
|
||
|
|
*coplanar = 1; \
|
||
|
|
return coplanar_tri_tri3d(p1,q1,r1,p2,q2,r2,N1,N2);\
|
||
|
|
} \
|
||
|
|
}} }
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
The following version computes the segment of intersection of the
|
||
|
|
two triangles if it exists.
|
||
|
|
coplanar returns whether the triangles are coplanar
|
||
|
|
source and target are the endpoints of the line segment of intersection
|
||
|
|
*/
|
||
|
|
|
||
|
|
int tri_tri_intersection_test_3d(double p1[3], double q1[3], double r1[3],
|
||
|
|
double p2[3], double q2[3], double r2[3],
|
||
|
|
int * coplanar,
|
||
|
|
double source[3], double target[3] )
|
||
|
|
|
||
|
|
{
|
||
|
|
double dp1, dq1, dr1, dp2, dq2, dr2;
|
||
|
|
double v1[3], v2[3], v[3];
|
||
|
|
double N1[3], N2[3], N[3];
|
||
|
|
double alpha;
|
||
|
|
|
||
|
|
// Compute distance signs of p1, q1 and r1
|
||
|
|
// to the plane of triangle(p2,q2,r2)
|
||
|
|
|
||
|
|
|
||
|
|
SUB(v1,p2,r2)
|
||
|
|
SUB(v2,q2,r2)
|
||
|
|
CROSS(N2,v1,v2)
|
||
|
|
|
||
|
|
SUB(v1,p1,r2)
|
||
|
|
dp1 = DOT(v1,N2);
|
||
|
|
SUB(v1,q1,r2)
|
||
|
|
dq1 = DOT(v1,N2);
|
||
|
|
SUB(v1,r1,r2)
|
||
|
|
dr1 = DOT(v1,N2);
|
||
|
|
|
||
|
|
if (((dp1 * dq1) > 0.0f) && ((dp1 * dr1) > 0.0f)) return 0;
|
||
|
|
|
||
|
|
// Compute distance signs of p2, q2 and r2
|
||
|
|
// to the plane of triangle(p1,q1,r1)
|
||
|
|
|
||
|
|
|
||
|
|
SUB(v1,q1,p1)
|
||
|
|
SUB(v2,r1,p1)
|
||
|
|
CROSS(N1,v1,v2)
|
||
|
|
|
||
|
|
SUB(v1,p2,r1)
|
||
|
|
dp2 = DOT(v1,N1);
|
||
|
|
SUB(v1,q2,r1)
|
||
|
|
dq2 = DOT(v1,N1);
|
||
|
|
SUB(v1,r2,r1)
|
||
|
|
dr2 = DOT(v1,N1);
|
||
|
|
|
||
|
|
if (((dp2 * dq2) > 0.0f) && ((dp2 * dr2) > 0.0f)) return 0;
|
||
|
|
|
||
|
|
// Permutation in a canonical form of T1's vertices
|
||
|
|
|
||
|
|
|
||
|
|
if (dp1 > 0.0f) {
|
||
|
|
if (dq1 > 0.0f) TRI_TRI_INTER_3D(r1,p1,q1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
else if (dr1 > 0.0f) TRI_TRI_INTER_3D(q1,r1,p1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
|
||
|
|
else TRI_TRI_INTER_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
} else if (dp1 < 0.0f) {
|
||
|
|
if (dq1 < 0.0f) TRI_TRI_INTER_3D(r1,p1,q1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
else if (dr1 < 0.0f) TRI_TRI_INTER_3D(q1,r1,p1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
else TRI_TRI_INTER_3D(p1,q1,r1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
} else {
|
||
|
|
if (dq1 < 0.0f) {
|
||
|
|
if (dr1 >= 0.0f) TRI_TRI_INTER_3D(q1,r1,p1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
else TRI_TRI_INTER_3D(p1,q1,r1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
}
|
||
|
|
else if (dq1 > 0.0f) {
|
||
|
|
if (dr1 > 0.0f) TRI_TRI_INTER_3D(p1,q1,r1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
else TRI_TRI_INTER_3D(q1,r1,p1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
if (dr1 > 0.0f) TRI_TRI_INTER_3D(r1,p1,q1,p2,q2,r2,dp2,dq2,dr2)
|
||
|
|
else if (dr1 < 0.0f) TRI_TRI_INTER_3D(r1,p1,q1,p2,r2,q2,dp2,dr2,dq2)
|
||
|
|
else {
|
||
|
|
// triangles are co-planar
|
||
|
|
|
||
|
|
*coplanar = 1;
|
||
|
|
return coplanar_tri_tri3d(p1,q1,r1,p2,q2,r2,N1,N2);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
*
|
||
|
|
* Two dimensional Triangle-Triangle Overlap Test
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
/* some 2D macros */
|
||
|
|
|
||
|
|
#define ORIENT_2D(a, b, c) ((a[0]-c[0])*(b[1]-c[1])-(a[1]-c[1])*(b[0]-c[0]))
|
||
|
|
|
||
|
|
|
||
|
|
#define INTERSECTION_TEST_VERTEX(P1, Q1, R1, P2, Q2, R2) {\
|
||
|
|
if (ORIENT_2D(R2,P2,Q1) >= 0.0f)\
|
||
|
|
if (ORIENT_2D(R2,Q2,Q1) <= 0.0f)\
|
||
|
|
if (ORIENT_2D(P1,P2,Q1) > 0.0f) {\
|
||
|
|
if (ORIENT_2D(P1,Q2,Q1) <= 0.0f) return 1; \
|
||
|
|
else return 0;} else {\
|
||
|
|
if (ORIENT_2D(P1,P2,R1) >= 0.0f)\
|
||
|
|
if (ORIENT_2D(Q1,R1,P2) >= 0.0f) return 1; \
|
||
|
|
else return 0;\
|
||
|
|
else return 0;}\
|
||
|
|
else \
|
||
|
|
if (ORIENT_2D(P1,Q2,Q1) <= 0.0f)\
|
||
|
|
if (ORIENT_2D(R2,Q2,R1) <= 0.0f)\
|
||
|
|
if (ORIENT_2D(Q1,R1,Q2) >= 0.0f) return 1; \
|
||
|
|
else return 0;\
|
||
|
|
else return 0;\
|
||
|
|
else return 0;\
|
||
|
|
else\
|
||
|
|
if (ORIENT_2D(R2,P2,R1) >= 0.0f) \
|
||
|
|
if (ORIENT_2D(Q1,R1,R2) >= 0.0f)\
|
||
|
|
if (ORIENT_2D(P1,P2,R1) >= 0.0f) return 1;\
|
||
|
|
else return 0;\
|
||
|
|
else \
|
||
|
|
if (ORIENT_2D(Q1,R1,Q2) >= 0.0f) {\
|
||
|
|
if (ORIENT_2D(R2,R1,Q2) >= 0.0f) return 1; \
|
||
|
|
else return 0; }\
|
||
|
|
else return 0; \
|
||
|
|
else return 0; \
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
#define INTERSECTION_TEST_EDGE(P1, Q1, R1, P2, Q2, R2) { \
|
||
|
|
if (ORIENT_2D(R2,P2,Q1) >= 0.0f) {\
|
||
|
|
if (ORIENT_2D(P1,P2,Q1) >= 0.0f) { \
|
||
|
|
if (ORIENT_2D(P1,Q1,R2) >= 0.0f) return 1; \
|
||
|
|
else return 0;} else { \
|
||
|
|
if (ORIENT_2D(Q1,R1,P2) >= 0.0f){ \
|
||
|
|
if (ORIENT_2D(R1,P1,P2) >= 0.0f) return 1; else return 0;} \
|
||
|
|
else return 0; } \
|
||
|
|
} else {\
|
||
|
|
if (ORIENT_2D(R2,P2,R1) >= 0.0f) {\
|
||
|
|
if (ORIENT_2D(P1,P2,R1) >= 0.0f) {\
|
||
|
|
if (ORIENT_2D(P1,R1,R2) >= 0.0f) return 1; \
|
||
|
|
else {\
|
||
|
|
if (ORIENT_2D(Q1,R1,R2) >= 0.0f) return 1; else return 0;}}\
|
||
|
|
else return 0; }\
|
||
|
|
else return 0; }}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
int ccw_tri_tri_intersection_2d(double p1[2], double q1[2], double r1[2],
|
||
|
|
double p2[2], double q2[2], double r2[2]) {
|
||
|
|
if ( ORIENT_2D(p2,q2,p1) >= 0.0f ) {
|
||
|
|
if ( ORIENT_2D(q2,r2,p1) >= 0.0f ) {
|
||
|
|
if ( ORIENT_2D(r2,p2,p1) >= 0.0f ) return 1;
|
||
|
|
else INTERSECTION_TEST_EDGE(p1,q1,r1,p2,q2,r2)
|
||
|
|
} else {
|
||
|
|
if ( ORIENT_2D(r2,p2,p1) >= 0.0f )
|
||
|
|
INTERSECTION_TEST_EDGE(p1,q1,r1,r2,p2,q2)
|
||
|
|
else INTERSECTION_TEST_VERTEX(p1,q1,r1,p2,q2,r2)}}
|
||
|
|
else {
|
||
|
|
if ( ORIENT_2D(q2,r2,p1) >= 0.0f ) {
|
||
|
|
if ( ORIENT_2D(r2,p2,p1) >= 0.0f )
|
||
|
|
INTERSECTION_TEST_EDGE(p1,q1,r1,q2,r2,p2)
|
||
|
|
else INTERSECTION_TEST_VERTEX(p1,q1,r1,q2,r2,p2)}
|
||
|
|
else INTERSECTION_TEST_VERTEX(p1,q1,r1,r2,p2,q2)}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
int tri_tri_overlap_test_2d(double p1[2], double q1[2], double r1[2],
|
||
|
|
double p2[2], double q2[2], double r2[2]) {
|
||
|
|
if ( ORIENT_2D(p1,q1,r1) < 0.0f )
|
||
|
|
if ( ORIENT_2D(p2,q2,r2) < 0.0f )
|
||
|
|
return ccw_tri_tri_intersection_2d(p1,r1,q1,p2,r2,q2);
|
||
|
|
else
|
||
|
|
return ccw_tri_tri_intersection_2d(p1,r1,q1,p2,q2,r2);
|
||
|
|
else
|
||
|
|
if ( ORIENT_2D(p2,q2,r2) < 0.0f )
|
||
|
|
return ccw_tri_tri_intersection_2d(p1,q1,r1,p2,r2,q2);
|
||
|
|
else
|
||
|
|
return ccw_tri_tri_intersection_2d(p1,q1,r1,p2,q2,r2);
|
||
|
|
|
||
|
|
};
|
||
|
|
|