JKA: MP Source

00001 /* Triangle/triangle intersection test routine,
00002  * by Tomas Moller, 1997.
00003  * See article "A Fast Triangle-Triangle Intersection Test",
00004  * Journal of Graphics Tools, 2(2), 1997
00005  *
00006  * int tri_tri_intersect(float V0[3],float V1[3],float V2[3],
00007  *                         float U0[3],float U1[3],float U2[3])
00008  *
00009  * parameters: vertices of triangle 1: V0,V1,V2
00010  *             vertices of triangle 2: U0,U1,U2
00011  * result    : returns 1 if the triangles intersect, otherwise 0
00012  *
00013  */
00014 
00015 #include <math.h>
00016 #include "../game/q_shared.h"
00017 #include "../game/g_local.h"
00018 
00019 /* if USE_EPSILON_TEST is true then we do a check: 
00020          if |dv|<EPSILON then dv=0.0;
00021    else no check is done (which is less robust)
00022 */
00023 #define USE_EPSILON_TEST 1
00024 #define EPSILON 0.000001
00025 
00026 
00027 /* some macros */
00028 #define CROSS(dest,v1,v2)                      \
00029               dest[0]=v1[1]*v2[2]-v1[2]*v2[1]; \
00030               dest[1]=v1[2]*v2[0]-v1[0]*v2[2]; \
00031               dest[2]=v1[0]*v2[1]-v1[1]*v2[0];
00032 
00033 #define DOT(v1,v2) (v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])
00034 
00035 #define SUB(dest,v1,v2)          \
00036             dest[0]=v1[0]-v2[0]; \
00037             dest[1]=v1[1]-v2[1]; \
00038             dest[2]=v1[2]-v2[2]; 
00039 
00040 /* sort so that a<=b */
00041 #define SORT(a,b)       \
00042              if(a>b)    \
00043              {          \
00044                float c; \
00045                c=a;     \
00046                a=b;     \
00047                b=c;     \
00048              }
00049 
00050 #define ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1) \
00051               isect0=VV0+(VV1-VV0)*D0/(D0-D1);    \
00052               isect1=VV0+(VV2-VV0)*D0/(D0-D2);
00053 
00054 
00055 #define COMPUTE_INTERVALS(VV0,VV1,VV2,D0,D1,D2,D0D1,D0D2,isect0,isect1) \
00056   if(D0D1>0.0f)                                         \
00057   {                                                     \
00058     /* here we know that D0D2<=0.0 */                   \
00059     /* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
00060     ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1);          \
00061   }                                                     \
00062   else if(D0D2>0.0f)                                    \
00063   {                                                     \
00064     /* here we know that d0d1<=0.0 */                   \
00065     ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1);          \
00066   }                                                     \
00067   else if(D1*D2>0.0f || D0!=0.0f)                       \
00068   {                                                     \
00069     /* here we know that d0d1<=0.0 or that D0!=0.0 */   \
00070     ISECT(VV0,VV1,VV2,D0,D1,D2,isect0,isect1);          \
00071   }                                                     \
00072   else if(D1!=0.0f)                                     \
00073   {                                                     \
00074     ISECT(VV1,VV0,VV2,D1,D0,D2,isect0,isect1);          \
00075   }                                                     \
00076   else if(D2!=0.0f)                                     \
00077   {                                                     \
00078     ISECT(VV2,VV0,VV1,D2,D0,D1,isect0,isect1);          \
00079   }                                                     \
00080   else                                                  \
00081   {                                                     \
00082     /* triangles are coplanar */                        \
00083     return coplanar_tri_tri(N1,V0,V1,V2,U0,U1,U2);      \
00084   }
00085 
00086 
00087 
00088 /* this edge to edge test is based on Franlin Antonio's gem:
00089    "Faster Line Segment Intersection", in Graphics Gems III,
00090    pp. 199-202 */ 
00091 #define EDGE_EDGE_TEST(V0,U0,U1)                      \
00092   Bx=U0[i0]-U1[i0];                                   \
00093   By=U0[i1]-U1[i1];                                   \
00094   Cx=V0[i0]-U0[i0];                                   \
00095   Cy=V0[i1]-U0[i1];                                   \
00096   f=Ay*Bx-Ax*By;                                      \
00097   d=By*Cx-Bx*Cy;                                      \
00098   if((f>0 && d>=0 && d<=f) || (f<0 && d<=0 && d>=f))  \
00099   {                                                   \
00100     e=Ax*Cy-Ay*Cx;                                    \
00101     if(f>0)                                           \
00102     {                                                 \
00103       if(e>=0 && e<=f) return 1;                      \
00104     }                                                 \
00105     else                                              \
00106     {                                                 \
00107       if(e<=0 && e>=f) return 1;                      \
00108     }                                                 \
00109   }                                
00110 
00111 #define EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2) \
00112 {                                              \
00113   float Ax,Ay,Bx,By,Cx,Cy,e,d,f;               \
00114   Ax=V1[i0]-V0[i0];                            \
00115   Ay=V1[i1]-V0[i1];                            \
00116   /* test edge U0,U1 against V0,V1 */          \
00117   EDGE_EDGE_TEST(V0,U0,U1);                    \
00118   /* test edge U1,U2 against V0,V1 */          \
00119   EDGE_EDGE_TEST(V0,U1,U2);                    \
00120   /* test edge U2,U1 against V0,V1 */          \
00121   EDGE_EDGE_TEST(V0,U2,U0);                    \
00122 }
00123 
00124 #define POINT_IN_TRI(V0,U0,U1,U2)           \
00125 {                                           \
00126   float a,b,c,d0,d1,d2;                     \
00127   /* is T1 completly inside T2? */          \
00128   /* check if V0 is inside tri(U0,U1,U2) */ \
00129   a=U1[i1]-U0[i1];                          \
00130   b=-(U1[i0]-U0[i0]);                       \
00131   c=-a*U0[i0]-b*U0[i1];                     \
00132   d0=a*V0[i0]+b*V0[i1]+c;                   \
00133                                             \
00134   a=U2[i1]-U1[i1];                          \
00135   b=-(U2[i0]-U1[i0]);                       \
00136   c=-a*U1[i0]-b*U1[i1];                     \
00137   d1=a*V0[i0]+b*V0[i1]+c;                   \
00138                                             \
00139   a=U0[i1]-U2[i1];                          \
00140   b=-(U0[i0]-U2[i0]);                       \
00141   c=-a*U2[i0]-b*U2[i1];                     \
00142   d2=a*V0[i0]+b*V0[i1]+c;                   \
00143   if(d0*d1>0.0)                             \
00144   {                                         \
00145     if(d0*d2>0.0) return 1;                 \
00146   }                                         \
00147 }
00148 
00149 qboolean coplanar_tri_tri(vec3_t N,vec3_t V0,vec3_t V1,vec3_t V2,
00150                      vec3_t U0,vec3_t U1,vec3_t U2)
00151 {
00152    vec3_t A;
00153    short i0,i1;
00154    /* first project onto an axis-aligned plane, that maximizes the area */
00155    /* of the triangles, compute indices: i0,i1. */
00156    A[0]=fabs(N[0]);
00157    A[1]=fabs(N[1]);
00158    A[2]=fabs(N[2]);
00159    if(A[0]>A[1])
00160    {
00161       if(A[0]>A[2])  
00162       {
00163           i0=1;      /* A[0] is greatest */
00164           i1=2;
00165       }
00166       else
00167       {
00168           i0=0;      /* A[2] is greatest */
00169           i1=1;
00170       }
00171    }
00172    else   /* A[0]<=A[1] */
00173    {
00174       if(A[2]>A[1])
00175       {
00176           i0=0;      /* A[2] is greatest */
00177           i1=1;                                           
00178       }
00179       else
00180       {
00181           i0=0;      /* A[1] is greatest */
00182           i1=2;
00183       }
00184     }               
00185                 
00186     /* test all edges of triangle 1 against the edges of triangle 2 */
00187     EDGE_AGAINST_TRI_EDGES(V0,V1,U0,U1,U2);
00188     EDGE_AGAINST_TRI_EDGES(V1,V2,U0,U1,U2);
00189     EDGE_AGAINST_TRI_EDGES(V2,V0,U0,U1,U2);
00190                 
00191     /* finally, test if tri1 is totally contained in tri2 or vice versa */
00192     POINT_IN_TRI(V0,U0,U1,U2);
00193     POINT_IN_TRI(U0,V0,V1,V2);
00194 
00195     return qfalse;
00196 }
00197 
00198 qboolean tri_tri_intersect(vec3_t V0,vec3_t V1,vec3_t V2,
00199                       vec3_t U0,vec3_t U1,vec3_t U2)
00200 {
00201   vec3_t E1,E2;
00202   vec3_t N1,N2;
00203   float d1,d2;
00204   float du0,du1,du2,dv0,dv1,dv2;
00205   vec3_t D;
00206   float isect1[2], isect2[2];
00207   float du0du1,du0du2,dv0dv1,dv0dv2;
00208   short index;
00209   float vp0,vp1,vp2;
00210   float up0,up1,up2;
00211   float b,c,max;
00212 
00213   /* compute plane equation of triangle(V0,V1,V2) */
00214   SUB(E1,V1,V0);
00215   SUB(E2,V2,V0);
00216   CROSS(N1,E1,E2);
00217   d1=-DOT(N1,V0);
00218   /* plane equation 1: N1.X+d1=0 */
00219 
00220   /* put U0,U1,U2 into plane equation 1 to compute signed distances to the plane*/
00221   du0=DOT(N1,U0)+d1;
00222   du1=DOT(N1,U1)+d1;
00223   du2=DOT(N1,U2)+d1;
00224 
00225   /* coplanarity robustness check */
00226 #if USE_EPSILON_TEST
00227   if(fabs(du0)<EPSILON) du0=0.0;
00228   if(fabs(du1)<EPSILON) du1=0.0;
00229   if(fabs(du2)<EPSILON) du2=0.0;
00230 #endif
00231   du0du1=du0*du1;
00232   du0du2=du0*du2;
00233 
00234   if(du0du1>0.0f && du0du2>0.0f) /* same sign on all of them + not equal 0 ? */
00235     return 0;                    /* no intersection occurs */
00236 
00237   /* compute plane of triangle (U0,U1,U2) */
00238   SUB(E1,U1,U0);
00239   SUB(E2,U2,U0);
00240   CROSS(N2,E1,E2);
00241   d2=-DOT(N2,U0);
00242   /* plane equation 2: N2.X+d2=0 */
00243 
00244   /* put V0,V1,V2 into plane equation 2 */
00245   dv0=DOT(N2,V0)+d2;
00246   dv1=DOT(N2,V1)+d2;
00247   dv2=DOT(N2,V2)+d2;
00248 
00249 #if USE_EPSILON_TEST
00250   if(fabs(dv0)<EPSILON) dv0=0.0;
00251   if(fabs(dv1)<EPSILON) dv1=0.0;
00252   if(fabs(dv2)<EPSILON) dv2=0.0;
00253 #endif
00254 
00255   dv0dv1=dv0*dv1;
00256   dv0dv2=dv0*dv2;
00257         
00258   if(dv0dv1>0.0f && dv0dv2>0.0f) /* same sign on all of them + not equal 0 ? */
00259     return 0;                    /* no intersection occurs */
00260 
00261   /* compute direction of intersection line */
00262   CROSS(D,N1,N2);
00263 
00264   /* compute and index to the largest component of D */
00265   max=fabs(D[0]);
00266   index=0;
00267   b=fabs(D[1]);
00268   c=fabs(D[2]);
00269   if(b>max) max=b,index=1;
00270   if(c>max) max=c,index=2;
00271 
00272         /* this is the simplified projection onto L*/
00273         vp0=V0[index];
00274         vp1=V1[index];
00275         vp2=V2[index];
00276 
00277         up0=U0[index];
00278         up1=U1[index];
00279         up2=U2[index];
00280 
00281   /* compute interval for triangle 1 */
00282   COMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,isect1[0],isect1[1]);
00283 
00284   /* compute interval for triangle 2 */
00285   COMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,isect2[0],isect2[1]);
00286 
00287   SORT(isect1[0],isect1[1]);
00288   SORT(isect2[0],isect2[1]);
00289 
00290   if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return qtrue;
00291   return qfalse;
00292 }
codemp/game/tri_coll_test.c
