Page 316 - The Combined Finite-Discrete Element Method

POTENTIAL CONTACT FORCE IN 3D 299

.............continued from previous listing..............
/* distances of C-points from S edges */
niners=0; ninerc=0;
for(i=0;i<nspoin;i++)
{ inext=i+1;
if(inext>=nspoin)inext=0;
for(j=0;j<3;j++)
{ jnext=j+1;
if(jnext>2)jnext=0;
dcs[j][i]=(uc[jnext]-uc[j])*(vs[i]-vc[j])-
(vc[jnext]-vc[j])*(us[i]-uc[j]);
dsc[i][j]=(us[inext]-us[i])*(vc[j]-vs[i])-
(vs[inext]-vs[i])*(uc[j]-us[i]);
if(dsc[i][j]>=R0)
{ innerc[j]=innerc[j]+1;
if(innerc[j]==nspoin)ninerc=ninerc+1;
}
if(dcs[j][i]>=R0)
{ inners[i]=inners[i]+1;
if(inners[i]==3)niners=niners+1;
}} }
.............continued in the next listing...........

Listing 10.12 Distance dcs[j][i] from the edges of a C-triangle to S-points (nodes of S-polygon);
and distance dsc[i][j] from the edges of an S-polygon to C-points (edges of C-triangle).

The intersection between the C-triangle and S-polygon is called a B-polygon. A B-
polygon is the area through which the current target sub-tetrahedron is interacting with
the current surface of the current contactor tetrahedron. The nodes of the B-polygon
polygon are called B-points.
Three sceanarios are possible:

• C-triangle is inside the S-polygon, as shown in Listing 10.13.
• S-polygon is inside the C-triangle (Listing 10.14).
• General case of polygon-triangle intersection (Listing 10.15).
A general case of polygon-triangle intersection is illustrated in Figure 10.2, where both
S and B points are shown. In the example shown in the figure, S-points form a triangle.

.............continued from previous listing..............
/* distances of C-points from S edges */
/* B-points */
if(ninerc==3) /* triangle inside polygon */
{ nbpoin=3;
for(i=0;i<nbpoin;i++)
{ ub[i]=uc[i]; vb[i]=vc[i];
}}
...........continued in the next listing...........
Listing 10.13 Calculation of B-points when the C-triangle is inside an S-polygon.