Hello. I am using Ubuntu 20.04 with a Beowulf Cluster with 20 processors to create animation in ParaView using C. The solution to the differential equation for the harmonic function in spherical coordinates does not converge at the poles of a sphere. If I draw a sphere and avoid the poles so that stresses on the sphere properly converge, then I get a hole in the sphere at the poles. I would like to completely draw the sphere and then add stress values on the sphere at locations away from the poles and yet have the sphere display data.

This is the code to draw the sphere:

fid = fopen(filenamesphere,“w”);

```
fprintf(fid,"# vtk DataFile Version 2.0\nSphere example\nASCII\n");
fprintf(fid,"DATASET STRUCTURED_GRID\n");
fprintf(fid,"DIMENSIONS %d %d %d\n",1,ntheta,nphi);
fprintf(fid,"POINTS %d float\n",npoints);
for (i=0;i<npoints;i++) fprintf(fid,"%f %f %f\n",x[i],y[i],z[i]);
fprintf(fid,"POINT_DATA %d\n",npoints);
fprintf(fid,"SCALARS stress float\n");
fprintf(fid,"LOOKUP_TABLE default\n");
for (i=0;i<npoints;i++) fprintf(fid,"%f\n",stress[i]);
fclose(fid);
```

Using this code, the stresses, stress(i), are at the same points as those used in drawing the sphere. How do I pass secondary locations on the sphere so that I can pass stresses to those locations and thereby avoid the poles where the solution does not converge?

Thank you for your help.