Lace-shell torus
Geometry
The pattern lives on the flat (u,v) parameter rectangle of the torus, not in space. That rectangle is divided into M cells around the ring and N cells around the tube, and one opening is centred in each cell.
P(u,v) = ((R + r cos v) cos u, (R + r cos v) sin u, r sin v)x = ((u − uc) M / π), y = ((v − vc) N / π) → cell coordinates in [−1,1]
Teardrops, diamonds, leaves and rounds are all simple tests on (x,y), so a change of shape is a change of one inequality. Any face whose centre falls inside an opening is simply not drawn — the mesh is not remapped, it is cut.
Opening size is then modulated by b(u) = (0.5 + 0.5 cos(k u))^p, and the opening shrinks to nothing where b is 1. Those are the solid bands: k of them around the ring, with p setting how narrow they are. They are what keeps a dense pattern legible.
Because the shell is perforated, nothing is culled: every face is drawn sorted by depth and shaded with |n · light|, so the far inner wall shows through the openings and the piece reads as a hollow vessel.