Trimming implicit surfaces

A B C

A = B \ C

A is a trimmed implicit surface (2-manifold with boundary) - set difference of B and C,
B is a spherical surface,
C is a solid constructed by sweeping and set-theoretic operations.

D E

D = E \ C

D is a trimmed blobby surface - set difference of E and C,
E is a blobby surface.

H F

F = H \ C

This work was inspired by art works of M.C. Escher, namely “Sphere Spirals” (1958) (see them redesigned in the top figure) and “Bond of Union” (1956), showing spiral shaped surface sheets cut of a sphere and human head surfaces.

K L
M

M = K \ L

G. Pasko, A. Pasko “Trimming implicit surfaces”, The Visual Computer, vol. 20, No. 7, 2004, pp. 437-447.
Electronic version: PDF (871 K)

B. Schmitt, A. Pasko, G. Pasko, T. Kunii , Rendering trimmed implicit surfaces and curves, AFRIGRAPH 2004 Proceedings, publication of ACM SIGGRAPH, 2004, pp. 7-13.