Trimming implicit surfaces

Escher's spirals A Simple sphere B Trimming solid 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.

Trimmed blobby D Blobby E
D = E \ C

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

Head H Trimmed head 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.

Superellipsoid K Trimming solid L
Trimmed surface 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.

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