CAD Tools for Creating Space-filling 3D Escher Tiles
We discuss the design and implementation of CAD tools for creating decorative solids that tile 3-space in a regular, isohedral manner. Starting with the simplest case of extruded 2D tilings, we describe geometric algorithms used for maintaining boundary representations of 3D tiles, including a Java implementation of an interactive constrained Delaunay triangulation library and a mesh-cutting algorithm used in layering extruded tiles to create more intricate designs. Finally, we demonstrate a CAD tool for creating 3D tilings that are derived from cubic lattices. The design process for these 3D tiles is more constrained, and hence more difficult, than in the 2D case, and it raises additional user interface issues.
Mark Howison and Carlo H. Séquin. "CAD Tools for Creating Space-filling 3D Escher Tiles". Computer-Aided Design and Applications, 6(6):737–748, June 2009.