Duality

In the present work, we attempted at expressing human “two-facedness” by the “two-sidedness” of the 3D structures. In the field of geometry, there exists a two-facedness called “duality,” which represents the relationship between diagrams that switch between faces (cells) and vertices. Delaunay diagram and Voronoi diagram give a typical example. We have developed an algorithm to generate a Poisson-disk distribution in an arbitrary shape to make sculptures with those diagrams. The Delaunay diagram generated by Poisson-disk distribution point cloud makes up the uniform tetrahedral mesh (except for the surface). Since those cells are close to a regular tetrahedron, Voronoi vertices located on the circumcenters also have an almost uniform distribution.