Hexagonal Meshes with Planar Faces
Wenping Wang, Yang Liu, Dong‐Ming Yan, Bin Chan, Ruotian Ling, Feng Rui Sun · 2008
Figure 1: (Left): A conceptual architectural structure as a P-Hex mesh, computed using the progressive conjugation method. The interior view (top right) shows that the shapes of the P-Hex faces transit smoothly across the parabolic curve. (Bottom right): another P-Hex mesh of free form shape. Free-form meshes with planar hexagonal faces, to be called P-Hex meshes, provide a useful surface representation in discrete differential geometry and are demanded in architectural design for representing surfaces built with planar glass/metal panels. We study the geometry of P-Hex meshes and present an algorithm for computing a free-form P-Hex mesh of a specified shape. Our algorithm first computes a regular triangulation of a given surface and then turns it into a P-Hex mesh approximating the surface. A novel local duality transformation, called Dupin duality, is introduced for studying relationship between triangular meshes and for controlling the face shapes of P-Hex meshes. This report is based on the results presented at Workshop ”Polyhedral Surfaces and Industrial Applications ” held on September 15-