Geometry and Computation of Mesh Surfaces with Planar Hexagonal Faces

Thursday, May 31, 2007 - 9:00am - 9:50am
EE/CS 3-180
Wenping Wang (University of Hong Kong)
Joint work with Yang Liu.

Motivated by applications in modeling glass structures in
architecture, we consider the geometry and computation of mesh
surfaces with planar hexagonal faces from the point of view
of discrete differential geometry. It is shown that the
mesh structure is naturally related to conjugate curve networks on
its underlying smooth surface; furthermore, the shape of each
hexagonal face is in the limit related to the Dupin indicatrix.
These results are used in combination with an optimization method
to compute a mesh surface with planar hexagonal faces to approximate
a given smooth surface.