Shape Optimization of Quad Mesh Elements(pdf)(slides)

Yufei Li, Wenping Wang, Ruotian Ling and Changhe Tu

To appear in Computers & Graphics (SMI 2011 - Shape Modeling International 2011).

We study the problem of optimizing the face elements of a quad mesh surface, that is, resampling a given quad mesh to make it possess, as much as possible, face elements of some desired aspect ratio and size. Unlike previous quad mesh optimization/improvement methods based on local operations on a small group of elements, we adopt a global approach that does not introduce extra singularities and therefore preserves the original quad structure of the input mesh. Starting from a collection of quad patches extracted from an input quad mesh, two global operations, i.e. resampling and re-distribution, are performed to optimize the number and spacings of grid lines in each patch. Both operations are formulated as simple optimization problems with linear constraints.

Optimal Sampling of Parametric Surfaces (pdf)(slides)

Yufei Li, Wenping Wang and Changhe Tu

To appear in Computer-Aided Design and Applications (CAD Conference and Exhibition 2011)

We study the problem of optimally sampling parametric surfaces by means of reparameterization. A criterion is first formulated for measuring the parameterization quality of a given surface. According to this criterion, the optimal parameterization is identified for the surface by exploring admissible reparameterizations. Then the optimal sampling of the surface is obtained by uniformly sampling the parameter domain of the optimal parameterization.

Hexagonal Meshes with Planar Faces (pdf) (examples)

Technical Report, TR-2008-13, 2008, HKU

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.