Shape optimization of quad mesh elements

We study the problem of optimizing the face elements of a quad mesh surface, that is, re-sampling 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. re-sampling 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.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (67 K)Download as PowerPoint slideHighlights► We have introduced a framework for optimizing the shape of quad mesh elements. ► It does not change the mesh structure or introduce extra singular vertices. ► It is simple and flexible, and can handle both isotropic and anisotropic cases.