Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features.

Figure optionsDownload high-quality image (192 K)Download as PowerPoint slideHighlights
► We present a novel technique for the construction of a base triangulation using linear system solves that reconstructs input feature sites and curves.
► We map quadrilateral elements over a base triangulation using templates that allow flexible and tuneable layout designs; as well as provide a means to generate regular connectivity aligned to important surface features.
► We apply a graph matching algorithm, in a novel way, to automatically arrange templates on the base triangulation in an optimal manner.
► We propose a novel metric to optimize the orthogonality and planarity during the graph matching template arrangement procedure.