Ziyan Yang
Dr. Dianna Xu
Computer Science

Provably good quadrilateral mesh generation

Polygon meshes define the shape of digital objects and are needed in digital modeling and simulations of all types. In my summer research project, my mentor and I focus on quadrilateral mesh construction of 2D polygons. We have existing quadtree-based quadrilateral mesh construction algorithms to create a quadrilateral mesh of simple polygons that can have holes. Our existing algorithms guarantee the minimum/maximum angles and aspect ratios of elements of mesh but do not mesh a polygon completely: there still exist gaps between edges of original polygons and our constructed mesh boundaries. Our next step is to smooth the boundaries of mesh to make them as parallel as possible to the polygon edges. First, we need to classify all the possible mesh boundaries and figure out different ways to optimize them. Then, I will modify the codes to test our assumptions and the solutions for smoothing. Finally, after optimizing the mesh boundaries, we can start think of how to make up the space between mesh boundaries and polygon edges. It may be useful to add buffer zones and re-mesh the space to guarantee our original minimum/maximum angles and aspect ratios because these criterion are significant in determining the quality of the mesh.