Computer Science Graduate Seminar
Monday, April 17, 2023, 10:00am
Quad Mesh Layout Structure Optimization
- Max Lyon M.Sc. - Chair of Computer Science 8
- Place: Building E3, seminar room 118, Ahornstr. 55
Quad meshes are very useful in many applications such as modeling and animation in the entertainment industry, simulation in the construction industry, or as intermediate representation to form easily editable spline surfaces. Some of the interesting properties of quad meshes compared to triangular meshes are natural alignment of edges to the surface's principal curvature directions and their ability to form highly anisotropic elements without the need of excessively small angles. Therefore, the computer aided or fully automatic generation of quad meshes has been a research focus for many years and is probably going to remain as such for the foreseeable future. One set of methods that have proven to be particularly well suited for the generation of high quality quad meshes are centered around the creation of an integer-grid map, i.e. a parametrization of the surface into the 2D domain whose parametric integer iso-lines induce a quad mesh structure on the input mesh. These methods offer a high degree of control over the desired sizing and alignment of the resulting quads and generally achieve high element quality. Unfortunately, they disregard the high level structure, i.e. how the irregular vertices of the resulting quad mesh are connected by edge strips. Ideally, these edges form a coarse quad layout, enabling the use of highly efficient multigrid solvers or the manual editing of a small number of spline patches. In this thesis we give an overview of current state-of-the-art quad meshing algorithms which we then improve upon in different aspects: We show how a valid quad mesh can always be extracted for the given layout via careful re-embedding of a so called motorcycle graph combined with patchwise harmonic parametrizations followed by a global optimization. We extend the motorcycle graph construction in order to lift the constraints of layouts having to exactly follow the boundaries of the mesh leading to meshes with less distortion whose quads can be cut off by the boundary at an arbitrary angle. Further, we present a method that is guaranteed to yield a coarse quad layout that adheres to a minimum quality as defined by the user defined maximal allowed deviation of layout arcs from desired direction. For cases where strict adherence to the input field is not required we show how singularities may be moved to better locations or removed entirely to further improve the resulting layout structure. Finally, we discuss how a quad mesh or layout may be refined in order to achieve a locally increased resolution or anisotropy.
The computer science lecturers invite interested people to join.