SIGGRAPH 2016

In this paper we present a novel method for non-linear shape opti- mization of 3d objects given by their surface representation. Our method takes advantage of the fact that various shape properties of interest give rise to underdetermined design spaces implying the existence of many good solutions. Our algorithm exploits this by performing iterative projections of the problem to local subspaces where it can be solved much more efficiently using standard numer- ical routines. We demonstrate how this approach can be utilized for various shape optimization tasks using different shape parameteri- zations. In particular, we show how to efficiently optimize natural frequencies, mass properties, as well as the structural yield strength of a solid body. Our method is flexible, easy to implement, and very fast.

SIGGRAPH 2016

State-of-the-art hex meshing algorithms consist of three steps: Frame-field design, parametrization generation, and mesh extraction. However, while the first two steps are usually discussed in detail, the last step is often not well studied. In this paper, we fully concentrate on reliable mesh extraction. Parametrization methods employ computationally expensive countermeasures to avoid mapping input tetrahedra to degenerate or flipped tetrahedra in the parameter domain because such a parametrization does not define a proper hexahedral mesh. Nevertheless, there is no known technique that can guarantee the complete absence of such artifacts. We tackle this problem from the other side by developing a mesh extraction algorithm which is extremely robust against typical imperfections in the parametrization. First, a sanitization process cleans up numerical inconsistencies of the parameter values caused by limited precision solvers and floating-point number representation. On the sanitized parametrization, we extract vertices and so-called darts based on intersections of the integer grid with the parametric image of the tetrahedral mesh. The darts are reliably interconnected by tracing within the parametrization and thus define the topology of the hexahedral mesh. In a postprocessing step, we let certain pairs of darts cancel each other, counteracting the effect of flipped regions of the parametrization. With this strategy, our algorithm is able to robustly extract hexahedral meshes from imperfect parametrizations which previously would have been considered defective. The algorithm will be published as an open source library.

SIGGRAPH Asia 2016

Pa­ra­met­ri­za­tion based methods have recently become very popular for the generation of high quality quad meshes. In contrast to previous approaches, they allow for intuitive user control in order to accommodate all kinds of application driven constraints and design intentions. A major obstacle in practice, however, are the relatively long computations that lead to response times of several minutes already for input models of moderate complexity. In this paper we introduce a novel strategy to handle highly complex input meshes with up to several millions of triangles such that quad meshes can still be created and edited within an interactive workflow. Our method is based on representing the input model on different levels of resolution with a mechanism to propagate pa­ra­met­ri­za­tions from coarser to finer levels. The major challenge is to guarantee consistent pa­ra­met­ri­za­tions even in the presence of charts, transition functions, and singularities. Moreover, the remaining degrees of freedom on coarser levels of resolution have to be chosen carefully in order to still achieve low distortion pa­ra­met­ri­za­tions. We demonstrate a prototypic system where the user can interactively edit quad meshes with powerful high-level operations such as guiding constraints, singularity repositioning, and singularity connections.