SIGGRAPH Asia 2013

The most popular and actively researched class of quad remeshing techniques is the family of parametrization based quad meshing methods. They all strive to generate an integer-grid map, i.e. a parametrization of the input surface into R² such that the canonical grid of integer iso-lines forms a quad mesh when mapped back onto the surface in R³. An essential, albeit broadly neglected aspect of these methods is the quad extraction step, i.e. the materialization of an actual quad mesh from the mere “quad texture”. Quad (mesh) extraction is often believed to be a trivial matter but quite the opposite is true: Numerous special cases, ambiguities induced by numerical inaccuracies and limited solver precision, as well as imperfections in the maps produced by most methods (unless costly countermeasures are taken) pose significant challenges to the quad extractor. We present a method to sanitize a provided parametrization such that it becomes numerically consistent even in a limited precision floating point representation. Based on this we are able to provide a comprehensive and sound description of how to perform quad extraction robustly and without the need for any complex tolerance thresholds or disambiguation rules. On top of that we develop a novel strategy to cope with common local fold-overs in the parametrization. This allows our method, dubbed QEx, to generate all-quadrilateral meshes where otherwise holes, non-quad polygons or no output at all would have been produced. We thus enable the practical use of an entire class of maps that was previously considered defective. Since state of the art quad meshing methods spend a significant share of their run time solely to prevent local fold-overs, using our method it is now possible to obtain quad meshes significantly quicker than before. We also provide libQEx, an open source C++ reference implementation of our method and thus significantly lower the bar to enter the field of quad meshing.

Eurographics 2014

In rigid body simulation, one must distinguish between contacts (so-called unilateral constraints) and articulations (bilateral constraints). For contacts and friction, iterative solution methods have proven most useful for interactive applications, often in combination with Shock-Propagation in cases with strong interactions between contacts (such as stacks), prioritizing performance and plausibility over accuracy. For articulation constraints, direct solution methods are preferred, because one can rely on a factorization with linear time complexity for tree-like systems, even in ill-conditioned cases caused by large mass-ratios or high complexity. Despite recent advances, combining the advantages of direct and iterative solution methods wrt. performance has proven difficult and the intricacy of articulations in interactive applications is often limited by the convergence speed of the iterative solution method in the presence of closed kinematic loops (i.e. auxiliary constraints) and contacts. We identify common performance bottlenecks in the dynamic simulation of unilateral and bilateral constraints and are able to present a simulation method, that scales well in the number of constraints even in ill-conditioned cases with frictional contacts, collisions and closed loops in the kinematic graph. For cases where many joints are connected to a single body, we propose a technique to increase the sparsity of the positive definite linear system. A solution to these bottlenecks is presented in this paper to make the simulation of a wider range of mechanisms possible in real-time without extensive parameter tuning.

Eurographics Symposium on Geometry Processing (SGP 2013)

The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low-level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms – some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface’s embedding in Euclidean space. Generalization to other, especially anisotropic, metrics – which more recently gained interest in several application areas – is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well-known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the Short-Term Vector Dijkstra. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.