Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

Hierarchical Path Finding to Speed Up Crowd Simulation

Path finding is a common problem in computer games. Most videogames require to simulate thousands or millions of agents who interact and navigate in a 3D world showing capabilities such as chasing, seeking or intercepting other agents. A new hierarchical path finding solution is proposed for large environments. Thus, a navigation mesh as abstract data structure is used in order to divide the 3D world. Then, a hierarchy of graphs is built to perform faster path finding calculations than a common A*. The benefits of this new approach are demonstrated on large world models

Improved Algorithms for Simulating Crystalline Membranes

The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. To understand their behavior, numerical simulations are commonly used. Unfortunately, traditional Monte Carlo algorithms suffer from very long auto-correlations and critical slowing down in the more interesting phases of the model. In this paper we study the performance of improved Monte Carlo algorithms for simulating crystalline membrane, such as hybrid overrelaxation and unigrid methods, and compare their performance to the more traditional Metropolis algorithm. We find that although the overrelaxation algorithm does not reduce the critical slowing down, it gives an overall gain of a factor 15 over the Metropolis algorithm. The unigrid algorithm does, on the other hand, reduce the critical slowing down exponent to z apprx. 1.7.Comment: 14 pages, 1 eps-figur

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accurac

A tetrahedral space-filling curve for non-conforming adaptive meshes

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table

Study and Development of Hierarchical Path Finding to Speed Up Crowd Simulation

We propose a new hierarchical path finding solution for large environments. We use a navigation mesh as abstract data structure to partition the 3D world. Then, we build a hierarchy of graphs that allow us to perform faster path finding calculations than a common A*