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

AlSub: Fully Parallel and Modular Subdivision

In recent years, mesh subdivision---the process of forging smooth free-form surfaces from coarse polygonal meshes---has become an indispensable production instrument. Although subdivision performance is crucial during simulation, animation and rendering, state-of-the-art approaches still rely on serial implementations for complex parts of the subdivision process. Therefore, they often fail to harness the power of modern parallel devices, like the graphics processing unit (GPU), for large parts of the algorithm and must resort to time-consuming serial preprocessing. In this paper, we show that a complete parallelization of the subdivision process for modern architectures is possible. Building on sparse matrix linear algebra, we show how to structure the complete subdivision process into a sequence of algebra operations. By restructuring and grouping these operations, we adapt the process for different use cases, such as regular subdivision of dynamic meshes, uniform subdivision for immutable topology, and feature-adaptive subdivision for efficient rendering of animated models. As the same machinery is used for all use cases, identical subdivision results are achieved in all parts of the production pipeline. As a second contribution, we show how these linear algebra formulations can effectively be translated into efficient GPU kernels. Applying our strategies to $\sqrt{3}$, Loop and Catmull-Clark subdivision shows significant speedups of our approach compared to state-of-the-art solutions, while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description

Hybrid Rugosity Mesostructures (HRMs) for fast and accurate rendering of fine haptic detail

The haptic rendering of surface mesostructure (fine relief features) in dense triangle meshes requires special structures, equipment, and high sampling rates for detailed perception of rugged models. Low cost approaches render haptic texture at the expense of fidelity of perception. We propose a faster method for surface haptic rendering using image-based Hybrid Rugosity Mesostructures (HRMs), paired maps with per-face heightfield displacements and normal maps, which are layered on top of a much decimated mesh, effectively adding greater surface detail than actually present in the geometry. The haptic probe’s force response algorithm is modulated using the blended HRM coat to render dense surface features at much lower costs. The proposed method solves typical problems at edge crossings, concave foldings and texture transitions. To prove the wellness of the approach, a usability testbed framework was built to measure and compare experimental results of haptic rendering approaches in a common set of specially devised meshes, HRMs, and performance tests. Trial results of user testing evaluations show the goodness of the proposed HRM technique, rendering accurate 3D surface detail at high sampling rates, deriving useful modeling and perception thresholds for this technique.Peer ReviewedPostprint (published version

Fast extraction of adaptive multiresolution meshes with guaranteed properties from volumetric data

We present a new algorithm for extracting adaptive multiresolution triangle meshes from volume datasets. The algorithm guarantees that the topological genus of the generated mesh is the same as the genus of the surface embedded in the volume dataset at all levels of detail. In addition to this "hard constraint" on the genus of the mesh, the user can choose to specify some number of soft geometric constraints, such as triangle aspect ratio, minimum or maximum total number of vertices, minimum and/or maximum triangle edge lengths, maximum magnitude of various error metrics per triangle or vertex, including maximum curvature (area) error, maximum distance to the surface, and others. The mesh extraction process is fully automatic and does not require manual adjusting of parameters to produce the desired results as long as the user does not specify incompatible constraints. The algorithm robustly handles special topological cases, such as trimmed surfaces (intersections of the surface with the volume boundary), and manifolds with multiple disconnected components (several closed surfaces embedded in the same volume dataset). The meshes may self-intersect at coarse resolutions. However, the self-intersections are corrected automatically as the resolution of the meshes increase. We show several examples of meshes extracted from complex volume datasets

Signal-Specialized Parameterization

To reduce memory requirements for texture mapping a model, we build a surface parametrization specialized to its signal (such as color or normal). Intuitively, we want to allocate more texture samples in regions with greater signal detail. Our approach is to minimize signal approximation error --- the difference between the original surface signal and its reconstruction from the sampled texture. Specifically, our signal-stretch parametrization metric is derived from a Taylor expansion of signal error. For fast evaluation, this metric is pre-integrated over the surface as a metric tensor. We minimize this nonlinear metric using a novel coarse-to-fine hierarchical solver, further accelerated with a fine-to-coarse propagation of the integrated metric tensor. Use of metric tensors permits anisotropic squashing of the parametrization along directions of low signal gradient. Texture area can often be reduced by a factor of 4 for a desired signal accuracy compared to non-specialized parametrizations.Engineering and Applied Science

Boundary element method modelling of KEMAR for binaural rendering: Mesh production and validation

Head and torso simulators are used extensively within acoustic research, often in place of human subjects in time-consuming or repetitive experiments. Particularly common is the Knowles Electronics Manikin for Acoustic Research (KEMAR), which has the acoustic auditory properties of an average human head. As an alternative to physical acoustic measurements, the boundary element method (BEM) is widely used to calculate the propagation of sound using computational models of a scenario. Combining this technique with a compatible 3D surface mesh of KEMAR would allow for detailed binaural analysis of speaker distributions and decoder design - without the disadvantages associated with making physical measurements. This paper details the development and validation of a BEM-compatible mesh model of KEMAR, based on the original computer-aided design (CAD) file and valid up to 20 kHz. Use of the CAD file potentially allows a very close match to be achieved between the mesh and the physical manikin. The mesh is consistent with the original CAD description, both in terms of overall volume and of local topology, and the numerical requirements for BEM compatibility have been met. Computational limitations restrict usage of the mesh in its current state, so simulation accuracy cannot as yet be compared with acoustically measured HRTFs. Future work will address the production of meshes suitable for use in BEM with lower computational requirements, using the process validated in this wor