Summary We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

Figure 1: A representative suite of visualization tasks being evaluated with MapReduce: isosurface extraction, volume and mesh rendering, and mesh simplification. Our MapReduce-based renderer can produce a giga pixel rendering of a 1 billion triangle mesh in just under two minutes. With the capability of sustaining high I/O rate with fault-tolerance, MapReduce methods can be used as tools for quickly exploring large datasets with isosurfacing and rendering in a batch-oriented manner. ABSTRACTLarge-scale visualization systems are typically designed to efficiently "push" datasets through the graphics hardware. However, exploratory visualization systems are increasingly expected to support scalable data manipulation, restructuring, and querying capabilities in addition to core visualization algorithms. We posit that new emerging abstractions for parallel data processing, in particular computing clouds, can be leveraged to support large-scale data exploration through visualization. In this paper, we take a first step in evaluating the suitability of the MapReduce framework to implement large-scale visualization techniques. MapReduce is a lightweight, scalable, general-purpose parallel data processing framework increasingly popular in the context of cloud computing. Specifically, we implement and evaluate a representative suite of visualization tasks (mesh rendering, isosurface extraction, and mesh simplification) as MapReduce programs, and report quantitative performance results applying these algorithms to realistic datasets. For example, we perform isosurface extraction of up to l6 isovalues for volumes composed of 27 billion voxels, simplification of meshes with 30GBs of data and subsequent rendering with image resolutions up to 80000 2 pixels. Our results indicate that the parallel scalability, ease of use, ease of access to computing resources, and fault-tolerance of MapReduce offer a promising foundation for a combined data manipulation and data visualization system deployed in a public cloud or a local commodity cluster.

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.

Figure 1: An example of input mesh, minimum error bridges, and final stencil image. AbstractCreating physical stencils from 3D meshes is a unique rendering challenge that has not been previously addressed. The task is a problem of two competing goals: forming a single, well-connected and stable stencil sheet, while simultaneously limiting the error introduced by pieces of bridging material. Under these conflicting goals, it can often be difficult to create visually pleasing stencils from complicated imagery by hand. Even for well-behaved images, expressive stencils can be time-consuming to craft manually.We present a method for generating expressive stencils from polygonal meshes or images. In our system, users provide input geometry and can adjust desired view, lighting conditions, line thickness, and bridge preferences to achieve their final desired stencil. The stencil creation algorithm makes use of multiple metrics to measure the appropriateness of connections between unstable stencil regions. These metrics describe local features to help minimize the distortion of the abstracted image caused by stabilizing bridges. The algorithm also uses local statistics to choose a best fit connection that maintains both structural integrity and local shape information. We demonstrate our algorithm on physical media including construction paper and sheet metal.