Davis King

An edgebreaker-based efficient compression scheme for regular meshes

Abstract One of the most natural measures of regularity of a triangular mesh homeomorphic to the two-dimensional sphere is the fraction of its vertices having degree 6. We construct a linear-time connectivity compression scheme build upon Edgebreaker which explicitly takes advantage of regularity and prove rigorously that, for sufficiently large and regular meshes, it produces encodings not longer than 0.811 bits per triangle: 50% below the information-theoretic lower bound for the class of all meshes. Our method uses predictive techniques enabled by the Spirale Reversi decoding algorithm.

Piecewise regular meshes: construction and compression

We present an algorithm which splits a 3D surface into reliefs, relatively fiat regions that have smooth boundaries. The surface is then resampled in a regular manner within each of the reliefs. As a result, we obtain a piecewise regular mesh (PRM) having a regular structure on large regions. Experimental results show that we are able to approximate the input surface with the mean square error of about 0.01- 0.02% of the diameter of the bounding box without increasing the number of vertices. We introduce a compression scheme tailored to work with our remeshed models and show that it is able to compress them losslessly (after quantizing the vertex locations) without significantly increasing the approximation error using about 4 bits per vertex of the resampled model.

Optimal bit allocation in compressed 3D models

Abstract To use 3D models on the Internet or in other bandwidth-limited applications, it is often necessary to compress their triangle mesh representations. We consider the problem of balancing two forms of lossy mesh compression: reduction of the number of vertices by simplification, and reduction of the number of bits per vertex coordinate. Let A(V,B) be a triangle mesh approximation for an original model O. Suppose that A(V,B) has V vertices, each represented using B bits per coordinate. Given a limit F on the file size for A(V,B), what are the optimal values of B and V that minimize the approximation error? Given a desired error bound E, what are optimal B and V, and how many total bits are needed? We develop answers to these questions by using a shape complexity measure K, which, for any given object approximates the product EV. We give formulae linking B, V, F, E and K, and we explore a simple algorithm for estimating K and the optimal B and V for piecewise spherical approximations of arbitrary triangle meshes.

An architecture for interactive tetrahedral volume rendering

We present a new architecture for interactive unstructured volume rendering. Our system moves all the computations necessary for order-independent transparency and volume scan conversion from the CPU to the graphics hardware, and it makes a software sorting pass unnecessary. It therefore provides the same advantages for volume data that triangle-processing hardware provides for surfaces. To address a remaining bottleneck — the bandwidth between main memory and the graphics processor — we introduce two new primitives, tetrahedral strips and tetrahedral fans. These primitives allow performance improvements in rendering tetrahedral meshes similar to the improvements triangle strips and fans allow in rendering triangle meshes. We provide new techniques for generating tetrahedral strips that achieve, on the average, strip lengths of 17 on representative datasets. The combined effect of our architecture and new primitives is a 72 to 85 times increase in performance over triangle graphics hardware approaches. These improvements make it possible to use volumetric tetrahedral meshes in interactive applications.

Steering data streams in distributed computational laboratories

This research supports the interactive access to large-scale scientific data by creation of active user interfaces (AUIs). An AUI continuously emits events describing its current information needs, based on which methods may be developed for controlling the potentially immense information streams directed at the interface. More precisely the purposes of stream control are twofold. First, stream control is performed to deal with heterogeneity in underlying systems, where low end displays may receive only small portions of the data shown at high end displays. Second, stream control is used to achieve scalability with respect to the size and complexity of data streams directed at a user interface, by filtering the data stream and by offloading certain computations from the AUI to the information generators or to information routing sites, by dynamically migrating such computations to appropriate locations, and by adapting these computations in order to effect tradeoffs in the amount of data moved across network links vs. the computations required.