Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the worst case storage required by previously reported schemes, most of which require O(nlogn) bits to store the incidence graph of a mesh of n triangles. Edgebreaker requires only 2n bits or less for simple meshes and can also support fully general meshes by using additional storage per handle and hole. Edgebreaker's compression and decompression processes perform the same traversal of the mesh from one triangle to an adjacent one. At each stage, compression produces an op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker's compression and decompression are independent of the vertex locations, they may be combined with a variety of vertex-compressing techniques that exploit topological information about the mesh to better estimate vertex locations. Edgebreaker may be used to compress the connectivity of an entire mesh bounding a 3D polyhedron or the connectivity of a triangulated surface patch whose boundary needs not be encoded. Its superior compression capabilities, the simplicity of its implementation, and its versatility make Edgebreaker particularly suitable for the emerging 3D data exchange standards for interactive graphic applications. The paper also offers a comparative survey of the rapidly growing field of geometric compression.

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,andwe explore a simple algorithm for estimating K and the optimal B and V for piecewise spherical approximations...

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called topology) of threedimensional triangle meshes. Edgebreakerimproves upon the worst case and the expected compression ratios of previously reportedschemes, most of which requireO(nlogn) bits to store the incidence graph of a mesh of n triangles. Edgebreaker requiresonly 2n bits or less for simple meshes and can also support fully general meshes by using additional storage per handleand hole. Edgebreaker'scompressionanddecompressionprocessesperforman identical traversalof the mesh from one triangle to an adjacent one. At each stage, compression producesan op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker'scompression and decompression are independent of the vertex locations, Edgebreaker may be combined with a variety of...

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 of resolution used per vertex coordinate via quantization. Let A be a triangle mesh approximation for an original model O. Suppose that A has V vertices, each represented using B bits per coordinate. Given a file size F for A, what are the optimal values of B and V? Given a desired error level E, what are estimates of B and V, and how many total bits are needed? We develop answers to these questions by using a shape complexity measure K that allows us to express the optimal value of B for a general model in terms of V and K alone. We give formulas linking B,V,F,E, and K, and we provide a simple algorithm for estimating the optimal B and V for an existing triangle mesh with a g...

Interactive visualization of large three-dimensional polygonal datasets is an important topic in the field of computer graphics and scientific visualization. These datasets can be static, such as many walkthrough applications, or dynamic, such as CAD scenarios where a designer moves, adds, or deletes parts. In many cases, the number of primitives in these models overwhelms the rendering performance of current graphics systems. In order to view these environments in real-time, approximation techniques must augment the capabilities of the hardware. One method for accelerating the rendering of these environments is polygonal simplification. This dissertation describes the creation and application of levels of detail, or LODs, and hierarchical levels of detail, or HLODs, to accelerate the rendering of large static and dynamic...

Introduction 3D models of terrain's, buildings, factories, airplanes, consumer products, human organs, and simulation results are at the heart of numerous applications that drive major segments of the manufacturing, architectural, geoscience, military, medical, and entertainment industries (see also [Rossignac94, Rossignac97]). 3D models will also enhance future computer-human interfaces and will benefit important areas of electronic commerce. They must be easily accessible and usable by all. Interactive 3D viewing makes users more effective Interactive 3D graphics helps viewers understand 3D models of products, buildings, biological structures, or simulation results. 3D views combine in a natural way the details being inspected and the larger perspective of their surroundings. Direct and intuitive control of the 3D viewing parameters leverages our natural ability to quickly identify areas of interest and to focus on them for closer inspection. To fully explo

We present a new approach for fast display of large static and dynamic environments. Given a geometric dataset, we represent it using a scene graph and automatically compute levels of detail (LODs) for each node in the graph. For drastic simplification, i.e., reducing the polygon count by an order of magnitude or more, we compute hierarchical levels of detail (HLODs) that represent portions of the scene graph. When objects move in a dynamic environment, we incrementally recompute a subset of the HLODs on the fly. Our approach can efficiently handle scenes with a limited amount of dynamic changes. Furthermore, it supports two rendering modes: one that renders at a specified image quality and another that targets a desired frame rate. We efficiently render LODs and HLODs using display lists and achieve significant speedups on rendering large static and dynamic environments composed of tens of millions of polygons. Keywords: interactive display, graphics systems, spatial data structures,...

3D graphics rendering is computationally very intensive particularly for interactive applications. The complexity of the 3D object databases becomes a major problem in a rendering pipeline as the number of polygons is increased with model complexity. Simplifying large object databases and eliminating some of the polygons in the database with minimal impact on visual quality is desirable for faster rendering. This paper discusses the necessity for simplifying 3D object databases in accelerating 3D graphics and introduces a new method based on vertex clustering technique.

Standard representations of 3D models are so verbose that only very simple models can be accessed over common communication links for immediate viewing. This situation is not likely to improve, since the need for more accurate 3D models and their deployment throughout a broader spectrum of industrial, scientific, and consumer application areas will outpace the improvements in transmission bandwidth to the office, home, or mobile worker or private user. Recently developed multi-resolution modeling technologies play an important role in addressing this bandwidth bottleneck, especially when combined with other approaches, such as intelligent culling, pre-fetching, and image-based rendering. This tutorial will discuss the details of compression, simplification, and progressive transmission techniques and of their interrelations.

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