... this article introduces a new compressed representation for complex triangulated models and simple, yet efficient, compression and decompression algorithms. In this scheme, vertex positions are quantized within the desired accuracy, a vertex spanning tree is used to predict the position of each vertex from 2, 3, or 4 of its ancestors in the tree, and the correction vectors are entropy encoded. Properties, such as normals, colors, and texture coordinates, are compressed in a similar manner. The connectivity is encoded with no loss of information to an average of less than two bits per triangle. The vertex spanning tree and a small set of jump edges are used to split the model into a simple polygon. A triangle spanning tree and a sequence of marching bits are used to encode the triangulation of the polygon. Our approach improves on Michael Deering's pioneering results by exploiting the geometric coherence of several ancestors in the vertex spanning tree, preserving the connectivity with no loss of information, avoiding vertex repetitions, and using about three times fewer bits for the connectivity. However, since decompression requires random access to all vertices, this method must be modified for hardware rendering with limited onboard memory. Finally, we demonstrate implementation results for a variety of VRML models with up to two orders of magnitude compression

In this paper we introduce the Progressive Forest Split (PFS) representation, a new adaptive refinement scheme for storing and transmitting manifold triangular meshes in progressive and highly compressed form. As in the Progressive Mesh (PM) method of Hoppe, a triangular mesh is represented as a low resolution polygonal model followed by a sequence of refinement operations, each one specifying how to add triangles and vertices to the previous level of detail to obtain a new level. The PFS format shares with PM and other refinement schemes the ability to smoothly interpolate between consecutive levels of detail. However, it achieves much higher compression ratios than PM by using a more complex refinement operation which can, at the expense of reduced granularity, be encoded more efficiently. A forest split operation doubling the number n of triangles of a mesh requires a maximum of approximately 3:5n bits to represent the connectivity changes, as opposed to approximately #5 + log 2 #n## n bits in PM. We describe

this paper focuses on polygon count reduction techniques that exploit an original triangular mesh and derive simplified models by eliminating vertices or triangles, by collapsing edges, or by merging adjacent faces.

A preliminary version of this paper has appeared as an extended abstract at CGI'98; see [26]. y

The manufacturing industry has invested vast amounts of resources in the deployment and use of solid modeling technology. Although expensive to generate and potentially very valuable in many product related activities, 3D models have rarely been exploited to support product management, documentation, collaborative review, and promotion, because they were only accessible to trained designers equipped with expensive graphics workstations. Intranet access, popular 3D exchange formats, and affordable 3D graphics chips permit to download and view 3D models using a personal computer. Although these basic capabilities are revolutionizing the entertainment and marketing industry and have reduced the cost of a design station, they are of little help to non-designers in the manufacturing industry. The author articulates a vision where 3D data is available and exploited at all phases of a product life cycle. The paper investigates the shortcomings of the current technology, identifies the fundame...

INTRODUCTION....................................................................................4 2. A SIMPLE DATASTRUCTURE FOR TRIANGULATED MESHES.................................6 3. TOPOLOGICAL CHARACTERIZATION OF POLYHEDRA........................................7 3.1 TOPOLOGICAL CONCEPTS AND DEFINITIONS .......................................................................................7 3.1.1 Topological closure, interior, and boundary............................................................................7 3.1.2 Dimensional homogeneity.................................................................................................8 3.1.3 Regularization and Boolean operations..................................................................................8 3.1.4 Connectedness, holes, and handles.......................................................................................9 3.1.5 Non-Manifold conditions..............................................................

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Data Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Problem Statement and Challenges . . . . . . . . . . . . . . . 4 1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Statistical-Model Codes and Other Compression Techniques . 7 1.2.2 Single-Resolution Mesh Compression and Coding . . . . . . . 8 1.2.3 Progressive Meshes and Multiresolution Surfaces . . . . . . . . 10 1.2.4 Polygonal Mesh Simplification . . . . . . . . . . . . . . . . . . 12 1.3 Outline of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2. PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1 Topological Concepts and Mesh Representation . . . . . . . . . . . . 16 2.2 Error Measur...

This paper presents a simple, robust and practical, yet fast algorithm for triangulation of points on the domain of trimmed Bzier surfaces. These R 2 points are input to this algorithm by a surface sampler. A set of polygons is formed from these samples, which are then triangulated. We also show how to update the triangulation when the samples, and hence the polygons, are updated. The output is a set of triangle strips. The algorithm includes heuristics to avoid long and thin triangles. In addition, it also detects if the sampling of the trimming curve forms any non-simple polygons and corrects the triangulation by adding more samples. The triangulation algorithm is more generally applicable to polygons in a plane. We report an implementation of the algorithm and its performance on extensive surface-model walkthrough. Keywords: Surface rendering, CAD, Triangulation, Polygon, PSLG, Computational geometry. 1 Supported in part by NSF Career grant 9733827, ARO grant DAAH04-96-1-0013 and NSF ERC grant 9731748. 1.

The metamorphosis between two user-specified objects offers an intuitive metaphor for designing animations of deforming shapes. We present a new technique for interactively editing such de- formations and for animating them in realtime. Besides the starting and ending shapes, our approach offers easy to use additional control over the deformations. The new Bezier Interpolating Polyhedron (BIP) provides a graphics representation of such a deforming object formulated mathematically as a point describing a Bezier curve in the space of all polyhedra. We replace, in the Bezier formulation, the traditional control points by arbitrary polyhedra and the vector addi- tion by the Minkowski sum. BIPs are composed of Animated GRaphic ELement (AGRELs), which are faces with constant orientation, but with parametrized vertices represented by Bezier curves. AGRELs were designed to efficiently support smooth realtime animation on commercially avail- able rendering hardware. We provide a tested algorithm for automatically computing BlPs from the sequence of control polyhedra and demonstrate its applications to animation design.

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.