Francis Lazarus

Progressive forest split 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 + log2(n))n bits in PM. We describe algorithms to efficiently encode and decode the PFS format. We also show how any surface simplification algorithm based on edge collapses can be modified to convert single resolution triangular meshes to the PFS format. The modifications are simple and only require two additional topological tests on each candidate edge collapse. We show results obtained by applying these modifications to the Variable Tolerance method of Gueziec. CR

Geometry coding and VRML

The virtual-reality modeling language (VRML) is rapidly becoming the standard file format for transmitting three-dimensional (3-D) virtual worlds across the Internet. Static and dynamic descriptions of 3-D objects, multimedia content, and a variety of hyperlinks can be represented in VRML files. Both VRML browsers and authoring tools for the creations of VRML files are widely available for several different platforms. In this paper, we describe the topologically assisted geometric compression technology included in our proposal for the VRML compressed binary format. This technology produces significant reduction of file sizes and, subsequently, of the time required for transmission of such filed across the Internet. Compression ratios of 50:1 or more are achieved for large models. The proposal also includes a binary encoding to create compact, rapidly parsable binary VRML files. The proposal is currently being evaluated by the Compressed Binary Format Working Group of the VRML consortium as a possible extension of the VRML standard. In the topologically assisted compression scheme, a polyhedron is represented using two interlocking trees: a spanning tree of vertices and a spanning tree of triangles. The connectivity information represented in other compact schemes, such as triangular strips and generalized triangular meshes, can be directly derived from this representation. Connectivity information for large models is compressed with storage requirements approaching one bit per triangle. A variable-length, optionally lossy compression technique is used for vertex positions, normals, colors, and texture coordinates. The format supports all VRML property binding conventions.

Three-dimensional metamorphosis: a survey

A metamorphosis or a (3D) morphing is the process of continuously transforming one object into another. 2D and 3D morphing are popular in computer animation, industrial design, and growth simulation. Since there is no intrinsic solution to the morphing problem, user interaction can be a key component of a morphing software. Many morphing techniques have been proposed in recent years for 2D and 3D objects. We present a survey of the various 3D approaches, giving special attention to the user interface. We show how the approaches are intimately related to the object representations. We conclude by sketching some morphing strategies for the future.

Extracting skeletal curves from 3D scattered data

We introduce a method for extracting skeletal curves from an unorganized collection of scattered data points lying on a surface. These curves may have a tree like structure to capture branching shapes such as blood vessels. The skeletal curves can be used for different applications ranging from surface reconstruction to object recognition.

Level set diagrams of polyhedral objects

Shape descriptors and feature-based representations are of primary interests in the area of solid modeling. They allow us for easier storage, recognition and general treatments of objects. Axial structures such as skeletons are popular shape descriptors which have been widely studied. Most of the studies focus on a particular type of skeleton called the Medial Axis. Medial Axes can be extracted from discrete volumetric data as well as boundary-based representations. In the later case, however, no algorithm is known to perform well and accurately. We propose a new paradigm for constructing one dimensional axial structures associated with a polyhedral object. These structures, called the level set diagrams, are associated with scalar functions defined over the set of vertices of a polyhedron. We study in details the level set diagram associated with the shortest path distance to a source point. This particular association fits nicely into a theoretical framework and presents interesting properties for the purpose of shape description.

Computing a canonical polygonal schema of an orientable triangulated surface

A closed orientable surface of genus

Cutting and stitching: converting sets of polygons to manifold surfaces

g

Harmonic skeleton for realistic character animation

can be obtained by appropriat e identification of pairs of edges of a

A framework for streaming geometry in VRML

4g

Optimal System of Loops on an Orientable Surface

-gon (the polygonal schema). The identified edges form