Jarek Rossignac

Geometric compression through topological surgery

The abundance and importance of complex 3-D data bases in major industry segments, the affordability of interactive 3-D rendering for office and consumer use, and the exploitation of the Internet to distribute and share 3-D data have intensified the need for an effective 3-D geometric compression technique that would significantly reduce the time required to transmit 3-D models over digital communication channels, and the amount of memory or disk space required to store the models. Because the prevalent representation of 3-D models for graphics purposes is polyhedral and because polyhedral models are in general triangulated for rendering, 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 Deerings 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 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.

Multi-resolution 3D approximations for rendering complex scenes

We present a simple, effective, and efficient technique for approximating arbitrary polyhedra. It is based on triangulation and vertex-clustering, and produces a series of 3D approximations (also called “levels of detail”) that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices. The simplification is more efficient than competing techniques because it does not require building and maintaining a topological adjacency graph. Furthermore, it is better suited for mechanical CAD models which often exhibit patterns of small features, because it automatically groups and simplifies features that are geometrically close, but need not be topologically close or even part of a single connected component Using a lower level of detail when displaying small, distant, or background objects improves graphic performance without a significant loss of perceptual information, and thus enables realtime inspection of complex scenes or a convenient environment for animation or walkthrough preview.

Full-range approximation of triangulated polyhedra

We propose a new algorithm for automatically computing approximations of a given polyhedral object at different levels of details. The application for this algorithm is the display of very complex scenes. where many objects are seen with a range of varying levels of detail. Our approach is similar to the region‐merging method used for image segmentation. We iteratively collapse edges, based on a measure of the geometric deviation from the initial shape. When edges are merged in the right order, this strategy produces a continuum of valid approximations of the original object, which can be used for faster rendering at vastly different scales.

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.

An Unconditionally Stable MacCormack Method

Abstract The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other non-reversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advection raising the method to second order accuracy, even though each individual step is only first order accurate. In this paper, we rewrite the MacCormack method to illustrate that it estimates the error in the same exact fashion as BFECC. The difference is that the MacCormack method uses this error estimate to correct the already computed forward advected data. Thus, it does not require the third advection step in BFECC reducing the cost of the method while still obtaining second order accuracy in space and time. Recent work replaced each of the three BFECC advection steps with a simple first order accurate unconditionally stable semi-Lagrangian method yielding a second order accurate unconditionally stable BFECC scheme. We use a similar approach to create a second order accurate unconditionally stable MacCormack method.

Solid-interpolating deformations : construction and animation of PIPS

Abstract Computer programs that simulate the deformations of geometric shapes have played a key role in the increasing popularity of software tools for artistic animation. Previously published techniques for specifying and animating deformations are either limited in their domain or ill-suited for interactive editing and visualization, because the effects of alterations performed by the animator on the models parameters may not always be anticipated, and because realtime animation may only be produced by visualizing precomputed sequences of 3D frames obtained by a slow process and require vast amounts of storage. To support an interactive environment for animation design, we have developed a new, simple, and efficient animation primitive: a Parameterized Interpolating Polyhedron (PIP). PIPs are easily specified and edited by providing their initial and final shapes, which may be any polyhedra, and need not have corresponding boundary elements, nor be convex. PIPs may be efficiently animated on standard graphic hardware because a PIP is a smoothly varying family of polyhedra bounded by faces that evolve with time. The faces have constant orientations and vertices that each move on a straight line between a vertex of the initial shape and a vertex of the final one. The cost of recalculating the time dependent information of a PIP is small in comparison to the display cost. We provide simple and efficient algorithms, based on Minkowski sum operations, for computing PIPs. When both the initial and final shapes are convex, the resulting faces are the true boundary of the deforming object, otherwise subsets of the resulting faces may lie inside the object. In both cases, correct images are automatically generated using standard depth-buffer hardware. The tools we have developed are convenient for interactively designing animation sequences that show the metamorphosis of 3D shapes. They may also be used to simulate the geometric effect of a variety of manufacturing operations, and for interactively selecting the optimal compromise between two or more shapes. They have been integrated in the LAMBADA design and inspection environment for animated assemblies, where deformations and rigid-body motions may be easily combined and synchronized using a hierarchical representation.

Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes

Abstract Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression and simplification of three-dimensional shapes. Different features, such as flats, limbs, tips, pits and various blending shapes that transition between them, may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated filters, that may capture the needs of a particular application.

Solid modeling and beyond

A survey of the field of solid modeling and an assessment of its strengths and limitations are presented. The survey covers mathematical foundations, representations, algorithms, applications, user interfaces and systems. The primary conferences for each of these five aspects of solid modeling are listed.<<ETX>>

Interactive inspection of solids: cross-sections and interferences

To reduce the cost of correcting design errors, assemblies of mechanical parts are modeled using CAD systems and verified electronically before the designs are sent to manufacturing. Shaded images are insufficient for examining the internal structures of assemblies and for detecting interferences. Thus, designers must rely on expensive numerical techniques that compute geometric representations of cross-sections and of intersections of solids. The solid-clipping approach presented here bypasses these geometric calculations and offers realtime rendering of cross-sections and interferences for solids represented by their facetted boundaries. In its simplest form, the technique is supported by contemporary highend graphics workstations. Its variations, independently developed elsewhere, have already been demonstrated. Our implementation is based on the concept of a cutvolume interactively manipulated to remove obstructing portions of the assembly and reveal its internal structure. For clarity, faces of the cut-volume which intersect a single solid are hatched and shaded with the color of that solid. Interference areas between two or more solids are highlighted. Furthermore, to help users find the first occurrence of an interference along a search direction, we have developed an adaptive subdivision search based on a projective approach which guarantees a sufficient condition for object disjointness. The additional performance cost for solid-clipping and interference highlighting is comparable to the standard rendering cost. An efficient implementation of the disjointness test requires a minor extension of the graphics functions currently supported on commercial hardware.

WRAP&Zip decompression of the connectivity of triangle meshes compressed with edgebreaker

Abstract The Edgebreaker compression (Rossignac, 1999; King and Rossignac, 1999) is guaranteed to encode any unlabeled triangulated planar graph of t triangles with at most 1.84t bits. It stores the graph as a CLERS string—a sequence of t symbols from the set { C,L,E,R,S} , each represented by a 1, 2 or 3 bit code. We show here that, in practice, the string can be further compressed to between 0.91t and 1.26t bits using an entropy code. These results improve over the 2.3t bits code proposed by Keeler and Westbrook (1995) and over the various 3D triangle mesh compression techniques published recently (Gumhold and Strasser, 1998; Itai and Rodeh, 1982; Naor, 1990; Touma and Gotsman, 1988; Turan, 1984), which exhibit either larger constants or cannot guarantee a linear worst case storage complexity. The decompression proposed by Rossignac (1999) is complicated and exhibits a non-linear time complexity. The main contribution reported here is a simpler and efficient decompression algorithm, called WrapZ King and Rossignac, 1999) yields a simple and effective solution for compressing the connectivity information of large and small triangle meshes that must be downloaded over the Internet. The CLERS stream may be interleaved with an encoding of the vertex coordinates and photometric attributes enabling inline decompression. The availability of local incidence information permits to use, during decompression, the location and attributes of neighboring vertices to predict new ones, and thus supports most of the recently proposed vertex compression techniques (Deering, 1995; Gumhold and Strasser, 1999; Taubin and Rossignac, 1998; Touma and Gotsman, 1998).