GVU Technical Report Series

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GVU Technical Report Series

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Now showing 1 - 10 of 26

Edgebreaker: A Simple Compression for Surfaces with Handles

(Georgia Institute of Technology, 2002) Rossignac, Jarek ; Lopes, Helio ; Safanova, Alla ; Tavares, Geovan ; Szymczak, Andrzej

The Edgebreaker is an efficient scheme for compressing triangulated surfaces. A surprisingly simple implementation of Edgebreaker has been proposed for surfaces homeomorphic to a sphere. It uses the Corner-Table data structure, which represents the connectivity of a triangulated surface by two tables of integers, and encodes them with less than 2 bits per triangle. We extend this simple formulation to deal with triangulated surfaces with handles and present the detailed pseudocode for the encoding and decoding algorithms (which take one page each). We justify the validity of the proposed approach using the mathematical formulation of the Handlebody theory for surfaces, which explains the topological changes that occur when two boundary edges of a portion of a surface are identified.
SwingWrapper: Retiling Triangle Meshes for Better Compression

(Georgia Institute of Technology, 2002) Attene, Marco ; Falcidieno, B. (Bianca) ; Spagnuolo, Michela ; Rossignac, Jarek

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply connected regions, called triangloids. From these, we generate a new mesh M'. Each triangle of M' is an approximation of a triangloid of M. By construction, the connectivity of M' is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M' are compactly encoded with our new prediction technique, which uses a single correction parameter per vertex. Differently from typical compression algorithms, SwingWrapper attempts to reach a user-defined output file size rather than, for example, not to exceed a given error bound. For a variety of popular models, a rate of 0.4 bits/triangle yields an L2 distortion of about 0.01% of the bounding box diagonal. The proposed solution may also be used to encode crude meshes for adaptive transmission or for controlling subdivision surfaces
Space-Time Surface Simplification and Edgebreaker Compression for 2D Cel Animations

(Georgia Institute of Technology, 2002) Kwatra, Vivek ; Rossignac, Jarek

Digitized cel animations are typically composed of frames containing a small number of regions; each region contains pixels of the same color and exhibits a significant level of shape coherence through time. To exploit this coherence, we treat the stack of frames as a $3D$ volume and represent the evolution of each region by the bounding surface of the $30$ sub-volume $V$ with constant-time planes. The intersection is generated in real-time with standard graphics hardware through an improved capping (i.e. solid chipping) technique, which correctly handles overlapping facets. We have tested this approach on real and synthetic black&white animations and report compression ratios that improve upon those produced using the MPEG, MRLE, and GZIP compression standards for an equivalent quality result.
Finger Sculpting with Digital Clay

(Georgia Institute of Technology, 2002) Gargus, Joshua ; Kim, Byungmoon ; Rossignac, Jarek ; Shaw, Christopher D.

"Digital Clay" is a term that signifies a computer-controlled physical surface, capable of taking any of a wide variety of possible shapes in response to changes in a digital 3D model or changes in the pressure exerted upon it by bare hands. The physical properties of such a device impose design and user-interface constraints not encountered in traditional, tracker-based software for the manipulation of virtual models. This paper describes the interaction techniques we have developed to work with this future medium. In particular, we present our solution for tracking the user's fingers using a local deformation of the surface, which we call a "blister", that senses the tangential and normal displacements of the finger. We also present a solution for creating variable-height bosses and creases with the simple sweep of a finger. Since the Digital Clay hardware is not yet operational, we have implemented a haptic simulation framework based on a PHANTOM device.
Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces

(Georgia Institute of Technology, 2001) Rossignac, Jarek ; Safanova, Alla ; Szymczak, Andrzej

A triangulated surface S with V vertices is sometimes stored as a list of T independent triangles, each described by the 3 floating-point coordinates of its vertices. This representation requires about 576V bits and provides no explicit information regarding the adjacency between neighboring triangles or vertices. A variety of boundary-graph data structures may be derived from such a representation in order to make explicit the various adjacency and incidence relations between triangles, edges, and vertices. These relations are stored to accelerate algorithms that visit the surface in a systematic manner and access the neighbors of each vertex or triangle. Instead of these complex data structures, we advocate a simple Corner Table, which explicitly represents the triangle/vertex incidence and the triangle/triangle adjacency of any manifold or pseudo-mainfold triangle mesh, as two tables of integers. The Corner Table requires about 12VlogxV bits and must be accompanied by a vertex table, which requires 96V bits, of Floats are used. The Corner Table may be derived from the list of independent triangles. For meshes homeomorphic to a sphere, it may be compressed to less than 4V bits by storing the "clers" sequence of triangle-labels from the set {C,L,E,$,S}. Further compression to 3.6V bits may be guaranteed by using context-based codes for the clers symbols. Entropy codes reduce the storage for large meshes to less than 2V bits. Meshes with more complex topologies may require O(log2V) additional bits per handle of hole. We present here a publicly available, simple, state-machine implementation of the Edgebreaker compression, which traverses the corner table, computes the CLERS symbols, and constructs an ordered list of vertex references. Vertices are encoded, in the order in which they appear on the list, as corrective displacements between their predicted and actual locations. Quantizing vertex coordinates to 12 bits and predicting each vertex as a linear combinations of its previously encoded neighbors leads to short displacements, for which entropy codes drop the total vertex location storage for heavily sampled typical meshes below 16V bits.
Compressed Piecewise Circular Approximation of 3D Curves

(Georgia Institute of Technology, 2001) Safanova, Alla ; Rossignac, Jarek

We propose a compact approximation scheme for 3D curves. Consider a polygonal curve P, whose n vertices have been generated through adaptive (and nearly minimal) sampling, so that P approximates some original 3D curve, O, withing tolerance e0. We present a practical and efficient algorithm for computing a continuous 3D curve C that approximates P within tolerance e1 and is composed of a chain of m circular arcs, whose end-points coincide with a subset of the vertices of P. We represent C using 5m+3 scalars, which we compress within a carefully selected quantization error e2. Our approximation uses a total of less than 7.5n bits, when O is a typical surface/surface intersection and when the error bound e1+e2 is less than 0.02% of the radius of a minimal sphere around O. For less accurate approximations, the storage size drops further, reaching for instance a total of n bits where e1+e2 is increased to 3%. The storage cost per vertex is also reduced when e0 is decreased to force a tighter fit for smooth curves. As expected, the compression deteriorates for jagged curves with a tight error bound. In any case, our representation of C is always more compact than a polygonal curve that approximate O with the same accuracy. To guarantee a correct fit, we introduce a new ereror metric for e1, which prevents discrepancies between P and C that are not detected by previously proposed Hausdorff or least-square error estimates. We provide the details of the algorithms and of the geometric constructions. We also introduce a conservative speed-up for computing C more efficiently and demonstrate that it is sub-optimal in only 2% of the cases. Finally, we report results on several types of curves and compare them to previously reported polygonal approximations, observing compression ratios that vary between 15:1 and 36:1.
Determination of the Correct Eye Position for Viewing Perspective Images of 3D Scenes

(Georgia Institute of Technology, 2001) Jang, Justin ; Rossignac, Jarek

Realistic viewing of perspective images requires placing the viewer at the correct location. In this paper, we present a technique for determining the correct viewing location for perspective images of 3D scenes. The technique is based on the determination of three vanishing points in mutually orthogonal directions. We also use this technique to devise a simple method for manually drawing images of rectangular prisms in correct perspective with respect to a viewpoint.
The Safari Interface for Visualizing Time-Dependent Volume Data Using Iso-Surfaces and a Control Plane

(Georgia Institute of Technology, 2001) Kettner, Lutz ; Rossignac, Jarek ; Snoeyink, Jack

We describe a prototype interface for the visualization of time-varying volume data of one or several variables as they occur in scientific and engineering applications. We partition the data dimensions into a 3D viewer for iso-surfaces and a 2D control plane where each point selects a particular iso-surface in 3D. A pre-computed color-coding of the control plane and a small preview window help the user to navigate the volune data. We use the number of connected components of the iso-surface as an example of a color-coding that we can compute efficiently and automatically using contour trees. The success of this interface opens interesting avenues of research into geometric data structures to support remote visualization of time-varying volume data.
SQUEEZE: Fast and Progressive Decompression of Triangle Meshes

(Georgia Institute of Technology, 2000) Pajarola, Renato B. ; Rossignac, Jarek

An ideal triangle mesh compression technology would simultaneously support the following three objectives: (1) progressive refinements of the received mesh during decompression, (2) nearly optimal compression ratios for both geometry and connectivity, and (3) in-line, real-time decompression algorithms for hardware or software implementations. Because these three objectives impose contradictory constraints, previously reported efforts focus primarily on one - sometimes two - of these objectives. The SQUEEZE technique introduced here addresses all three constraints simultaneously, and attempts to provide the best possible compromise. For a mesh of T triangles, SQUEEZE compresses the connectivity to 3.7T bits, which is competitive with the best progressive compression techniques reported so far. The geometry prediction error encoding technique introduced here leads to 20% improved geometry compression over previous schemes. Our initial implementation on a 300 Mhz CPU achieves a decompression rate of up to 46'000 triangles per second. SQUEEZE downloads a model through a number of successive refinement stages, providing the benefit of progressivity.
Compressed Progressive Meshes

(Georgia Institute of Technology, 2000) Pajarola, Renato B. ; Rossignac, Jarek

Most systems that support the visual interaction with 3D models use shape representations based on triangle meshes. The size of these representations imposes limits on applications, for which complex. 3D models must be accessed remotely. Techniques for simplifying and compressing 3D models reduce the transmission time. Multi-resolution formats provide quick access to a crude model and then refine it progressively. Unfortunately, compared to the best non-progressive compression methods, previously proposed progressive refinement techniques impose a significant overhead when the full resolution model must be downloaded. The CPM (Compressed Progressive Meshes) approach proposed here eliminates this overhead. It uses a new "Implant Sprays" technique, which refines the topology of the mesh in batches, which each increase the number of vertices by up to 50%. Less than an amoritized total of 4 bits per triangle encode where and how the topological refinements should be applied. We estimate the position of new vertices from the positions of their topological neighbors in the less refined mesh using a new estimator that leads to representations of vertex coordinates that are 50% more compact than previously reported progressive geometry compression techniques.