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GVU Technical Report Series

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Author: Rossignac, Jarek × End date: 2000 × Start date: 1997 × search.filters.applied.f.isSeriesOfPublicationTitle: GVU Technical Report Series ×

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Now showing 1 - 10 of 16
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SQUEEZE: Fast and Progressive Decompression of Triangle Meshes

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.

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Connectivity Compression for Irregular Quadrilateral Meshes

1999 , King, Davis , Szymczak, Andrzej , Rossignac, Jarek

Many 3D models used in engineering, scientific, and visualization applications are represented by an irregular mesh of bounding quadrilaterals. We propose a scheme for compressing the connectivity of irregular quadrilateral meshes in 0.26-1.7 bits/quad, a 25-45% savings over randomly splitting quads into triangles and applying triangle mesh compression. Our approach is an extension of the Edgebreaker compression approach and of the Wrap&Zip decompression technique.

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Wrap&zip: Linear decoding of planar triangle graphs

1999 , Rossignac, Jarek , Szymczak, Andrzej

The Edgebreaker compression technique, introduced by Rossignac, encodes any unlabeled triangulated planar graph of t triangles using a string of 2t bits. The string contains a sequence of t letters from the set {C, L, E, R, S} and 50% of these letters are C. Exploiting constraints on the sequence, we show that the string may in practice be further compressed to 1.6t bits using model independent codes and even more using model specific entropy codes. These results improve over the 2.3t bits needed by Keeler and Westbrook and over the various 3D triangle mesh compression techniques published recently, which all exhibit larger constants or non-linear worst case storage costs. As in Edgebreaker, we compress the mesh using a spiraling triangle-spanning tree and generate the same sequence of letters. Edgebreaker's decompression uses a look-ahead procedure to identify the third vertex of split triangles (S letter) by counting letter occurrences in the remaining part of the sequences. We introduce here a new decompression technique, which eliminates this look-ahead and thus exhibits a linear asymptotic time complexity. Wrap&zip converts the string into the corresponding triangle-spanning tree and assigns orientations to each one of its free edges. During that "wrapping" process, whenever two consecutive edges point to the same vertex, it glues them together, possibly continuing the "zip" along the next pair of edges that just became adjacent. By labeling the vertices according to the order in which they first appear in the triangle-spanning tree, this compression approach may be used to encode the connectivity (incidence of labeled graphs) of three-dimensional triangle meshes that are homeomorphic to a sphere. Being able to decompress connectivity prior to vertex locations is essential for the most advanced geometry compression schemes, which use connectivity to predict the location of a vertex from the location of its previously decoded neighbors.

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Guaranteed 3.67V Bit Encoding of Planar Triangle Graphs

1999 , King, Davis , Rossignac, Jarek

We present a new representation that is guaranteed to encode any planar triangle graph of V vertices in less than 3.67V bits. Our code improves on all prior solutions to this well studied problem and lies within 13% of the theoretical lower limit of the worst case guaranteed bound. It is based on a new encoding of the CLERS string produced by Rossignac's Edgebreaker compression [Rossignac99]. The elegance and simplicity of this technique makes it suitable for a variety of 2D and 3D triangle mesh compression applications. Simple and fast compression/decompression algorithms with linear time and space complexity are available.

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Compressed Progressive Meshes

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.

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Optimal Bit Allocation in 3D Compression

1999 , King, Davis , Rossignac, Jarek

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 given file size F.

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Implant Sprays: Compression of Progressive Tetrahedral Mesh Connectivity

1999 , Pajarola, Renato B. , Rossignac, Jarek , Szymczak, Andrzej

Irregular tetrahedral meshes, which are popular in many engineering and scientific applications, often contain a large number of vertices. A mesh of V vertices and T tetrahedra requires 48-V bits or less to store the vertex coordinates, 4-T-log₂(V) bits to store the tetrahedra-vertex incidence relations, also called connectivity information, and k-V bits to store the k-bit value samples associated with the vertices. Given that T is 5 to 7 times larger than V and that V often exceeds 32², the storage space required for the connectivity is larger than 300-V bits and thus dominates the overall storage cost. Our "implants spray" compression approach introduced in this paper reduces this cost to about 30-V bits or less - a 10:1 compression ratio. Furthermore, implant spray supports the progressive refinement of a crude model through a series of vertex-splits operations.

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Matchmaker: Manifold Breps for Non-manifold r-sets

1999 , Rossignac, Jarek , Cardoze, David Enrique Fabrega

Many solid modeling construction techniques produce non-manifold r-sets (solids). With each non-manifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each non-manifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some non-manifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a non-manifold solid may be encoded using simpler and more compact data-structures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a non-manifold representation for a variety of tasks, such as simplification, compression, interference detection or rendering. Most choices of the map A lead to invalid (self-intersecting) boundaries and to unnecessary vertex replications for M. We propose an efficient algorithm, called Matchmaker, which computes a map A, such that there exists an infinitely small perturbation of the vertices and edges of M that produces a valid (non self-intersecting) boundary of a manifold solid. Furthermore, our approach avoids most unnecessary vertex replications.

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Compressed Progressive Meshes

1999 , 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, where 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 signitifant overhead when the full resolution model must be downloaded. The CPM (Compressed Progressive Meshes) appreach proposed here eliminates this overhead. It uses a new "patching" technique, which refines the topology of the mesh in batches, which each increase the number of vertices by up to 50%. Less than 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.

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Connectivity Compression for Irregular Quadrilateral Meshes

1999 , King, Davis , Rossignac, Jarek , Szymczak, Andrzej

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads.

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