Polygonal models acquired with emerging 3D scanning technology or from large scale CAD applications easily reach sizes of several gigabytes and do not fit in the address space of common 32-bit desktop PCs. In this paper we propose an out-of-core mesh compression technique that converts such gigantic meshes into a streamable, highly compressed representation. During decompression only a small portion of the mesh needs to be kept in memory at any time. As full connectivity information is available along the decompression boundaries, this provides seamless mesh access for incremental in-core processing on gigantic meshes. Decompression speeds are CPU-limited and exceed one million vertices and two million triangles per second on a 1.8 GHz Athlon processor.

Summary. 3D meshes are widely used in graphic and simulation applications for approximating 3D objects. When representing complex shapes in a raw data format, meshes consume a large amount of space. Applications calling for compact storage and fast transmission of 3D meshes have motivated the multitude of algorithms developed to efficiently compress these datasets. In this paper we survey recent developments in compression of 3D surface meshes. We survey the main ideas and intuition behind techniques for single-rate and progressive mesh coding. Where possible, we discuss the theoretical results obtained for asymptotic behavior or optimality of the approach. We also list some open questions and directions for future research. 1

... this paper we introduce a connectivity encoding method which extends these ideas to 2manifold meshes consisting of faces with arbitrary degree. The encoding algorithm exploits duality by applying valence enumeration to both the primal and dual mesh in a symmetric fashion. It generates two sequences of symbols, vertex valences and face degrees, and encodes them separately using two context-based arithmetic coders. This allows us to exploit vertex and/or face regularity if present. When the mesh exhibits perfect face regularity (e.g., a pure triangle or quad mesh) and/or perfect vertex regularity (valence six or four respectively) the corresponding bit rate vanishes to zero asymptotically. For triangle meshes, our technique is equivalent to earlier valence driven approaches. We report compression results for a corpus of standard meshes. In all cases we are able to show coding gains over earlier coders, sometimes as large as 50%. Remarkably, we even slightly gain over coders specialized to triangle or quad meshes. A theoretical analysis reveals that our approach is near-optimal as we achieve the Tutte entropy bound for arbitrary planar graphs of 2 bits per edge in the worst case.

We present Angle-Analyzer, a new single-rate compression algorithm for triangle-quad hybrid meshes. Using a carefully-designed geometry-driven mesh traversal and an efficient encoding of intrinsic mesh properties, AngleAnalyzer produces compression ratios 40% better in connectivity and 20% better in geometry than the leading Touma and Gotsman technique for the same level of geometric distortion. The simplicity and performance of this new technique is demonstrated, and we provide extensive comparative tests to contrast our results with the current state-of-the-art techniques.

Unstructured hexahedral volume meshes are of particular interest for visualization and simulation applications. They allow regular tiling of the three-dimensional space and show good numerical behaviour in finite element computations. Beside such appealing properties, volume meshes take huge amount of space when stored in a raw format. In this paper we present a technique for encoding connectivity and geometry of unstructured hexahedral volume meshes. For

The sizeof geometric data sets in scientific and industrial applications is constantly increasing. Storing surfng or volume meshes in standard uncompressedf ormats results in large files that are expensive to store and slow to load and transmit. Scientists and engineersofne refeer ff using mesh compression because currently available schemes modif the mesh data. While connectivity is encoded in a lossless manner, the floating-point coordinates associated with the vertices are quantized onto aunif6: integer grid to enable e#cient predictive compression. Although a fine enough grid can usually represent the data with su#cient precision, the original floating-point values will change, regardless of grid resolution. In this paper we describe a methodf or compressing floating-point coordinates with predictive coding in a completely lossless manner. The initial quantization step is omitted and predictions are calculated in floating-point. The predicted and the actual floating-point values are broken up into sign, exponent, and mantissa and their corrections are compressed separately with context-based arithmetic coding. As the quality of the predictions varies with the exponent, we use the exponent to switch between di#erent arithmetic contexts. We report compression results using the popular parallelogram predictor, but our approach will work with any prediction scheme. The achieved bit-ratesf or lossless floating-point compression nicely complement those resultingfsu unifting quantizing with di#erent precisions.

We show that the average entropy of the distribution of valences in valence sequences for the class of manifold 3D triangle meshes and the class of manifold 3D polygon meshes is strictly less than the entropy of these classes themselves. This implies that, apart from a valence sequence, another essential piece of information is needed for valence-based connectivity coding of manifold 3D meshes. Since there is no upper bound on the size of this extra piece of information, the result implies that the question of optimality of valence-based connectivity coding is still open.

In this paper we describe a strategy for efficient predictive compression of texture coordinates. Previous works in mesh compression often claim that this mesh property can simply be compressed with the same predictor that is already used for vertex positions. However, in the presence of discontinuities in the texture mapping such an approach results in unreasonable predictions. Our method avoids such predictions altogether. Rather than performing an unreasonable prediction, we switch to a less promising, but at least reasonable predictor. The resulting correctors are then compressed with different arithmetic contexts.

Approved for public release; further dissemination unlimited

We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding. Furthermore, we introduce a novel linear prediction scheme for geometry compression of 3D meshes. Together, these approaches yield a significant entropy reduction for mesh encoding with an average of 20-30 % over leading single-rate regiongrowing coders, both for connectivity and geometry. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Surface mesh compression, connectivity coding, geometry coding. 1.