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Geometric Compression through Topological Surgery
 ACM TRANSACTIONS ON GRAPHICS
, 1998
"... ... 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 ..."
Abstract

Cited by 251 (26 self)
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... 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 Deering's 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 times 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
Streaming simplification of tetrahedral meshes
 IEEE Transactions on Visualization and Computer Graphics
, 2005
"... Abstract—Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can ac ..."
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Cited by 14 (6 self)
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Abstract—Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish realtime visualization necessary for scientific analysis. We propose a twostep approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/Oefficient format that allows coherent access to the tetrahedral cells. A quadricbased simplification is sequentially performed on small portions of the mesh incore. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates outofcore to process meshes too large for main memory. Index Terms—Computational geometry and object modeling, outofcore algorithms, streaming algorithms, mesh simplification, large meshes, tetrahedral meshes. 1
Feline Horse
"... A new progressive lossless 3D triangular mesh encoder is proposed in this work, which can encode any 3D triangular mesh with an arbitrary topological structure. Given a mesh, the quantized 3D vertices are first partitioned into an octree (OT) structure, which is then traversed from the root and grad ..."
Abstract
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A new progressive lossless 3D triangular mesh encoder is proposed in this work, which can encode any 3D triangular mesh with an arbitrary topological structure. Given a mesh, the quantized 3D vertices are first partitioned into an octree (OT) structure, which is then traversed from the root and gradually to the leaves. During the traversal, each 3D cell in the tree front is subdivided into eight childcells. For each cell subdivision, both local geometry and connectivity changes are encoded, where the connectivity coding is guided by the geometry coding. Furthermore, prioritized cell subdivision is performed in the tree front to provide better ratedistortion (RD) performance. Experiments show that the proposed mesh coder outperforms the kdtree algorithm in both geometry and connectivity coding efficiency. For the geometry coding part, the range of improvement is typically around 10%∼20%, but may go up to 50%∼60 % for meshes with highly regular geometry data and/or tight clustering of vertices.
Eurographics Symposium on Geometry Processing (2004)
"... We propose a metric for surface parameterization specialized to its signal that can be used to create more efficient, highquality texture maps. Derived from Taylor expansion of signal error, our metric predicts the signal approximation error  the difference between the original surface signal an ..."
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We propose a metric for surface parameterization specialized to its signal that can be used to create more efficient, highquality texture maps. Derived from Taylor expansion of signal error, our metric predicts the signal approximation error  the difference between the original surface signal and its reconstruction from the sampled texture.