Arithmetic coding for data compression
Communications of the ACM
Face fixer: compressing polygon meshes with properties
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Progressive lossless compression of arbitrary simplicial complexes
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Compressing polygon mesh geometry with parallelogram prediction
Proceedings of the conference on Visualization '02
Near-optimal connectivity encoding of 2-manifold polygon meshes
Graphical Models - Special issue: Processing on large polygonal meshes
Compression of Large 3D Engineering Models using Automatic Discovery of Repeating Geometric Features
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Delphi: geometry-based connectivity prediction in triangle mesh compression
The Visual Computer: International Journal of Computer Graphics
Journal of Visual Communication and Image Representation
A logistic model for the degradation of triangle mesh normals
Proceedings of the 7th international conference on Curves and Surfaces
| Hi-index | 0.00 |
The parallelogram rule is a simple, yet effective scheme to predict the position of a vertex from a neighboring triangle. It was introduced by Touma and Gotsman [1998] to compress the vertex positions of triangular meshes. Later, Isenburg and Alliez [2002] showed that this rule is especially efficient for quad-dominant polygon meshes when applied "within" rather than across polygons. However, for hexagon-dominant meshes the parallelogram rule systematically performs miss-predictions.In this paper we present a generalization of the parallelogram rule to higher degree polygons. We compute a Fourier decomposition for polygons of different degrees and assume the highest frequencies to be zero for predicting missing points around the polygon. In retrospect, this theory also validates the parallelogram rule for quadrilateral surface mesh elements, as well as the Lorenzo predictor [Ibarria et al. 2003] for hexahedral volume mesh elements.