SGP07: Eurographics Symposium on Geometry Processing
https://diglib.eg.org:443/handle/10.2312/440
2024-03-29T12:01:41ZDelaunay Mesh Construction
https://diglib.eg.org:443/handle/10.2312/SGP.SGP07.273-282
Delaunay Mesh Construction
Dyer, Ramsay; Zhang, Hao; Moeller, Torsten
Alexander Belyaev and Michael Garland
We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometrypreserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a poorly sampled input mesh may yield unflippable edges necessitating refinement to ensure a Delaunay mesh output. Multiresolution Delaunay meshes can be obtained via constrained mesh decimation. We further examine the usefulness of trading off the geometry-preserving feature of our algorithm with the ability to create fewer triangles. We demonstrate the performance of our algorithms through several experiments.
2007-01-01T00:00:00ZFast Normal Vector Compression with Bounded Error
https://diglib.eg.org:443/handle/10.2312/SGP.SGP07.263-272
Fast Normal Vector Compression with Bounded Error
Griffith, E. J.; Koutek, M.; Post, Frits H.
Alexander Belyaev and Michael Garland
We present two methods for lossy compression of normal vectors through quantization using base polyhedra. The first revisits subdivision-based quantization. The second uses fixed-precision barycentric coordinates. For both, we provide fast (de)compression algorithms and a rigorous upper bound on compression error. We discuss the effects of base polyhedra on the error bound and suggest polyhedra derived from spherical coverings. Finally, we present compression and decompression results, and we compare our methods to others from the literature.
2007-01-01T00:00:00ZRidge Based Curve and Surface Reconstruction
https://diglib.eg.org:443/handle/10.2312/SGP.SGP07.243-251
Ridge Based Curve and Surface Reconstruction
Suessmuth, Jochen; Greiner, Guenther
Alexander Belyaev and Michael Garland
This paper presents a new method for reconstructing curves and surfaces from unstructured point clouds, allowing for noise in the data as well as inhomogeneous distribution of the point set. It is based on the observation that the curve/surface is located where locally the point cloud has highest density. This idea is pursued by a differential geometric analysis of a smoothed version of the density function. More precisely we detect ridges of this function and have to single out the relevant parts. An efficient implementation of this approach evaluates the differential geometric quantities on a regular grid, performs local analysis and finally recovers the curve/surface by an isoline extraction or a marching cubes algorithm respectively. Compared to existing surface reconstruction procedures, this approach works well for noisy data and for data with strongly varying sampling rate. Thus it can be applied successfully to reconstruct surface geometry from time-of-flight data, overlapping registered point clouds and point clouds obtained by feature tracking from video streams. Corresponding examples are presented to demonstrate the advantages of our method.
2007-01-01T00:00:00ZSurface Reconstruction using Local Shape Priors
https://diglib.eg.org:443/handle/10.2312/SGP.SGP07.253-262
Surface Reconstruction using Local Shape Priors
Gal, Ran; Shamir, Ariel; Hassner, Tal; Pauly, Mark; Or, Daniel Cohen
Alexander Belyaev and Michael Garland
We present an example-based surface reconstruction method for scanned point sets. Our approach uses a database of local shape priors built from a set of given context models that are chosen specifically to match a specific scan. Local neighborhoods of the input scan are matched with enriched patches of these models at multiple scales. Hence, instead of using a single prior for reconstruction, our method allows specific regions in the scan to match the most relevant prior that fits best. Such high confidence matches carry relevant information from the prior models to the scan, including normal data and feature classification, and are used to augment the input point-set. This allows to resolve many ambiguities and difficulties that come up during reconstruction, e.g., distinguishing between signal and noise or between gaps in the data and boundaries of the model. We demonstrate how our algorithm, given suitable prior models, successfully handles noisy and under-sampled point sets, faithfully reconstructing smooth regions as well as sharp features.
2007-01-01T00:00:00Z