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Generating textures on arbitrary surfaces using reaction-diffusion
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Guaranteed-quality mesh generation for curved surfaces
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Using particles to sample and control implicit surfaces
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A Delaunay refinement algorithm for quality 2-dimensional mesh generation
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Guaranteeing the topology of an implicit surface polygonization for interactive modeling
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Surface reconstruction by Voronoi filtering
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Multiresolution signal processing for meshes
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Surface approximation and geometric partitions
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Nice point sets can have nasty Delaunay triangulations
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Hierarchical extraction of iso-surfaces with semi-regular meshes
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Complexity of the delaunay triangulation of points on surfaces the smooth case
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Variational shape approximation
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Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
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Interpolating and approximating implicit surfaces from polygon soup
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Provably good moving least squares
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SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Triangulating point set surfaces with bounded error
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Provably good moving least squares
ACM Transactions on Algorithms (TALG)
Direct sampling on surfaces for high quality remeshing
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Computational Geometry: Theory and Applications
Direct sampling on surfaces for high quality remeshing
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Convex hull and voronoi diagram of additively weighted points
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Quality tetrahedral mesh generation for macromolecules
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ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
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We present an algorithm for meshing surfaces that is a simple adaptation of a greedy "farthest point" technique proposed by Chew. Given a surface S, it progressively adds points on S and updates the 3-dimensional Delaunay triangulation of the points. The method is very simple and works in 3d-space without requiring to parameterize the surface. Taking advantage of recent results on the restricted Delaunay triangulation, we prove that the algorithm can generate good samples on S as well as triangulated surfaces that approximate S. More precisely, we show that the restricted Delaunay triangulation Del\S of the points has the same topology type as S, that the Hausdorff distance between Del\S and S can be made arbitrarily small, and that we can bound the aspect ratio of the facets of Del\S. The algorithm has been implemented and we report on experimental results that provide evidence that it is very effective in practice. We present results on implicit surfaces, on CSG models and on polyhedra. Although most of our theoretical results are given for smooth closed surfaces, the method is quite robust in handling smooth surfaces with boundaries, and even non-smooth surfaces.