STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Journal of Algorithms
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Information-based complexity
Non-convex contour reconstruction
Journal of Symbolic Computation
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Geometric reconstruction problems
Handbook of discrete and computational geometry
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design
Complexity and information
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Guaranteed Quality Triangulation of Molecular Skin Surfaces
VIS '04 Proceedings of the conference on Visualization '04
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Learning smooth objects by probing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Building triangulations using ε-nets
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
From Segmented Images to Good Quality Meshes Using Delaunay Refinement
Emerging Trends in Visual Computing
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We consider the problem of discovering a smooth unknown surface S bounding an object O in R^3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated that approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, normal approximation, etc.