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
Geometric reconstruction problems
Handbook of discrete and computational geometry
Complexity and information
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Learning smooth objects by probing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Learning smooth shapes by probing
Computational Geometry: Theory and Applications
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
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We consider the problem of discovering a smooth unknown surface S bounding an object O in R3. 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 which 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.