Computational geometry: an introduction
Computational geometry: an introduction
Combinatorial optimization: algorithms and complexity
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Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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Information Processing Letters
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Graphical Models and Image Processing
Erased arrangements of lines and convex decompositions of polyhedra
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Pattern Recognition Letters
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DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
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IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Maximal digital straight segments and convergence of discrete geometric estimators
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
On the polyhedral complexity of the integer points in a hyperball
Theoretical Computer Science
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
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In recent years the problem of obtaining a reversible discrete surface polyhedrization (DSP) is attracting an increasing interest within the discrete geometry community. In this paper we propose the first algorithm for obtaining a reversible polyhedrization with a guaranteed performance, i.e., together with a bound on the ratio of the number of facets of the obtained polyhedron and one with a minimal number of facets. The algorithm applies to the case of a convex DSP when a discrete surface M is determined by a convex body in ℝ3. The performance estimation is based on a new lower bound (in terms of the diameter of M) on the number of 2-facets of an optimal polyhedrization. That bound easily extends to an arbitrary dimension n. We also discuss on approaches for solving the general 3D DSP.