Computational geometry: an introduction
Computational geometry: an introduction
CVGIP: Graphical Models and Image Processing
Discrete Combinatorial Surfaces
Graphical Models and Image Processing
A definition of surfaces of Z3 . A new 3D discrete Jordan theorem
Theoretical Computer Science
Combinatorics of patterns of a bidimensional Sturmian sequence.
Theoretical Computer Science
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
About local configurations in arithmetic planes
Theoretical Computer Science
Local Configurations of Digital Hyperplanes
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
(n, m)-Cubes and Farey Nets for Naive Planes Understanding
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Naive Planes as Discrete Combinatorial Surfaces
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Recognition of Digital Naive Planes and Polyhedrization
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Two-dimensional iterated morphisms and discrete planes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Lattices and multi-dimensional words
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Digital lines with irrational slopes
Theoretical Computer Science
Functional stepped surfaces, flips, and generalized substitutions
Theoretical Computer Science
Local rule substitutions and stepped surfaces
Theoretical Computer Science
A characterization of flip-accessibility for rhombus tilings of the whole plane
Information and Computation
Consistency of multidimensional combinatorial substitutions
Theoretical Computer Science
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A standard discrete plane is a subset of ℤ3 verifying the double Diophantine inequality μ ≤ ax + by + cz μ + ω, with (a,b,c) ≠ (0,0,0). In the present paper we introduce a generalization of this notion, namely the (1,1,1)-discrete surfaces. We first study a combinatorial representation of discrete surfaces as two-dimensional sequences over a three-letter alphabet and show how to use this combinatorial point of view for the recognition problem for these discrete surfaces. We then apply this combinatorial representation to the standard discrete planes and give a first attempt of to generalize the study of the dual space of parameters for the latter [VC00].