Tilings and patterns
Discrete analytical hyperplanes
Graphical Models and Image Processing
Discrete Applied Mathematics
Functional stepped surfaces, flips, and generalized substitutions
Theoretical Computer Science
On some applications of generalized functionality for arithmetic discrete planes
Image and Vision Computing
On the tiling by translation problem
Discrete Applied Mathematics
Minimal arithmetic thickness connecting discrete planes
Discrete Applied Mathematics
Lyndon + Christoffel = digitally convex
Pattern Recognition
On the connecting thickness of arithmetical discrete planes
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A linear time and space algorithm for detecting path intersection
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
About thin arithmetic discrete planes
Theoretical Computer Science
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Arithmetic discrete planes can be considered as liftings in the space of quasicrystals and tilings of the plane generated by a cut and project construction. We first give an overview of methods and properties that can be deduced from this viewpoint. Substitution rules are known to be an efficient construction process for tilings. We then introduce a substitution rule acting on discrete planes, which maps faces of unit cubes to unions of faces, and we discuss some applications to discrete geometry.