The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Detection of the discrete convexity of polyominoes
Discrete Applied Mathematics
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
On the tiling by translation problem
Discrete Applied Mathematics
Lyndon + Christoffel = digitally convex
Pattern Recognition
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A note on a result of daurat and nivat
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Arithmetic discrete planes are quasicrystals
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 in Zd
Theoretical Computer Science
About thin arithmetic discrete planes
Theoretical Computer Science
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For discrete sets coded by the Freeman chain describing their contour, several linear algorithms have been designed for determining their shape properties. Most of them are based on the assumption that the boundary word forms a closed and non-intersecting discrete curve. In this article, we provide a linear time and space algorithm for deciding whether a path on a square lattice intersects itself. This work removes a drawback by determining efficiently whether a given path forms the contour of a discrete figure. This is achieved by using a radix tree structure over a quadtree, where nodes are the visited grid points, enriched with neighborhood links that are essential for obtaining linearity.