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
Polygonal Representations of Digital Sets
Algorithmica
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
What Does Digital Straightness Tell about Digital Convexity?
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Two linear-time algorithms for computing the minimum length polygon of a digital contour
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
A note on a result of daurat and nivat
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
A linear algorithm for polygonal representations of digital sets
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
A parallelogram tile fills the plane by translation in at most two distinct ways
Discrete Applied Mathematics
A decomposition theorem for homogeneous sets with respect to diamond probes
Computer Vision and Image Understanding
Combinatorial properties of double square tiles
Theoretical Computer Science
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The Freeman chain code is a common and useful way for representing discrete paths by means of words such that each letter encodes a step in a given direction. In the discrete plane Z^2 such a coding is widely used for representing connected discrete sets by their contour which forms a closed and intersection free path. In this paper, we use a multidimensional radix tree like data structure for storing paths in the discreted-dimensional space Z^d. It allows to design a simple and efficient algorithm for detecting path intersection. Even though an extra initialization is required, the time and space complexities remain linear for any fixed dimension d. Several problems that are solved by adapting our algorithm are also discussed.