O. Figueiredo, J.P. Reveillès

Proceedings 5th Colloquium Discrete Geometry and Computer Imagery, September 25-27, 1995, Clermont Ferrand, 187-198

We propose in this paper a new approach to three-dimensional digital lines
(3DDLs) based on the study of the integer lattice generated by the
projection of Z^{3} onto an euclidean plane which
reduces the problem to dimension 2. The many properties of this lattice
lead to an arithmetical definition of 3DDLs in accordance with a
topological characterization. This definition is then used in an
algorithm that calculates the intersection between a naive 3DDL and an
arbitrary digital plane. We also show that this algorithm can be extended
to calculate the intersection between a plane and a set of adjacent 3DDLs
incrementally in a very efficient manner.

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