Publication

A Contribution to 3D Digital Lines

1995
Conference Papers

Abstract

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 Z3 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.

Official source

https://infoscience.epfl.ch/entities/publication/b88e1509-7cb1-45f6-bf6a-820d58229d80

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1995
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b88e1509-7cb1-45f6-bf6a-820d58229d80

About this result

Related concepts (32)

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.

Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E2. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement. A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane.

Euclidean plane isometry

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below under ). The set of Euclidean plane isometries forms a group under composition: the Euclidean group in two dimensions. It is generated by reflections in lines, and every element of the Euclidean group is the composite of at most three distinct reflections.

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A Contribution to 3D Digital Lines

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