Characterization of the Closest Discrete Approximation of a Line in the 3-Dimensional Space

Toutant, Jean-Luc

doi:10.1007/11919476_62

Cited by 10 publications

(4 citation statements)

References 10 publications

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“…Then a tripod algorithm which generates an exact 3D discrete line on the cubic lattice [6] is considered. Furthermore, an algorithm for naive 3D discrete line drawing [7] is given. An algorithm based on a linear incremental algorithm which recognizes any set of points on the cubic lattice [8] is proposed.…”

Section: Introductionmentioning

confidence: 99%

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

He¹,

Liu²,

Jian³

et al. 2013

JMM

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New line generation algorithm is proposed for generating lines over 3D body-centered cubic lattice, a kind of optimal lattice in 3D space. The main contribution in this paper is employing the 3D Bresenham algorithm, a popular algorithm for generating 3D lines on a cubic lattice, to produce the BCC lattice occupied by 3D lines, with the help of the adjunct parallelepiped space, having the same center and basis vectors with the BCC lattice. The adjunct parallelepiped line is easy to generate by employing the existed 3D cubic Bresenhan algorithm. Due to the one-to-one correspondence between the parallelogram cells of parallelepiped space and the voxels of the BCC space, the 3D BCC line generation algorithm is gained. The whole procedure is characterized by a simple discriminator and a derivation for this discriminator given in the paper confirms that all calculations can be realized using only integer arithmetic which is to implement on computer

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Section: Introductionmentioning

confidence: 99%

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

He¹,

Liu²,

Jian³

et al. 2013

JMM

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“…With no claim for being exhaustive, let us quote e.g. [1,12,18,8,9]. The approach we follow here is motivated by the study of Sturmian words.…”

Section: Introductionmentioning

confidence: 99%

An Arithmetic and Combinatorial Approach to Three-Dimensional Discrete Lines

Berthé

Labbé

2011

Discrete Geometry for Computer Imagery

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Abstract. The aim of this paper is to discuss from an arithmetic and combinatorial viewpoint a simple algorithmic method of generation of discrete segments in the three-dimensional space. We consider discrete segments that connect the origin to a given point (u1, u2, u3) with coprime nonnegative integer coordinates. This generation method is based on generalized three-dimensional Euclid's algorithms acting on the triple (u1, u2, u3). We associate with the steps of the algorithm substitutions, that is, rules that replace letters by words, which allow us to generate the Freeman coding of a discrete segment. We introduce a dual viewpoint on these objects in order to measure the quality of approximation of these discrete segments with respect to the corresponding Euclidean segment. This viewpoint allows us to relate our discrete segments to finite patches that generate arithmetic discrete planes in a periodic way.

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“…With no claim for being exhaustive, let us quote e.g. [2,9,14,23]. Nevertheless, they do not fulfill Condition 1. on the linear complexity.…”

Section: Introductionmentioning

confidence: 99%

Uniformly balanced words with linear complexity and prescribed letter frequencies

Berthé

Labbé²

2011

Electron. Proc. Theor. Comput. Sci.

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We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying the following conditions: u has linear complexity function, u is uniformly balanced, the letter frequencies in u are given by the given d-uple. This paper investigates a construction method for such words based on the use of mixed multidimensional continued fraction algorithms

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Characterization of the Closest Discrete Approximation of a Line in the 3-Dimensional Space

Cited by 10 publications

References 10 publications

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

A Line Generation Algorithm over 3D Body-centered Cubic Lattice

An Arithmetic and Combinatorial Approach to Three-Dimensional Discrete Lines

Uniformly balanced words with linear complexity and prescribed letter frequencies

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