Distance-Driven Curve-Thinning on the Face-Centered Cubic Grid

Karai, Gábor

doi:10.1007/978-3-031-19897-7_28

Cited by 1 publication

(1 citation statement)

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“…boundary tracking of objects built by Voronoi voxels of the f.c.c. lattice (Gardun ˜o et al, 1998;Herman, 1998), multispeed fuzzy segmentation algorithm (Carvalho et al, 2001), supercover (Linh et al, 2004), distance transform (Chen & Zhao, 2009;Fouard et al, 2007;Strand, 2005), surface skeletons (Strand, 2004;Karai, 2021), distance-driven curvethinning (Karai, 2022), topology-preserving marching cube like algorithms (Strand & Stelldinger, 2007), and ray-tracing and the object description method for objects sampled in the f.c.c. grid (Iba ´n ˜ez et al, 1997).…”

Section: Literature Reviewmentioning

confidence: 99%

Distances in the face-centered cubic crystalline structure applying operational research

Stomfai,

Kovács,

Nagy

et al. 2023

Acta Cryst Sect A

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The f.c.c. (face-centered cubic) grid is the structure of many crystals and minerals. It consists of four cubic lattices. It is supposed that there are two types of steps between two grid points. It is possible to step to one of the nearest neighbors of the same cubic lattice (type 1) or to step to one of the nearest neighbors of another cubic lattice (type 2). Steps belonging to the same type have the same length (weight). However, the two types have different lengths and thus may have different weights. This paper discusses the minimal path between any two points of the f.c.c. grid. The minimal paths are explicitly given, i.e. to obtain a minimal path one is required to perform only O(1) computations. The mathematical problem can be the model of different spreading phenomena in crystals having the f.c.c. structure.

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