Best simple octagonal distances in digital geometry

The Geometry of Triadic Distances

Triadic distances t defined as functions of the Euclidean (dyadic) distances a1, a2, a3 between three points are studied. Special attention is paid to the contours of all points giving the same value of t when a3 is kept constant . These isocontours allow some general comments to be made about the suitability, or not, for practical investigations of certain definitions of triadic distance. We a...

Computing Distances between Surfaces Using Line Geometry

We present an algorithm for computing the distance between two free-form surfaces. Using line geometry, the distance computation is reformulated as a simple instance of a surface-surface intersection problem, which leads to lowdimensional root finding in a system of equations. This approach produces an efficient algorithm for computing the distance between two ellipsoids, where the problem is r...

Distances on a Lattice From Noncommutative Geometry

Using the tools of noncommutative geometry we calculate the distances between the points of a lattice on which the usual discretized Dirac operator has been defined. We find that these distances do not have the expected behaviour, revealing that from the metric point of view the lattice does not look at all as a set of points sitting on the continuum manifold. We thus have an additional criteri...

Protein Geometry: Volumes, Areas, and Distances

On approximating Euclidean metrics by digital distances in 2D and 3D

In this paper a geometric approach is suggested to ®nd the closest approximation to Euclidean metric based on geometric measures of the digital circles in 2D and the digital spheres in 3D for the generalized octagonal distances. First we show that the vertices of the digital circles (spheres) for octagonal distances can be suitably approximated as a function of the number of neighborhood types ...