Planes with analogues to Euclidean angular bisectors.

On bisectors in normed planes

In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors...

Euclidean Skeletons and Conditional Bisectors

This paper deals with the determination of skeletons and conditional bisectors in discrete binary images using the Euclidean metrics. The algorithm, derived from [18], proceeds in two steps: rst, the Centers of the Euclidean Maximal Discs (CMD) included in the set to skeletonize are characterized and robustly identi ed. Second, a refront propagation is simulated starting from the set boundaries...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

New Discretization of Complex Analysis: The Euclidean and Hyperbolic Planes

Few years ago we developed jointly with I.Dynnikov new discretization of complex analysis (DCA) based on the two-dimensional manifolds with colored black/white triangulation (see [1]). Especially deep results were obtained for the Euclidean plane with equilateral triangle lattice. In the present work we develop a DCA theory for the analogs of equilateral triangle lattice in Hyperbolic plane. So...

A Combinatorial Distinction Between the Euclidean and Projective Planes

Let nand m be integers with n = m 2 + m + 1. Then the projective plane of order m has n points and" lines with each line containing m + 1 ""n 1/2 points. In this paper, we consider the analogous problem for the Euclidean plane and show that there cannot be a comparably large collection of lines each of which contains approximately n 1/ 2 points from a given set of n points. More precisely, we s...