Generalised Triangular Grids in Digital Geometry
نویسنده
چکیده
The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as oneand two-planes triangular grids). This family comes from the mapping their points to Z3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this paper we analyze this grid and its dual from view of neighbouring conditions. After this we consider the n-planes grid. We prove that for n > 3 the n-planes triangular grids are non-planar. We also examine the ‘circular’ three-planes grid and the higher dimensional triangular grids.
منابع مشابه
Shortest Paths in Triangular Grids with Neighbourhood Sequences
In this paper we analyse some properties of the triangular and hexagonal grids in the 2D digital space. We define distances based on neighbourhood relations that can be introduced in these grids. We present an algorithm, which calculates the distance from an arbitrary point to another one for a given neighbourhood sequence in the triangular grid. Moreover, this algorithm produces the shortest p...
متن کاملNumerical Integration of Fluid Flow over Triangular Grids
Discrete approximations to hyperbolic partial differential equations governing frictionless two-dimensional fluid flow are developed in Cartesian geometry for use over arbitrary triangular grids. A class of schemes is developed that conserves mass, momentum, and total energy. The terms of the governing equations are also approximated individually and their truncation error is examined. For test...
متن کاملGeneralised primal-dual grids for unstructured co-volume schemes
The generation of high-quality staggered unstructured grids for computational simulation is considered; leading to the development of a new optimisation-based strategy for the construction of weighted ‘RegularPower’ tessellations appropriate for co-volume type numerical techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble gen...
متن کاملSpecial Issue: Discrete Geometry for Computer Imagery Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic grids
On the classical discrete grid, the analysis of digital straight lines (DSL for short) has been intensively studied for nearly half a century. In this article, we are interested in a discrete geometry on irregular grids. More precisely, our goal is to define geometrical properties on irregular isothetic grids that are tilings of the Euclidean plane with different sized axis parallel rectangles....
متن کامل