Binary Tomography on Triangular Grid Involving Hexagonal Grid Approach

Regularized binary tomography on the hexagonal grid

Physica Scripta ◽

10.1088/1402-4896/aafbcb ◽

2019 ◽

Vol 94 (2) ◽

pp. 025201 ◽

Cited By ~ 5

Author(s):

Tibor Lukić ◽

Benedek Nagy

Keyword(s):

Hexagonal Grid ◽

Binary Tomography

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Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi7100391 ◽

2018 ◽

Vol 7 (10) ◽

pp. 391 ◽

Cited By ~ 5

Author(s):

Lingyu Du ◽

Qiuhe Ma ◽

Jin Ben ◽

Rui Wang ◽

Jiahao Li

Keyword(s):

Dimensionality Reduction ◽

Path Model ◽

Triangular Grid ◽

Weak Duality ◽

Vector Data ◽

Hexagonal Grid ◽

Generation Algorithm ◽

Discrete Line ◽

Hexagonal Grids ◽

Line Generation

Vectors are a key type of geospatial data, and their discretization, which involves solving the problem of generating a discrete line, is particularly important. In this study, we propose a method for constructing a discrete line mathematical model for a triangular grid based on a “weak duality” hexagonal grid, to overcome the drawbacks of existing discrete line generation algorithms for a triangular grid. First, a weak duality relationship between triangular and hexagonal grids is explored. Second, an equivalent triangular grid model is established based on the hexagonal grid, using this weak duality relationship. Third, the two-dimensional discrete line model is solved by transforming it into a one-dimensional optimal wandering path model. Finally, we design and implement the dimensionality reduction generation algorithm for a discrete line in a triangular grid. The results of our comparative experiment indicate that the proposed algorithm has a computation speed that is approximately 10 times that of similar existing algorithms; in addition, it has better fitting effectiveness. Our proposed algorithm has broad applications, and it can be used for real-time grid transformation of vector data, discrete global grid system (DGGS), and other similar applications.

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A ray-tracing method based on the triangular grid approach and application to propagation prediction in urban environments

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2002.1011243 ◽

2002 ◽

Vol 50 (5) ◽

pp. 750-758 ◽

Cited By ~ 68

Author(s):

Zhengqing Yun ◽

Zhijun Zhang ◽

M.F. Iskander

Keyword(s):

Ray Tracing ◽

Urban Environments ◽

Triangular Grid ◽

Ray Tracing Method ◽

Grid Approach ◽

Propagation Prediction ◽

Tracing Method

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AN IMPLEMENTATION OF THE PROCEDURAL GENERATION OF UNSTRUCTURED QUADRANGULAR GRID ALGORITHM BASED ON A STRUCTURED TRIANGULAR GRID IN REGULAR HEXAGONS ON THE PLANE

СИСТЕМЫ УПРАВЛЕНИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ ◽

10.36622/vstu.2021.86.4.019 ◽

2021 ◽

pp. 88-95

Author(s):

Н.М. Чернышов ◽

О.В. Авсеева

Keyword(s):

Coordinate System ◽

Real Time ◽

Triangular Grid ◽

Large Area ◽

Hexagonal Grid ◽

Procedural Generation ◽

Grid Algorithm

Работа посвящена реализации алгоритма процедурной генерации нерегулярной четырехугольной сетки, позволяющего рассчитывать сетку для большой области в реальном времени. При генерации используются кубическая система координат, в которой строится регулярная треугольная сетка для каждой ячейки шестиугольной сетки, процедура релаксации четырехугольной сетки. This work is devoted to the implementation of an algorithm for procedural generation of an unstructured quadrangular grid, which allows to calculate the grid for a large area in real time. When building the grid, a cubic coordinate system, in which a structured triangular grid is built for each cell of a hexagonal grid, and a relaxation of the quadrangular grid algorithm are used.

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