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

Abstract

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.

Indexing Mixed Aperture Icosahedral Hexagonal Discrete Global Grid Systems

“…Current research indicates that the discretization of vector lines is the premise and basis of the discretization of vector data [35]. Most of study on the rasterization of line features is based on triangular or quadrilateral grids on the planes and fewer are based on hexagonal grids.…”

“…Our research group has proposed one algorithm to solve the above problems, called "duality and dimensionality reduction discrete line generation algorithm" [35]. In this algorithm, the index arithmetics of hexagonal grids is used to replace spherical geometry operation of coordinates of cells in generating the discrete vector line.…”

“…The two algorithms are both implemented in C++ and compiled into the release version and executed on a Figure 15. Flowchart of discretizing the vector line on the sphere using hexagonal grids: the process in this algorithm (except the index addition) is referred to the literature [35] (source-partly cited from [35] and changed according to own study).…”

General Method for Extending Discrete Global Grid Systems to Three Dimensions

“…Many different DGGSs have been proposed and compared [16][17][18][19], each with strengths and weaknesses. Likewise, there have been many works on algorithms for DGGSs, including more efficient indexing [29,30], faster and more accurate vector rasterization [31], and conversions of indices between different DGGSs [32]. A comprehensive overview of DGGSs in the context of a globe-based Digital Earth can be found in [9,11].…”

A Topology Preserving Gridding Method for Vector Features in Discrete Global Grid Systems

“…Therefore, the gridding of line features is the transformation from connected geometric straight-line segments to continuous grid cell strings. In this regard, a series of mature algorithms [20] have been proposed by scholars.…”