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A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication

1
Institute of Remote Sensing and GIS, Peking University, Beijing 100871, China
2
Information Engineering University, Zhengzhou 450001, China
3
College of Engineering, Peking University, Beijing 100871, China
4
Logistics Science Research Institute, Beijing 100166, China
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2019, 8(3), 146; https://doi.org/10.3390/ijgi8030146
Received: 4 February 2019 / Revised: 6 March 2019 / Accepted: 15 March 2019 / Published: 19 March 2019
(This article belongs to the Special Issue GIS Software and Engineering for Big Data)
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Abstract

Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which are the position of the starting point, the length of the starting edge, and the direction of the starting edge. On this basis, the effective boundary of a multiscale grid can be determined and the grid coordinates of a multiscale grid can be obtained. A one-to-one correspondence between the multiscale grids and subdivision types can be established. Through the appropriate rotation, translation and scaling of the multiscale grid, the node coordinates of a single triangular grid system are calculated, and the relationships between the nodes of different levels are established. Finally, this paper takes a hexagonal grid as an example to carry out the experiment verifications by converting a single triangular grid system (plane) directly to a single triangular grid with a positive icosahedral surface to generate a positive icosahedral surface grid. The experimental results show that the algorithm has good universality and can generate the multiscale grid of an arbitrary grid configuration by adjusting the corresponding starting transformation parameters. View Full-Text
Keywords: unit replication; regional control; discrete global grid system; hexagonal grid; regular icosahedron unit replication; regional control; discrete global grid system; hexagonal grid; regular icosahedron
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Meng, L.; Tong, X.; Fan, S.; Cheng, C.; Chen, B.; Yang, W.; Hou, K. A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication. ISPRS Int. J. Geo-Inf. 2019, 8, 146.

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