Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid
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 du...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | ISPRS International Journal of Geo-Information |
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| Online Access: | http://www.mdpi.com/2220-9964/7/10/391 |
| _version_ | 1818950962871533568 |
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| author | Lingyu Du Qiuhe Ma Jin Ben Rui Wang Jiahao Li |
| author_facet | Lingyu Du Qiuhe Ma Jin Ben Rui Wang Jiahao Li |
| author_sort | Lingyu Du |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T09:26:56Z |
| format | Article |
| id | doaj.art-7631472702134782a7847dd77f753791 |
| institution | Directory Open Access Journal |
| issn | 2220-9964 |
| language | English |
| last_indexed | 2024-12-20T09:26:56Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | ISPRS International Journal of Geo-Information |
| spelling | doaj.art-7631472702134782a7847dd77f7537912022-12-21T19:45:10ZengMDPI AGISPRS International Journal of Geo-Information2220-99642018-09-0171039110.3390/ijgi7100391ijgi7100391Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular GridLingyu Du0Qiuhe Ma1Jin Ben2Rui Wang3Jiahao Li4Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, ChinaInstitute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, ChinaInstitute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, ChinaInstitute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, ChinaThe Army Infantry Academy, Nanchang 330103, ChinaVectors 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.http://www.mdpi.com/2220-9964/7/10/391vectorgrid transformationtrianglehexagondualitydimensionality reduction |
| spellingShingle | Lingyu Du Qiuhe Ma Jin Ben Rui Wang Jiahao Li Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid ISPRS International Journal of Geo-Information vector grid transformation triangle hexagon duality dimensionality reduction |
| title | Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid |
| title_full | Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid |
| title_fullStr | Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid |
| title_full_unstemmed | Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid |
| title_short | Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid |
| title_sort | duality and dimensionality reduction discrete line generation algorithm for a triangular grid |
| topic | vector grid transformation triangle hexagon duality dimensionality reduction |
| url | http://www.mdpi.com/2220-9964/7/10/391 |
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