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A Vertex Concavity-Convexity Detection Method for Three-Dimensional Spatial Objects Based on Geometric Algebra

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Natural Resources and Planning Bureau of Xuzhou City, Xuzhou 221006, China
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School of Environment Science and Spatial Information, China University of Mining and Technology, Xuzhou 221018, China
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College of Geographic Science, Nantong University, Nantong 226019, China
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Geological Exploration Technology Institute of Jiangsu Province, Nanjing 210046, China
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Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China
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Natural Resources and Planning Bureau of Xinyi City, Xuzhou 221400, China
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2020, 9(1), 25; https://doi.org/10.3390/ijgi9010025
Received: 19 November 2019 / Revised: 15 December 2019 / Accepted: 17 December 2019 / Published: 1 January 2020
Vertex concavity-convexity detection for spatial objects is a basic algorithm of computer graphics, as well as the foundation for the implementation of other graphics algorithms. In recent years, the importance of the vertex concavity-convexity detection algorithm for three-dimensional (3D) spatial objects has been increasingly highlighted, with the development of 3D modeling, artificial intelligence, and other graphics technologies. Nonetheless, the currently available vertex concavity-convexity detection algorithms mostly use two-dimensional (2D) polygons, with limited research on vertex concavity-convexity detection algorithms for 3D polyhedrons. This study investigates the correlation between the outer product and the topology of the spatial object based on the unique characteristic that the outer product operation in the geometric algebra has unified and definitive geometric implications in space, and with varied dimensionality. Moreover, a multi-dimensional unified vertex concavity-convexity detection algorithm framework for spatial objects is proposed, and this framework is capable of detecting vertex concavity-convexity for both 2D simple polygons and 3D simple polyhedrons. View Full-Text
Keywords: concavity-convexity detection; geometric algebra; outer product; multidimensional unified concavity-convexity detection; geometric algebra; outer product; multidimensional unified
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Yin, P.; Zhang, J.; Sun, X.; Hu, D.; Shi, Z.; Wu, C. A Vertex Concavity-Convexity Detection Method for Three-Dimensional Spatial Objects Based on Geometric Algebra. ISPRS Int. J. Geo-Inf. 2020, 9, 25.

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