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首页> 外文期刊>Progress in Artificial Intelligence >A Vertex Concavity-Convexity Detection Method for Three-Dimensional Spatial Objects Based on Geometric Algebra
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A Vertex Concavity-Convexity Detection Method for Three-Dimensional Spatial Objects Based on Geometric Algebra

机译：基于几何代数的三维空间对象的顶点凹凸凸性检测方法

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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.
机译：空间对象的顶点凹凸凸性检测是计算机图形学的基本算法，以及实现其他图形算法的基础。近年来，随着3D建模，人工智能和其他图形技术的发展，三维（3D）空间物体的顶点凹凸凸性检测算法的重要性已经越来越突出显示。尽管如此，目前可用的顶点凹凸凸性检测算法主要使用二维（2D）多边形，对3D多面体的顶点凹凸凸性检测算法有限。本研究研究了外部产品与空间物体拓扑之间的相关性，基于几何代数中的外部产品操作在空间中具有统一和明确的几何影响，并且具有不同的维度。此外，提出了一种用于空间对象的多维统一顶点凹凸检测算法框架，并且该框架能够检测2D简单多边形和3D简单多面体的顶点凹凸凸性。

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