Time complexity analysis for two non-angle algorithms to determine the radial spatial adjacent relationship

Angle is an essential parameter in describing and analysing the spatial object correlation. Several important algorithms adopt an azimuth angle or angle as the parameter in spatial analysis. How to select a credible algorithm with high efficiency is of great concern, especially for mass data processing and applications demanding real-time analysis. Taking the arc–arc topological relationship established on the nodes as an example, the time complexity for two non-angle algorithms to determine the radial spatial adjacent relationship is comparatively analysed. The effectiveness of the two algorithms is also discussed when the application range is extended to determine the spatial relationship of point sets. It is shown that, in such a spatial analysis, Qi based on Qi ( x i , y i ) is an algorithm with low time complexity and high credibility. It allows people to keep using the azimuth angle in spatial analysis. At the same time, it provides an efficient approach with the same function as the azimuth angle but with lower time complexity. It can be used to improve on the time complexity for some important related algorithms. The result of this paper has a useful effect on how to select a credible algorithm with high efficiency according to the problems occurring in the related area of spatial analysis software engineering.