Multi-line Stochastic Boundary Intersection Method forGeometric Property Computation скачать в хорошем качестве

Multi-line Stochastic Boundary Intersection Method forGeometric Property Computation

Abstract This paper presents a novel computational method for determining geometric properties—area, perimeter, and volume—of irregular two-dimensional and three-dimensional shapes through multi-line stochastic boundary intersection (MSBI). The method employs an iterative ray-casting algorithm that systematically probes shape boundaries from multiple origin points using discrete angular distributions. By retaining only rays that maintain complete boundary intersection while filtering premature exits, the algorithm constructs a comprehensive boundary point network. The resulting point cloud enables accurate property estimation through tessellation and numerical integration techniques. We demonstrate theoretical convergence properties and empirical validation on both synthetic and real-world geometries.