Betti Number for Point Sets

Abstract Topology is the foundation for many industrial applications ranging from CAD to simulation analysis. Computational topology mostly focuses on structured data such as mesh. However, unstructured datasets point sets remain a virgin land scientists. The significance of point-based can never be overemphasized, especially in area reverse engineering, geometric modeling, and algorithmic In this paper, we propose novel approach compute Betti number set illustrate its usefulness real-world examples. To best our knowledge, work pioneering first kind field computational topology.