Computing the intersection between two parametric surfaces (SSI) is one of the most fundamental problems in geometric and solid modeling. Maintaining the SSI topology is critical to its computation robustness. We propose a topology-driven hybrid symbolic-numeric framework to approximate rational parametric surface-surface intersection (SSI) based on a concept of interval algebraic topology analysis (IATA), which configures within a 4D interval box the SSI topology. We map the SSI topology to an algebraic system's solutions within the framework, classify and enumerate all topological cases as a mixture of four fundamental cases (or their specific sub-cases). Various complicated topological situations are covered, such as cusp points or curves, tangent points (isolated or not) or curves, tiny loops, self-intersections, or their mixtures. The theoretical formulation is also implemented numerically using advanced real solution isolation techniques, and computed within a topology-driven framework which maximally utilizes the advantages of the topology maintenance of algebraic analysis, the robustness of iterative subdivision, and the efficiency of forward marching. The approach demonstrates improved robustness under benchmark topological cases when compared with available open-source and commercial solutions, including IRIT, SISL, and Parasolid.  

　　Publication:  

　　ACM Transactions on Graphics, Volume 42, Issue 401, August 2023  

　　https://doi.org/10.1145/3592452  

　　Author:  

　　Jin-San Cheng  

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China  

　　Email: jcheng@amss.ac.cn  

　　Bingwei Zhang  

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China  

　　Yikun Xiao  

　　State Key Lab of CAD and CG, Zhejiang University, Hangzhou, China  

　　Ming Li  

　　State Key Lab of CAD and CG, State Key Lab of CAD and CG, Zhejiang University, Hanzhou, China