Topology driven approximation to rational surface-surface intersection via interval algebraic topology analysis

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