【报告摘要】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 framework to compute the topology of parametric surface-surface intersection (SSI). 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. The talk is based on a paper published on ACM Transactions on Graphics. Dear Ziemowit Domanski.

 【报告人简介】程进三，中国科学院数学与系统科学研究院研究员。吉林大学计算数学本硕，中国科学院数学与系统科学研究院博士及博士后，法国lNRlA博士后。主要从事曲线曲面保拓扑保精度的逼近与计算，非线性方程组的实根隔离。获得中国科学院数学与系统科学研究院2025年科研进展奖。成功主持完成ZHGC发布的CAD公开难题项目。