Shenzhen University School of Mathematical Sciences

Liyuan Scholars Colloquium Session 150

Lecture Title: Recent Advances in CAD Surface Intersection and Boolean Operations

Speaker: Researcher Jia Xiaohong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Time: 10:00–11:00, November 10, 2025 (Monday)

Location: Classroom 1, Huixing Building, Yuehai Campus, Shenzhen University

Abstract:

The geometric kernel serves as the common geometric foundation for CAD-CAE-CAM R&D-oriented industrial software. Surface intersection and Boolean operations are the most critical underlying functions within the geometric kernel; the topological stability of the related algorithms directly determines the stability of a CAD system. CAD models composed of trimmed-and-stitched NURBS spline surfaces, following industrial standards, often suffer from watertightness issues. A fundamental reason is the difficulty in accurately representing and computing the intersection curves between NURBS surfaces, which also creates challenges in bridging from CAD geometric design to CAE physical simulation within industrial workflows. Challenging problems in surface intersection include: automatic determination of intersection curve topology, computation of the topological graph of intersection curves, singularity computation, small loop detection, overlapping surface detection, tolerance-based intersection, and high-precision, efficient model Boolean operations based on surface intersection. Even in mainstream international geometric kernels like Acis or Parasolid, surface intersection or Boolean operations often fail when surfaces are in critical configurations, sometimes leading to system crashes. This report will systematically introduce the role and challenges of surface intersection and Boolean operations in the CAD-CAE-CAM pipeline, and present our recent theoretical progress and software development in these areas.

Speaker Profile:

Jia Xiaohong is a Researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Her research focuses on symbolic computation, computational algebraic geometry, and CAD. She has presided over National Natural Science Foundation of China (NSFC) Youth Science Fund Projects (Category A and B), projects under the National Key R&D Program of China, the Young Scientist Project of the Key R&D Program, and sub-projects of NSFC Major Programs. She has received awards including the Zhongchuang Software Talent Award (2025), the CSIAM Award for Young Scientists in Applied Mathematics (2020), and the Chinese "Geometric Design and Computing" Young Scholar Award (2017).

All faculty and students are welcome!

School of Mathematical Sciences

November 7, 2025