Parametric Curve and Surface Intersections
Date:
The computation of intersections between parametric curves and surfaces remains one of the most persistent bottlenecks in ComputerAided Design (CAD) and downstream engineering analysis. In particular, robust surface–surface intersection algorithms are still a major source of topological inconsistencies and data gaps in complex geometric models, as highlighted by Farouki (1999). The inherent difficulty lies in the extreme algebraic complexity of the problem; for instance, even two standard bicubic patches can result in an intersection curve of degree 324, as demonstrated by Sederberg (1983). This talk discusses strategies for both parametric curve and surface intersection problems within the context of isogeometric analysis (IGA). We present an algorithmic framework that balances numerical stability with computational efficiency.