Parametric curve and surface intersections
Date:
The computation of intersections between parametric curves and surfaces remains one of the most persistent bottlenecks in Computer-Aided Design (CAD) and downstream engineering analysis. In particular, surface–surface intersection algorithms are still a major source of topological inconsistencies and 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 produce an intersection curve of degree 324, as shown by Sederberg (1983). This talk discusses strategies for both parametric curve and surface intersection problems in the context of isogeometric analysis (IGA). We present an algorithmic framework that balances numerical stability with computational efficiency.
Keywords: Surface Intersection, Parametric Curves and Surfaces, Computer-Aided Design, Isogeometric Analysis, Numerical Stability