Robust Containment Queries over Collections of Parametric Curves via Generalized Winding Numbers

Watch a technical presentation from the 2024 MFEM Workshop where Jacob Spainhour from CU Boulder explores robust containment queries for parametric curves in scientific simulations. Dive into the development of a containment query method for 2D regions defined by rational Bezier curves, focusing on its application in multiphysics simulations like Arbitrary Lagrangian-Eulerian (ALE). Learn how the generalized winding number (GWN) enables direct operation on curved objects and provides robustness against non-watertightness issues. Understand the adaptive algorithm that computes the GWN field exactly, allowing efficient evaluation of distant points while maintaining numerical stability for points close to curves. Discover how this classification approach expands the possibilities for bounding geometry in shaping applications without requiring expensive repair techniques, with potential extensions to 3D shapes defined by parametric surfaces.