G(1) hierarchical Bezier surface over arbitrary meshes
This paper presents a method for constructing composite surfaces based on a collection of quadrilateral parches. A global parameterization using bilinear quadrilateral meshes and FEM like,minimization procedure are introduced. Smoothing conditions such as C-1 and G(1) arehandled by constraint equation and a related duality argument is implemented. The surfaces that can be constructed in this way, include conforming and non-conforming connections (3 less than or equal to n less than or equal to 6, T-nodes) between elementary patches. Non-manifold surfaces are automatically treated also by this data structure. The underlying quadratic programming with linear constraints is solved by duality methods. Hierarchical data structure with bordering matrices methods are implemented to deal with local refinement (subdivision). The present work details the actual implementation for the case of Bezier patches.
hierarchical data structure local refinement finite element method (fem) duality, minimization under constraints