G1 Hierarchical Bézier Surface over Arbitrary Meshes

This paper presents a method for constructing composite surfaces based on a collection of quadrilateral patches. A global parameterization using bilinear quadrilateral meshes and FEM like minimization procedure are introduced. Smoothing conditions such as C1 and G1 are handled 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 n 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 Bézier patches.