C^0 Generalized Coons Patches for High-order Cage-based Deformation

Space deformations deform the ambient space and thus implicitly deform the embedded objects. Free-Form Deformation allows high-order deformation to the embedding space, yet the lattice may fail to conform to the object and involves many internal control points. Cage-based Deformation utilizes a cage space that conforms to the object, obviating the need for additional internal control points, but it is typically linear at edges. In this paper, we propose a simple and general method with both advantages while avoiding their drawbacks, allowing users to implement high-order cage-based deformation. To achieve this goal, we introduce a new parametric transfinite interpolation scheme based on generalized barycentric coordinates, which unifies and generalizes the rectangular and triangular Coons patch. This C 0 Generalized Coons patch can be defined not only over 2D domains but also 3D domains or even higher-dimensional domains, with arbitrary polytopes, even including non-manifold topologies. Moreover, the C 0 Generalized Coons patch has an elegant mathematical expression.