2D High-Order Cage-Based Deformation by Polygonal Surface Patches

This paper presents a novel method for 2D high-order cage-based deformation using polygonal surface patches, providing a unified framework that supports various types of polygonal patches. The proposed deformation process comprises two main components: the contribution from the cage corner points and the influence of the middle control points along each boundary curve. First, a coarse deformation is reconstructed using generalized barycentric coordinates derived from the deformed cage corners. Then, displacement curves defined by the middle control points on each cage edge are employed to refine the deformation, precisely relocating the transition points to their final positions. Extensive experimental results demonstrate that our method produces high-quality results across diverse 2D deformation scenarios.