Cage-free local deformations using Green coordinates

Green coordinates require to build an enclosing cage around a shape that is deformed by manipulating the cage. In this paper, we build upon the local differences of Green coordinates and propose a method to deform a shape locally without constructing a cage. Second, we derive linear formulas to directly interpolate points on the shape to desired locations using an umbrella shaped cell. Moreover, we set up an influence region to confine the deformation in a local area. Finally, we suggest a method to automatically construct an umbrella shaped cell and thus update it consecutively while the shape is deforming. Experiments have shown that the suggested approach delivers smooth local deformations and enables shape manipulations at an interactive rate.