Geometry plays a key role in the world of modern computing. In science and engineering, mathematical models of geometry are crucial for applications like simulation and manufacturing. In the arts and entertainment, mathematical models of geometry are ubiquitous in applications like games and movies, and are useful even for image editing. Developing new variants of these models that are both intuitive and computationally efficient remains an area of intense research in computer graphics.
One classical problem in this area is that of deformable modeling; that is, deforming a given shape into a target shape via some type of mathematical method (ideally an interactive one). Solutions to this problem lie at the core of most current computer animation systems. One standard approach for these methods is to view the shape as being comprised of a deformable material and having a collection of embedded shape handles. Typically, these shape handles are either points or piecewise linear shapes connecting these points that a user may manipulate interactively. In this framework, the deformation method computes a "reasonable" deformation of the shape based on some simple physical model.