Deformable models are a useful tool in computer vision and computer graphics. A deformable model is a curve (in two dimensions) or a surface (in three dimensions), whose shape, position, and orientation are controlled through a set of parameters. Deformable models can represent manufactured objects, human faces and skeletons, and even bodies of fluid. In computer graphics, we use deformable models for animations and simulations, whereas in computer vision applications, such as tracking and fitting, deformable models help to restrict the family of possible solutions. We introduce the use of a directed acyclic graph (DAG) to describe the position and Jacobian of each point on the surface of deformable models. This data structure, combined with a topological description of the points, is simple, powerful, and extremely useful for both computer vision and computer graphics applications. We show a computer vision application, 3D deformable face tracking, and a computer graphics application, cyberglove data visualization and calibration.