We present an approach to modeling with truly mutable yet completely controllable free-form surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patch-based approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patch-based and particle-based representations. Automatic refinement, mesh smoothing, and re-triangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time.

We describe a fast method for creating physically based animation of non-rigid objects. Rapid simulation of nonrigid behavior is based on global deformations. Constraints are used to connect non-rigid pieces to each other, forming complex models. Constraints also provide motion control, allowing model points to be moved accurately along specified trajectories. The use of deformations that are linear in the state of the system causes the constraint matrices to be constant. Pre-inverting these matrices therefore yields an enormous benefit in performance, allowing reasonably complex models to be manipulated at interactive speed.

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Our goal is to use physical simulation as an interactiv e medium for building and manipulating a wide rang e of models . A key to achieving this goal is the ability to create complex physical models dynamically b y snapping simple pieces together, integrating the process of model creation into the ongoing simulation . We present a mathematical and computational formulation for constrained dynamics that makes thi s possible, allowing encapsulated objects, constraints , and forces to be combined dynamically and simulate d efficiently . The formulation handles arbitrary objects , including nonrigid bodies . We describe an implementation for interactive dynamics, and discuss applications to mechanism construction, geometric modeling, interactive optimization data fitting, and animation .

Our goal is to use physical simulation as an interactiv e medium for building and manipulating a wide rang e of models . A key to achieving this goal is the ability to create complex physical models dynamically b y snapping simple pieces together, integrating the process of model creation into the ongoing simulation . We present a mathematical and computational formulation for constrained dynamics that makes thi s possible, allowing encapsulated objects, constraints , and forces to be combined dynamically and simulate d efficiently . The formulation handles arbitrary objects , including nonrigid bodies . We describe an implementation for interactive dynamics, and discuss applications to mechanism construction, geometric modeling, interactive optimization data fitting, and animation .