Using particles to sample and control more complex implicit surfaces

In 1994, Witkin and Heckbert developed a method for interactively modeling implicit surfaces by simultaneously constaining a particle system to lie on an implicit surface and vice-versa. This interface was demonstrated to be effective and easy to use on example models containing a few blobby spheres and cylinders. This system becomes much more difficult to implement and operate on more complex implicit models. The derivatives needed for the particle system behavior can become laborious and error-prone when implemented for more complex models. We have developed, implemented and tested techniques for automatic and numerical differentiation of the implicit surface function. Complex models also require a large number of parameters, and the management and control of these parameters is often not intuitive. We have developed adapters, which are special shape-transformation operators that automatically adjust the underlying parameters to yield the same effect as the transformation. These new techniques allow constrained particle systems to sample and control more complex models than before possible.