Sweepers: Swept user-defined tools for modeling by deformation.

We present sweepers, a new class of space deformations suitable for interactive virtual sculpture. The artist describes a basic deformation as a path through which a tool is moved. Our tools are simply shapes, subsets of 3D space. So we can use shapes already created as customized tools to make more complex shapes or to simplify the modeling process. When a tool is moved it causes a deformation of the working shape along the path of the tool. This is in accordance with a clay modeling metaphor and easy to understand and predict. More complicated deformations are achieved by using several tools simultaneously in the same region. It is desirable that deformations for modeling are 'foldover-free'. that is parts of deformed space cannot overlap so that the deformations are reversible. There are good intuitive reasons to believe that our deformations are foldover-free but we have not yet completed a Proof. We have an efficient formulation for a single tool following a simple path (translation, scaling or rotation) and we can demonstrate the effects of multiple tools used simultaneously. For representing shapes, we present a mesh refinement and decimation algorithm that takes advantage of the definition of our deformations. The prototype implementation described has been used to create a variety of models quickly and conveniently.