Shape control using primitive decompositions

Presents novel techniques to modify free-form shapes defined by implicit algebraic models. These models are first simplified by introducing a decomposition in terms of conic-line primitives, and then the desired local/global shape changes are produced by varying the parameters of these primitives. A decomposed model provides efficient control of each primitive using its canonical frame. To make the analysis simpler, we restrict our attention to free-form curves modeled by a 4th-degree (quartic) equation. However, all of the analysis can be directly extended to higher-degree models. We also provide some 3D interpolation procedures based on the resulting primitives to illustrate the potential of our methods in 3D.