Parameterization of freeform features

Freeform features can be regarded as key elements of shape modeling. Commonly, features are defined, controlled and computed using parameters. We propose a feature formulation strictly based on the parameterization, as a mapping from an arbitrary set to some domain of interest. This formalism accommodates many of the common representation forms and in addition allows: the uniform definition of freeform features; the analysis of feature properties, such as their spatial coverage, differentiability, uniqueness, overlap; and the comparison of alternative parameterizations for a given type of feature, regarding user control and computation. We have investigated in detail two feature types, the ridge and the hole. The proposed parameterizations indeed provide both interactive control and automatic feature extraction, are the key functions of a flexible forward/backward design support tool. Numerical results of the freeform feature parameter extraction process are presented.