Automatic fitting and control of complex freeform shapes

Abstract

In many computer graphics and computer-aided design problems, it is very common to find a smooth and well structured surface to fit a set of unstructured 3-dimensional data. Although general approaches of fitting give satisfactory results, the computation time and the complexity often prevent their further developments in more complex cases especially in reusing an existing design. In this paper, for a better control of existing freeform shapes, they are approximated by feature templates, with emphasis on extendable templates. By the advantage of the small number of intrinsic parameters in the feature based deformable templates, fitting procedures are faster and more robust. Three key types of simple freeform templates, the bump, the ridge and the hole, are introduced first. With distance measuring methods, a uniform optimization function is presented to achieve automatic feature recognition and fitting. By introducing the extendable template, the hole and the ridge template are further developed to match complex freeform shapes. Based on the approximated template, further shape manipulations can be conducted effectively using the shape intrinsic parameters. Numerical experiments are conducted in order to verify the proposed algorithms. It is also described how the matching technique can be applied in computer graphics and computer-aided design applications.