Modeling generalized cylinders via Fourier morphing

Abstract

Generalized cylinders provide a compact representation for modeling many components of natural objects as well as a great variety of human-made industrial parts. This paper presents a new approach to modeling generalized cylinders based on cross-sectional curves defined using Fourier descriptors. This modeling is based on contour interpolation and is implemented using a subdivision technique. The definition of generalized cylinders uses a three-dimensional trajectory which provides an adequate control for the smoothness of bend with a small number of parameters and includes the orientation of each cross-section (i.e, the local coordinate system) in the interpolation framework. Fourier representations of cross-sectional curves are obtained from contours in digital images, and corresponding points are identified by considering angular and arc-length parametrizations. Changes in cross-section shape through the trajectory are performed using Fourier morphing. The technique proposed provides a comprehensive definition that allows the modeling of a wide variety of shapes, while maintaining a compact characterization to facilitate the description of shapes and displays.