A Basic Study of 2D-CAD Representation Method based on G-Type Fourier Descriptor

Abstract

This paper describes a representation method of a single closed loop defined by two-dimensional CAD system based on G-type Fourier descriptor. Traditionally, equal length polygonal approximation method is used to get sampling points for calculating discrete fourier descriptor. However, this approach requires many sampling points depending on the complexity of the shape. This study describes a method for the reduction of the number of sampling points and discusses the geometrical error between the original sampling points and the reconstructed points using inverse fourier transformation. First, an equal angle polygonal approximation method is proposed to reduce the number of sampling points. It means that the length between neighboring two sampling points is unequal. As a result of experiments with thirty-one shapes, the equal angle method is concluded to be sufficient for the reconstruction of the shapes. Second, to improve the geometrical error of inverse fourier transformation of the shape with acute angle, a fourier descriptor with multiple vertices is proposed. Using this method, it is possible to reconstruct the shape without higher order harmonics. Finally, it is proposed that the fourier synthesis method for generating a new shape from fourier descriptors of two shapes.