Fourier Coding and Reconstruction of Complicated Contours

Polygonal two-dimensional curves are coded by means of a finite number of their Fourier coefficients and then reconstructed by the corresponding Fourier sums. This mechanism is studied for an interesting class of contours whose members exhibit detail at a wide range of scales. Two bounds (one cheaply computed, one with high performance) are given on the number of Fourier coefficients needed to obtain a given accuracy in a reconstruction.