Fourier descriptors for computer graphics

The two dimensional coding of contours by Fourier descriptors which have been used extensively in shape discrimination and pattern recognition in the past is extended into three dimensions so as to enhance the ability to geometrically transform surfaces in Euclidean space. A set of Fourier descriptors are used as a specific example of a linear transform for arbitrary closed shape contours in three dimensional Cartesian space which enhance data compression compared to computer graphics storage algorithms utilizing raw data. The Fourier descriptors can also be used for three dimensional graphical reconstruction of objects represented by data sets depicting consecutive contours or collections of quadrilaterals in space. These descriptors maintain linearity, thus they can be utilized for geometric transformations of these data sets, which may not be possible with non-linear data compression such as Huffman coding. Thus geometric transformations, such as those utilized in computer aided design (CAD) systems, of such contour data sets can be performed with less computation and storage requirements in the linear transform space than current techniques that transform data in the data space