Picture representation and transformations by computer

摘要

Surface representation with a computer assumes that at any point (x, y) one may restore the surface value with a certain accuracy, ε. This is done through interpolation computation from a set of samples kept in memory. We propose a local interpolation method, fit to automatic computation. The interpolating function gR1R2(x, y) is of bounded support, symmetrical and made of polynomial arcs of n1 and n2 degrees in x and y.We give the upper limit of error, and restore the surface by giving it the same order of error as that of the digitized sample error.Picture representations are studied with this process, and error limits are given. Numerical results have been computed and have verified the theory both for representation and transformation.