Anti-Aliasing through the Use of Coordinate Transformations

Abstract

The use of the perpendicular point-line distance in evaluating the two-dimensional anti-aliasing convolution is studied. Transformations of the point-spread function (PSF) that give the effective convolution in terms of the point-line distance when the class of object space primitives is limited to lines and polygons are derived. Because the quality of filtering is embedded in a table indexed by the point-line distance, this approach allows one to use arbitrarily complex PSFs; only the width and not the shape of the PSF affects the amount of computation. The CORDIC algorithm is applied to point-line distance evaluation, and its merits are shown. Also shown are the more standard uses of the CORDIC algorithm for coordinate rotation, for polar-to-rectangular and rectangular-to-polar conversion, and for calculating the Euclidean norm of a vector. Rounded endpoints can be achieved by using the point-segment distance, and computational methods are given, including CORDIC implementation. The CORDIC algorithms for the aforementioned geometric operations are prime candidates for VLSI implementation because of their inherent parallel/pipeline nature. © 1982, ACM. All rights reserved.