Anti-Aliasing through the Use of Coordinate Transformations
Kenneth Turkowski · ACM Transactions on Graphics · 1982
Use of CoordinateThe 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.