Anti-aliasing through the use of coordinate transformations

Ken Turkowski
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引用次数: 2

Abstract

The use of the point-line distance in evaluating the 2-dimensional anti-aliasing convolution is studied. We derive 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. Because the quality of filtering is embedded in a table indexed by the point-line distance, this approach allows one to use arbitrarily complex PSF's, only the width and not the shape of the PSF affects the amount of computation. We apply the CORDIC algorithm to point-line distance evaluation, and show its merits. Also, we show the more standard use of the CORDIC algorithm for coordinate rotation, polar-to-rectangular and rectangular-to-polar conversion, and calculating the norm of a vector. Rounded end points can be achieved by using the point-segment distance, 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.
通过使用坐标变换来抗锯齿
研究了用点线距离评价二维抗混叠卷积的方法。我们推导了点扩展函数(PSF)的变换,当对象空间原语的类别被限制为直线和多边形时,它给出了点线距离的有效卷积。因为过滤的质量嵌入到一个由点线距离索引的表中,这种方法允许使用任意复杂的PSF,只有宽度而不是PSF的形状会影响计算量。我们将CORDIC算法应用于点线距离评估,并展示了它的优点。此外,我们还展示了CORDIC算法在坐标旋转、极坐标到矩形和矩形到极坐标转换以及计算向量范数方面的更标准使用。利用点段距离可以得到圆角端点,给出了计算方法,包括CORDIC实现。用于上述几何运算的CORDIC算法由于其固有的并行/管道特性而成为VLSI实现的主要候选者。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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