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This article introduces quadrature prefiltering, an accurate, efficient, and fairly simple algorithm for prefiltering polygons for scanline rendering. It renders very high quality images at reasonable cost, strongly suppressing aliasing artifacts. For equivalent RMS error, quadrature prefiltering is significantly faster than either uniform or jittered supersampling. Quadrature prefiltering is simple to implement and space-efficient; it needs only a small two-dimensional lookup table, even when computing nonradially symmetric filter kernels. Previous algorithms have required either three-dimensional tables or a restriction to radially symmetric filter kernels. Though only slightly more complicated to implement than the widely used box prefiltering method, quadrature prefiltering can generate images with much less visible aliasing artifacts.