Antialiasing is a necessary component of any high quality renderer. An antialiased image is produced by convolving the scene with an antialiasing filter and sampling the result, or equivalently by solving the antialiasing integral at each pixel. Though methods for analytically computing this integral exist, they require the continuous two-dimensional result of visible-surface computations. Because these computations are expensive, most renderers use supersampling, a discontinuous approximation to the integral. We present a new algorithm, line sampling, combining a continuous approximation to the integral with a simple visible-surface algorithm. Line sampling provides high quality antialiasing at significantly lower cost than analytic methods while avoiding the visual artifacts caused by supersampling's discontinuous nature. A line sample is a line segment in the image plane, centered at a pixel and spanning the footprint of the antialiasing filter. The segment is intersected with scene polygons, visible subsegments are determined, and the antialiasing integral is computed with those subsegments and a one-dimensional reparameterization of the integral. On simple scenes where edge directions can be precomputed, one correctly oriented line sample per pixel suffices for antialiasing. Complex scenes can be antialiased by combining multiple line samples weighted according to the orientation of the edges they intersect.