Another popular method of doing this is a variant on the area mapping technique, except that instead of taking the weighted average of the four nearest pixels,

Another popular method of doing this is a variant on the area mapping technique, except that instead of taking the weighted average of the four nearest pixels, it instead creates a 2-D spline across the R/G/B "heights" of the image, and interpolate with the spline. The reason the triple-sheared images look crappy is because the three shears themselves are subject to pixel aliasing. Still pretty cool.