Anti-Aliasing in triangular pixels

Publisher Summary Much of graphics rendering today takes place in a square pixel grid. This is because the boundaries of the square grid are all vertical and horizontal lines, which eases the computational burden of sampling, filtering, and reconstruction. But it is well-known that the square grid is not the most uniform in terms of sampling densities. In two dimensions, the triangular lattice is more isotropic. Triangular lattice permits two tilings by regular polygons: hexagonal and triangular. Both unit cells have been used for image processing. This chapter presents an inexpensive antialiasing technique for triangular pixels. The prefiltered contribution of the polygon can be parameterized to each element of the grid by building a look-up table based on the vertices of the polygon and the polygon's intersections with the edges of the triangle. A simple box filter simply returns the amount of area within the triangle; higher-order filters may apply a weighting mask first.