1. A computer-implemented method comprising: receiving, at a computer system, a request to render on a display a shape that is to be anti-aliased; creating, for the shape, a bounding box that is defined by a plurality of vertices in pixel space, wherein the bounding box comprises i) a central region that is opaque and ii) at least one boundary region that has multiple levels of opacity; providing, by the computer system, the plurality of vertices to a shader program that interpolates locations for pixels that are included, at least partially, in the bounding box that is defined by the plurality of vertices; determining, by the shader program and for each of at least a portion of the pixels in the bounding box, whether each of at least a portion of the pixels is i) located at least partially within the at least one boundary region of the bounding box and ii), for particular pixels that are located within at least a portion of the boundary region, membership values that indicate degrees to which the particular pixels have been determined to be located in the boundary region, wherein the membership values comprise area values that correspond to percentages of the particular pixels that are located within the at least one boundary region; determining shapes of the particular pixels that are located within the at least one boundary region; accessing predetermined formulas for the shapes, each of the predetermined formulas providing a mechanism for determining an area for one or more of the shapes; determining, using the predetermined formulas, the area values for the particular pixels; determining opacity values for at least the particular pixels based, at least in part, on the membership values for the particular pixels, the opacity values indicate levels of opacity for the particular pixels that are located at least in part within the boundary region; and determining color values for the particular pixels based, at least in part, on the opacity values; and causing the particular pixels in the boundary region to be displayed using the determined color values.