One embodiment of the present invention sets forth a technique for improved rasterization of round points mapped into a tile space within a graphics processing pipeline. A set of candidate tiles are selected based on proximity to a round point. A tile within the set of candidate tiles may be rejected based on a rejection boundary. A tile may be rejected if no vertex associated with the tile is within the coverage area. Performance is improved by rejecting certain unneeded tiles that would otherwise be included in conventional rasterization. One embodiment advantageously enlists line drawing circuitry to determine whether a given tile intersects the coverage area.