System and method for generating hard and soft extruded image shadows with ray-coherent integration of extruded transparency maps. The ends of rays are positioned along a set of spokes radiating from the background point to be illuminated. In some embodiments, the weighted sum of integrals along a dense cone of rays from each point on the background is computed to determine the fraction of light obscured by the extruded artwork. The end points of the rays may be placed on lines that converge to the background point, according to some embodiments. Thus, intermediate line integrals of the alpha matte may be used to compute values for multiple rays. In other words, since the endpoints of multiple rays are placed along a single line, the results of computing the weighted sums for shorter rays may be used when calculating the sums for longer rays.