1. A method for using a successive-convolution technique to render shadows produced by a set of shadowing sprites onto a shadowed sprite, comprising: initializing a shadow map; and iteratively processing each shadowing sprite starting at a furthest shadowing sprite from the shadowed sprite and iterating through successively nearer shadowing sprites until a nearest shadowing sprite is processed, wherein processing each shadowing sprite involves, transforming the shadowing sprite's coverage map to a parametric space of the shadowed sprite, compositing the transformed shadowing sprite into the shadow map, and incrementally blurring the resultant shadow map, wherein incrementally blurring the resultant shadow map comprises performing an incremental convolution which is functionally related to the distance between the shadowing sprite and the next-nearest shadowing sprite, wherein the initializing, the iterative processing, the transforming, the compositing and the incremental blurring are executed by a computer processor.