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Abstract

Methods for solving shadow problems by solving instances of visibility problems have long been known and exploited. There are, however, other potent uses of such a reduction of shadow problems, several of which we explore in this paper. Specifically, we describe algorithms that use a resolution--independent, or object--space, visibility structure for the computation of object--space shadows under point, linear, and area light sources. The connection between object--space visibility and shadow computation is well--known in computer graphics. We show how that fundamental observation can be recast and generalized within an object--space visibility structure. The edges in such a structure contain exactly the information needed to determine shadow edges under a point light source. Also, the locations along a linear or an area light source at which visibility changes (termed critical points and critical lines) provide the necessary information for computing shadow edges resulting from linear and area light sources. Not only are instances of all shadow problems thus reduced to visibility problems, but instances of shadow problems under linear and area light sources are also reduced to instances of shadow generation under point and linear light sources, respectively.