Computation and Maintenance of Visibility and Shadows in the Plane

We consider visibility and shadow problems in the plane under static and dynamic conditions. We show that several problems in this domain are intimately related and that a careful formulation of the requirements of each problem can lead to a great deal of reuse in the implementation. This is of interest to the practitioner who may find it difficult to implement visibility and shadow algorithms given their complexity. A solution of these problems in the plane turns out to be a necessary component of their solution in space and by separating these components, difficult issues of implementation are taken care of at the design level. We also give specific algorithmic results. We show a reduction between shadow and visibility computations under a point light source, between static and dynamic computations under a point light source, and visibility and shadow computations between a point and a linear light source.