Abstract: Shadows play an important role in perceiving the shape and texture of an object. While some previous interactive shadowing methods are appropriate for casting shadows on other geometry they cannot be applied to bump maps (which contain no explicit geometry.) Horizon Mapping is a technique used to compute shadows for bump-mapped surfaces. We map the technique into modern graphics API's and extend it to account more accurately for the geometry of the underlying surface. We also use it to represent limited self-shadowing for pure geometry. In mapping the algorithm to hardware, we use a novel method to interpolate orientation in tangent space over the surface. We show results of self-shadowing at frame rates.