Linus Upson

Penumbral shadows

The shadows cast by polygonal occluding objects illuminated by polygonal light sources are complicated. Unlike shadows cast by point sources, they are divided into regions where the shadow intensity changes at different rates. The boundaries between these different regions form the shadow diagram. The video tape depicts shadows cast by a square light source with a square occluding object. We have included two types of images: flat shadow scenes and perspective views. The flat shadow images were calculated using the exact formula for radiative energy transfer. This calculation depends only on the boundary of the visible light source. For polygons, it can be reduced to a simple summation. [1] Finding the boundary of the visible portion of the illuminating polygon when it is occluded by a second polygon requires computing the intersection of two polygons. General purpose algorithms for computing intersections of arbitrary polygons in the plane are quite complicated, so we used the Sutherland–Hodgman algorithm [2] which cannot handle concave polygons, but which is much simpler than the fully general methods [3]. We created the three-dimensional perspective views from the flat images using the texture mapping capabilities of Rayshade. The shadow diagrams can be obtained by projecting