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Excerpt from An Efficient Approximation for Penumbra Shadow Ray tracing algorithms generate excellent realistic images, but in general they are compu tationally very expensive. Simple ray tracing has aliasing problems as well. [1] presented a cone tracing technique for anti-aliasing, fuzzy shadows, and dull reflections. To improve the efficiency of ray tracing created a hierarchy of bounding volumes to reduce the number. Of bounding volume intersection checks; employed 3d space subdivision in culling objects; [12] made use of the coherence which exists between similar rays. Though a certain degree of improvement in efficiency has been attained by the above efforts. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.