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Excerpt from An Efficient Approximation for Penumbra Shadow <p>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. <p>About the Publisher <p>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com <p>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.