Fast computation of shadow boundaries using spatial coherence and backprojections

This paper describes a fast, practical algorithm to compute the shadow boundaries in a polyhedral scene illuminated by a polygonal light source. The shadow boundaries divide the faces of the scene into regions such that the structure or “aspect” of the visible area of the light source is constant within each region. The paper also describes a fast, practical algorithm to compute the structure of the visible light source in each region. Both algorithms exploit spatial coherence and are the most efficient yet developed. Given the structure of the visible light source in a region, queries of the form “What specific areas of the light source are visible?” can be answered almost instantly from any point in the region. This speeds up by several orders of magnitude the accurate computation of first level diffuse reflections due to an area light source. Furthermore, the shadow boundaries form a good initial decomposition of the scene for global illumination computations.

[1]  O. Veblen.  Projective geometry, by Oswald Veblen and John Wesley Young , .

[2]  G. M.,et al.  Projective Geometry , 1938, Nature.

[3]  George Salmon.  A Treatise on the Analytic Geometry of Three Dimensions , 1912 .

[4]  W. Mccrea.  Analytical Geometry of Three Dimensions , 1943, Nature.

[5]  Franklin C. Crow,et al.  Shadow algorithms for computer graphics , 1977, SIGGRAPH.

[6]  Donald P. Greenberg,et al.  The hemi-cube: a radiosity solution for complex environments , 1985, SIGGRAPH.

[7]  Otto Nurmi,et al.  Algorithms for computational geometry , 1987 .

[8]  Jorge Stolfi,et al.  Oriented projective geometry , 1987, SCG '87.

[9]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[10]  Michael McKenna.  Worst-case optimal hidden-surface removal , 1987, TOGS.

[11]  Jitendra Malik,et al.  Computing the aspect graph for line drawings of polyhedral objects , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[12]  Donald P. Greenberg,et al.  A progressive refinement approach to fast radiosity image generation , 1988, SIGGRAPH.

[13]  Steven K. Feiner,et al.  Near real-time shadow generation using BSP trees , 1989, SIGGRAPH '89.

[14]  Ketan Mulmuley,et al.  An efficient algorithm for hidden surface removal , 1989, SIGGRAPH.

[15]  Donald S. Fussell,et al.  Adaptive mesh generation for global diffuse illumination , 1990, SIGGRAPH.

[16]  Jitendra Malik,et al.  Computing the Aspect Graph for Line Drawings of Polyhedral Objects , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Raimund Seidel,et al.  Efficiently Computing and Representing Aspect Graphs of Polyhedral Objects , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  A. T. Campbell,et al.  An Analytic Approach to Illumination with Area Light Sources , 1991 .

[19]  Pat Hanrahan,et al.  A rapid hierarchical radiosity algorithm , 1991, SIGGRAPH.

[20]  Seth J. Teller,et al.  Computing the antipenumbra of an area light source , 1992, SIGGRAPH.

[21]  Dani Lischinski,et al.  Discontinuity meshing for accurate radiosity , 1992, IEEE Computer Graphics and Applications.

[22]  Seth Teller,et al.  Visibility Computations in Densely Occluded Polyhedral Environments , 1992 .

[23]  Dani Lischinski,et al.  Combining hierarchical radiosity and discontinuity meshing , 1993, SIGGRAPH.

[24]  A. James Stewart,et al.  An Output Sensitive Algorithm for the Computation of Shadow Boundaries , 1993, CCCG.

[25]  E. Fiume,et al.  Structured sampling and reconstruction of illumination for image synthesis , 1994 .

[26]  George Drettakis,et al.  A fast shadow algorithm for area light sources using backprojection , 1994, SIGGRAPH.