Binary Space Partitions in Plücker Space

One of the important potential applications of computational geometry is in the field of computer graphics. One challenging computational problem in computer graphics is that of rendering scenes with nearly photographic realism. A major distinction in lighting and shading models in computer graphics is between local illumination models and global illumination models. Local illumination models are available with most commercial graphics software. In such a model the color of a point on an object is modeled as a function of the local surface properties of the object and its relation to a typically small number of point light sources. The other objects of scene have no effect. In contrast, in global illumination models, the color of a point is determined by considering illumination both from direct light sources as well as indirect lighting from other surfaces in the environment. In some sense, there is no longer a distinction between objects and light sources, since every surface is a potential emitter of (indirect) light. Two physical-based methods dominate the field of global illumination. They are ray tracing [8] and radiosity [3].

[1]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[2]  J. H. G..  A Treatise on the Line Complex , 1903, Nature.

[3]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[4]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[5]  Komei Fukuda,et al.  Double Description Method Revisited , 1995, Combinatorics and Computer Science.

[6]  Leonidas J. Guibas,et al.  Cylindrical static and kinetic binary space partitions , 1997, SCG '97.

[7]  David M. Mount,et al.  Data structures for global illumination computation and visibility queries in 3-space , 1998 .

[8]  Mark de Berg,et al.  New Results on Binary Space Partitions in the Plane , 1997, Comput. Geom..

[9]  F. Frances Yao,et al.  Optimal binary space partitions for orthogonal objects , 1990, SODA '90.

[10]  Joseph O'Rourke,et al.  Arrangements of lines in 3-space: a data structure with applications , 1988, SCG '88.

[11]  T. M. Murali,et al.  Practical techniques for constructing binary space partitions for orthogonal rectangles , 1997, SCG '97.

[12]  H. Levy,et al.  Differential line geometry , 1955, The Mathematical Gazette.

[13]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[14]  M. Pellegrini,et al.  Finding stabbing lines in 3-space , 1992, Discret. Comput. Geom..

[15]  Charles B. Morrey,et al.  Analytic Geometry in Three Dimensions , 1985 .

[16]  Donald Ervin Knuth,et al.  The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information , 1978 .

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

[18]  H. Raiffa,et al.  3. The Double Description Method , 1953 .

[19]  Roman Kuchkuda,et al.  An introduction to ray tracing , 1993, Comput. Graph..

[20]  Michael F. Cohen,et al.  Radiosity and realistic image synthesis , 1993 .

[21]  F. Frances Yao,et al.  Efficient binary space partitions for hidden-surface removal and solid modeling , 1990, Discret. Comput. Geom..