Interactive ray tracing with the visibility complex

Abstract We describe a method of producing ray-traced images of 2D environments at interactive rates. The 2D environment consists of a set of disjoint, convex polygons. Our technique is based on the visibility complex [17] , [19] [Pocchiola M, Vegter G. Proc Int J Comput Geom Applic 1996;6(3):279–308. Riviere S. Visibility computations in 2D polygonal scenes. PhD thesis, Univ. Joseph Fourier, Grenoble I, France], a data structure in a dual space where a face of the visibility complex corresponds to a contiguous set of rays in the primary space with the same forward and backward views. Sweeping the viewing ray around a viewpoint corresponds to walking along a trajectory on the visibility complex. Producing a ray-traced image is equivalent to walking along and maintaining a set of trajectories. Generating ray-traced images with the visibility complex is very efficient since it uses the coherence among the rays effectively. We have developed a new algorithm for the randomized incremental construction of the visibility complex. The advantage of using an incremental algorithm is that the history of the incremental construction yields an efficient ray-query data structure, which is required for casting secondary rays. The performance of our algorithm is analyzed and a comparison is made with the classical ray-tracing algorithm.

[1]  Michel Pocchiola,et al.  Topologically sweeping visibility complexes via pseudotriangulations , 1996, Discret. Comput. Geom..

[2]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[3]  Marc Levoy,et al.  Light field rendering , 1996, SIGGRAPH.

[4]  Seth Teller,et al.  Frustum Casting for Progressive, Interactive Rendering , 1998 .

[5]  Pat Hanrahan,et al.  Beam tracing polygonal objects , 1984, SIGGRAPH.

[6]  Mark de Berg,et al.  Efficient algorithms for ray shooting and hidden surface removal , 1992 .

[7]  Stéphane Rivière.  Walking in the visibility complex with applications to visibility polygons and dynamic visibility , 1997, CCCG.

[8]  Frédo Durand,et al.  Radiosity for dynamic scenes in flatland with the visibility complex , 1996, Comput. Graph. Forum.

[9]  Ari Rappoport,et al.  Interactive reflections on curved objects , 1998, SIGGRAPH.

[10]  Stéphane Rivière.  Topologically sweeping the visibility complex of polygonal scenes , 1995, SCG '95.

[11]  David P. Luebke,et al.  Portals and mirrors: simple, fast evaluation of potentially visible sets , 1995, I3D '95.

[12]  Michel Pocchiola,et al.  Pseudo-triangulations: theory and applications , 1996, SCG '96.

[13]  Richard Szeliski,et al.  The lumigraph , 1996, SIGGRAPH.

[14]  F. Durand,et al.  The Visibility Skeleton: A Powerful and Multi-Purpose Global Visibility Tool , 1997 .

[15]  László Szirmay-Kalos,et al.  Analysis and construction of worst-case optimal ray shooting algorithms , 1998, Comput. Graph..

[16]  Norman I. Badler,et al.  Pipeline rendering: interactive refractions, reflections and shadows , 1994 .

[17]  Frédo Durand,et al.  The 3D Visibility Complex: A New Approach to the Problems of Accurate Visibility , 1996, Rendering Techniques.

[18]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[19]  Michel Pocchiola,et al.  The visibility complex , 1993, SCG '93.

[20]  Ketan Mulmuley,et al.  Computational geometry : an introduction through randomized algorithms , 1993 .

[21]  John Edward Warnock,et al.  A hidden surface algorithm for computer generated halftone pictures , 1969 .

[22]  Norman I. Badler,et al.  Multi-pass pipeline rendering: realism for dynamic environments , 1997, SI3D.

[23]  Stéphane Rivière,et al.  Calculs de visibilité dans un environnement polygonal 2D. (Visibility computations in 2D polygonal scenes) , 1997 .

[24]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[25]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[26]  Kavita Bala,et al.  Bounded-Error Interactive Ray Tracing , 1998 .

[27]  James Arvo,et al.  Fast ray tracing by ray classification , 1987, SIGGRAPH '87.