Interactive ray tracing with the visibility complex

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. Rivière 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 e$cient since it uses the coherence among the rays e!ectively. We have developed a new algorithm for the randomized incremental construction of the visibility complex. The advantage of using an incremental algorithm is that the history of the incremental construction yields an e$cient 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. ( 1999 Elsevier Science Ltd. All rights reserved.