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Topologically Sweeping Visibility Complexes via Pseudotriangulations
, 1996
"... This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal run ..."
Abstract

Cited by 86 (9 self)
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This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal running time, this is the first optimal algorithm that uses only linear space. The visibility graph or the visibility complex can be computed in the same time and space. The only complicated data structure used by the algorithm is a splittable queue, which can be implemented easily using redblack trees. The algorithm is conceptually very simple, and should therefore be easy to implement and quite fast in practice. The algorithm relies on greedy pseudotriangulations, which are subgraphs of the visibility graph with many nice combinatorial properties. These properties, and thus the correctness of the algorithm, are partially derived from properties of a certain partial order on the faces of th...
Making Geometry Visible: An introduction to the Animation of Geometric Algorithms
, 1997
"... ion There are times when the amount of data produced by a program overwhelms the user. When this happens, an animation confuses more than it educates. If the algorithm is complex, and uses several different data structures and subalgorithms, the user may get lost in the details and not see the ov ..."
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Cited by 11 (1 self)
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ion There are times when the amount of data produced by a program overwhelms the user. When this happens, an animation confuses more than it educates. If the algorithm is complex, and uses several different data structures and subalgorithms, the user may get lost in the details and not see the overall picture. In such cases, the programmer should condense complicated parts of the scene into simpler items, like boxes. This is the approach taken in several videos we have reviewed. Time can also be abstracted, if several phases of an algorithm are omitted and only the final result of several program steps is presented. An ideal system should include facilities that help the programmer implement this sort of abstraction. Ideally, all the detail should be accessible to the user if he/she needs to see it. This is called semantic zooming. Sometimes, of course, it may be desirable to present the viewer with large amounts of information. This occurs when several sorts are simultaneously c...
Using the Visibility Complex for Radiosity Computation
 In ACM Workshop Appl. Comput. Geom
, 1996
"... The radiosity method is particularly suitable for global illumination calculations in static environments. Nonetheless, for applications of image synthesis such as lighting design or architectural simulation, we have to deal with dynamic environments. To make the method usable in a real case, the il ..."
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Cited by 10 (2 self)
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The radiosity method is particularly suitable for global illumination calculations in static environments. Nonetheless, for applications of image synthesis such as lighting design or architectural simulation, we have to deal with dynamic environments. To make the method usable in a real case, the illumination has to be updated as fast as possible after an object moves. The e#cient way is to find the calculations strictly necessary to be recomputed after a change in the scene. The largest part of the computation time is spent on visibility calculation. In this paper, we investigate the possible speed ups in those calculations. We propose the use of the visibility complex for radiosity calculations. The presented study is realized for 2D scenes of convex objects in the static case. We show that the visibility complex is very suitable for radiosity calculations in this context, and that it also allows for e#cient updates in the dynamic case. Keywords: radiosity, discontinuity meshing, for...