John H. Halton

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The results presented here refer to the determination of the thickness of a graph; that is, the minimum number of planar subgraphs into which the graph can be decomposed. A useful general, preliminary result obtained is Theorem 8: that a planar graph always has a planar representation in which the nodes are placed in arbitrary given positions. It is then(More)
In this paper we extend the reuse of paths to the shot from a moving light source. In the classical algorithm new paths have to be cast from each new position of a light source. We show that we can reuse all paths for all positions, obtaining in this way a theoretical maximum speed-up equal to the average length of the shooting path
s — Random walk solutions are commonly used to solve Fredholm equations of the second kind in various linear transport problems such as neutron transport and light transport for photorealistic computer image synthesis. However, they have the drawback that many paths have to be simulated before an acceptable solution is obtained. Often in such applications,(More)