Cost prediction for ray shooting

Aronov, Boris; Brönnimann, Hervé; Chang, Allen Y.; Chiang, Yi‐Jen

doi:10.1145/513400.513438

Cited by 3 publications

(14 citation statements)

References 16 publications

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“…The simplified cost measure has a very similar predicting power for many scenes encountered in computer graphics. This has been experimentally verified [1,2]. We conjecture it would take a very artificially constructed and unrealistic scene to bring forth a discrepancy.…”

Section: Introductionmentioning

confidence: 70%

“…But this is also true in an amortized sense for octrees, see [1] for the technical details. 4 Strictly speaking, the average cost of shooting a ray is c * S (T )/µ where µ is the total density of the ray distribution, i.e., the surface area of the outer perimeter of T plus the total surface area of the objects in S. For the purpose of optimizing ray shooting costs, however, if the outer bounding box and the scene are given, the denominator is constant and we need only concentrate on finding the best T optimizing c * S (T ) or c S (T ).…”

Section: Motivation Definitions and Problem Statementmentioning

confidence: 88%

“…In fact, this is rigorous for line traversal if the line distribution is the rigid-motion invariant distribution, but this is ill-defined for rays. In [1], we observed that for a uniform distribution of rays originating either outside the subdivision or on the surface of objects, the density of rays traversing a cell was proportional to the area of the perimeter plus the total area of the perimeter of the objects contained in the cell. The average cost of traversing a cell is proportional to the number of intersection tests performed multiplied by the density, plus some overhead γ for finding the next cell in the traversal, 3 and thus the following cost measure should be considered for modeling the total traversal costs [1]…”

Section: Motivation Definitions and Problem Statementmentioning

confidence: 99%

“…In [1], we proposed a measure for bounded-degree space decompositions, based on the surface area heuristic. This cost measure is a simplification of a more complicated but theoretically sound cost measure: under certain assumptions on the ray distribution, the more complicated cost measure provably reflects the cost of shooting an average ray using the space decomposition.…”

Section: Introductionmentioning

confidence: 99%

“…In a follow-up paper [2] to [1], we evaluate empirically several heuristics, including those presented here, to optimize the cost value of an octree for a given scene. Both our algorithm (3-greedy in this paper's terminology) and a simpler heuristic (which we call 1-greedy or greedy without lookahead) give the best cost.…”

Section: Introductionmentioning

confidence: 99%

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Octrees with near optimal cost for ray-shooting

Brönnimann¹,

Glisse

2006

Computational Geometry

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Predicting and optimizing the performance of ray shooting is a very important problem in computer graphics due to the severe computational demands of ray tracing and other applications, e.g., radio propagation simulation. Aronov and Fortune were the first to guarantee an overall performance within a constant factor of optimal in the following model of computation: build a triangulation compatible with the scene, and shoot rays by locating origin and traversing until hit is found. Triangulations are not a very popular model in computer graphics, but space decompositions like kd-trees and octrees are used routinely. Aronov et al. in [B. Aronov, H. Brönnimann, A.Y. Chang, Y.-J. Chiang, Cost prediction for ray shooting, in: Proc. 18th Annu. ACM Sympos. Comput. Geom., ACM, New York, 2002, pp. 293-302; Computational Geometry, submitted for publication] developed a cost measure for such decompositions, and proved it to reliably predict the average cost of ray shooting.In this paper, we address the corresponding optimization problem on octrees with the same cost measure as the optimizing criterion. More generally, we solve the generalization for generalized octrees in any d dimensions with scenes made up of (d − 1)-dimensional simplices. We give a construction of trees which yields cost O(M), where M is the infimum of the cost measure on all trees. Sometimes, a balance condition is important (informally, balanced trees ensures that adjacent leaves have similar size): we also show that rebalancing does not affect the cost by more than a constant multiplicative factor. These are the first and only known results that provide performance guarantees on the approximation factor for 3-dimensional ray shooting with this realistic model of computation. Our results have been validated experimentally by Aronov et al. in [B. Aronov, H. Brönnimann, A.Y. Chang, Y.-J. Chiang, Cost-driven octree construction schemes: an experimental study, in:

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Section: Introductionmentioning

confidence: 70%

Section: Motivation Definitions and Problem Statementmentioning

confidence: 88%

Section: Motivation Definitions and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Octrees with near optimal cost for ray-shooting

Brönnimann¹,

Glisse

2006

Computational Geometry

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Cost-Optimal Trees for Ray Shooting

Brönnimann¹,

Glisse²

2004

LATIN 2004: Theoretical Informatics

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Predicting and optimizing the performance of ray shooting is a very important problem in computer graphics due to the severe computational demands of ray tracing and other applications, e.g., radio propagation simulation. Aronov and Fortune were the first to guarantee an overall performance within a constant factor of optimal in the following model of computation: build a triangulation compatible with the scene, and shoot rays by locating origin and traversing until hit is found. Triangulations are not a very popular model in computer graphics, but space decompositions like kd-trees and octrees are used routinely. Aronov et al.[1] developed a cost measure for such decompositions, and proved it to reliably predict the average cost of ray shooting. In this paper, we address the corresponding optimization problem, and more generally d-dimensional trees with the cost measure as the optimizing criterion. We give a construction of quadtrees and octrees which yields cost O(M ), where M is the infimum of the cost measure on all trees, for points or for (d − 1)-simplices. Sometimes, a balance condition is important. (Informally, balanced trees ensures that adjacent leaves have similar size.) We also show that rebalancing does not affect the cost by more than a constant multiplicative factor, for both points and (d − 1)-simplices. To our knowledge, these are the only results that provide performance guarantees within approximation factor of optimality for 3-dimensional ray shooting with the octree model of computation.

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Cost-driven octree construction schemes

Aronov¹,

Brönnimann²,

Chang³

et al. 2003

Proceedings of the Nineteenth Annual Symposium on Computational Geometry

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Many algorithmic problems are interesting to both theoreticians and practitioners, but in a different manner. While the theoreticians have traditionally focused on worst-case scenarios which is often not very useful in practice, the practitioners are sometimes stuck in the hacking culture and arrive at solutions that only work well in a few specific cases. An example of such an algorithmic problem is ray shooting.Imposing some data structure to support ray-shooting queries usually helps to improve the efficiency of the algorithm. We focus on one such data structure-the octree. It is flexible and adaptive and has many applications. However, its degree of adaptiveness usually depends on manually selected parameters controlling its termination criteria. It is difficult to fix a set of parameter values that is good for all possible scenes. One approach to resolve this problem is to construct a data structure which "tunes itself" to the input without using arbitrary preset parameters, so that a single algorithm is suitable for all situations. Surprisingly, only a few investigations have focused on this approach compared to the huge amount of research papers on ray shooting from both the theoreticians and the practitioners. We take some steps in this direction by evaluating several octree construction schemes for use in ray shooting, some widely used in the computer graphics literature (such as bounding the number of objects in a leaf and the maximum depth) and some developed in companion papers as part of this research (costdriven k-greedy termination criteria). Our experimental results show that the octrees constructed using our schemes are better than those built with a priori fixed parameters.Our octree construction algorithm is driven by a simple * cost predictor and has been proven elsewhere to approximate the optimal tree to within a constant factor. We finetune the predictor and observe the behavior of our algorithm on octrees built to support a simple ray-tracing engine and compare its performance with those of commonly used alternatives. It appears to work well in practice.

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Cost prediction for ray shooting

Cited by 3 publications

References 16 publications

Octrees with near optimal cost for ray-shooting

Octrees with near optimal cost for ray-shooting

Cost-Optimal Trees for Ray Shooting

Cost-driven octree construction schemes

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