Cost-driven octree construction schemes: an experimental study

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

doi:10.1016/j.comgeo.2004.07.005

Cited by 9 publications

(9 citation statements)

References 13 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: 77%

“…MacDonald and Booth [16] (for bintrees) and Aronov et al [1,2] (for boundeddegree spatial subdivisions, with extensive experimentation for octree) argue and provide ample experimental evidence that this cost function also reflects the average cost of ray shooting using the spatial subdivision induced by the leaves of T .…”

Section: Motivation Definitions and Problem Statementmentioning

confidence: 95%

“…There is no guarantee that this cost is within (1 + ε) of optimal, though. The polynomial-time algorithm suggested in the remark of Section 3.4 (full subdivision to depth log 2 n + C followed by dynamic programming) would be guaranteed to give a O(1) approximation factor as well, and we'd even expect it to be very close to optimal, but it was too timeand space-consuming for us to try in [2]. Nevertheless, we find it hard to believe that the cost to which all these variants converge could be sub-optimal, and it thus appears experimentally that our procedure yields a near-optimal tree in practice.…”

Section: Introductionmentioning

confidence: 96%

“…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: 77%

Section: Motivation Definitions and Problem Statementmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 96%

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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“…However, giving exact costs and approximations on adaptive versions is very difficult. A comprehensive study of the costs for various construction schemes of octrees is presented in [24]. For precomputed visibility, the size of the data stored for the view cells may become so large that the total size of the PVSs is much larger than the size of the scene.…”

Section: Benefits Of Slicingmentioning

confidence: 99%

Conservative occlusion culling for urban visualization using a slice-wise data structure

Yılmaz

Güdükbay

2007

Graphical Models

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Fig. 1. An occlusion culling algorithm using our slice-wise data structure sends approximately 54 % fewer triangles to the graphics pipeline and increases frame rate by 46 %, as compared to an occlusion culling algorithm using building-level granularity of visibility in this 1.5M-triangle environment. The red colored sections show occluded regions, which are discarded from the graphics pipeline. In addition, the data structure decreases Potentially Visible Set (PVS) storage requirement drastically. AbstractIn this paper, we propose a new shrinking process for conservative from-point occlusion culling algorithms and a data structure for the visualization of urban environments. The visible geometry in a typical urban walkthrough mainly consists of partially visible buildings. Occlusion-culling algorithms, in which the granularity is based on buildings, render these partially visible buildings completely. We observe that the visibility in urban walkthroughs shows certain characteristics. The proposed slice-wise data structure represents the buildings, exploiting these characteristics, in terms of slices parallel to the coordinate axes. This forms the base for occlusion culling where the occlusion granularity is at slice level. The proposed slice-wise data structure has minimal storage requirements. The visible parts can be accessed at constant time during navigation with the help of a preprocessing stage. We also propose to shrink the occluders in a scene. This is necessary for a conservative from-point occlusion culling algorithm, which can also be applied to nonconvex general 3D occluders. Empirical results show that a 54 % decrease in the number of processed polygons and 46 % speed-up in frame-rate can be achieved by using the proposed conservative occlusion-culling algorithm with rather than an occlusion-culling method where the granularity is based on individual buildings.

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Orthogonal Subdivisions with Low Stabbing Numbers

Tóth

2005

Lecture Notes in Computer Science

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Cost-driven octree construction schemes: an experimental study

Cited by 9 publications

References 13 publications

Octrees with near optimal cost for ray-shooting

Octrees with near optimal cost for ray-shooting

Conservative occlusion culling for urban visualization using a slice-wise data structure

Orthogonal Subdivisions with Low Stabbing Numbers

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