Cost-driven octree construction schemes

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

doi:10.1145/777792.777827

Cited by 7 publications

(2 citation statements)

References 29 publications

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“…In practice, we find that greedy with or without lookahead yield near-optimal octrees, hence the approximation ratio seems close to one. 2 All the results stated in this paper should extend easily to recursive grids and simplicial trees as well, in two and higher dimensions, with only small differences. However, the constants involved in the analysis would be even higher than they are here.…”

Section: Discussionmentioning

confidence: 86%

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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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Section: Discussionmentioning

confidence: 86%

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

Section: Our Resultsmentioning

confidence: 99%

Cost-Optimal Trees for Ray Shooting

Brönnimann¹,

Glisse²

2004

LATIN 2004: Theoretical Informatics

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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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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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Cost-driven octree construction schemes

Cited by 7 publications

References 29 publications

Cost-Optimal Trees for Ray Shooting

Cost-Optimal Trees for Ray Shooting

Octrees with near optimal cost for ray-shooting

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

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