## Abstract

Given a scene consisting of objects, ray shooting queries answer with the first object encountered by a given ray, and are used in ray tracing and radiosity for rendering photo-realistic images in graphics, radio propagation simulation, and many other problems. We focus on one popular data structure for answering ray shooting queries - 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. While practitioners usually rely on experience and heuristics, it is difficult to fix a set of parameter values that is good for all possible scenes. Recently, we introduced a simple cost predictor that reflects the average cost of ray shooting with a given octree (Cost prediction for ray shooting, in: Proc. 18th Annu. ACM Sympos. Comput. Geom., ACM, New York, 2002, pp. 293-302), and showed a termination criterion (cost-driven k-greedy) that guarantees a cost within a constant factor of optimal (Cost-optimal trees for ray shooting, in: Proc. LATIN'04, Lecture Notes in Comput. Sci., vol. 2976, Springer, Berlin, 2004, pp. 349-358). In this study, we compare this criterion with several octree construction schemes widely used in the computer graphics literature (such as bounding the number of objects in a leaf and the maximum depth). Our experimental results show that the octrees constructed using our schemes are generally comparable to or better than those built with a priori fixed parameters. We then fine-tune the predictor and observe the behavior of our algorithm on octrees built to support a simple ray-tracing engine. It appears to work well in practice.

Original language | English (US) |
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Pages (from-to) | 127-148 |

Number of pages | 22 |

Journal | Computational Geometry: Theory and Applications |

Volume | 31 |

Issue number | 1-2 |

DOIs | |

State | Published - May 2005 |

## Keywords

- Average performance
- Cost model
- Cost prediction
- Octree
- Ray shooting
- Space decomposition

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics