## An Efficient Parametric Algorithm for Octree Traversal (2000)

Venue: | Journal of WSCG |

Citations: | 26 - 3 self |

### BibTeX

@INPROCEEDINGS{Revelles00anefficient,

author = {J. Revelles and C. Ureña and M. Lastra},

title = {An Efficient Parametric Algorithm for Octree Traversal},

booktitle = {Journal of WSCG},

year = {2000},

pages = {212--219}

}

### Years of Citing Articles

### OpenURL

### Abstract

An octree is a well known hierarchical spatial structure which is widely used in Computer Graphics algorithms. One of the most frequent operations is the computation of the octree voxels intersected by a straight line. This has a number of applications, such as ray-object intersection tests speed-up and visualisation of hierarchical density models by ray-casting. Several methods have been proposed to achieve this goal, which differ in the order in which intersected voxels are visited. In this paper we introduce a new top-down parametric method. The main difference with previously proposed methods is related to descent movements, that is, the selection of a child sub-voxel from the current one. This selection, as the algorithm, is based on the parameter of the ray and comprises simple comparisons. The resulting algorithm is easy to implement, and efficient when compared to other related top-down and bottom-up algorithms for octrees. Finally, a comparison with Kelvin's method for binary trees is presented. Keywords: Octree, Binary tree, Ray Tracing, Acceleration Techniques 1

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Citation Context ...the use of a nine parameter set to compute which voxel is pierced first. This computation avoids neighbour finding to obtain the first voxel, as it is the case for the algorithm introduced by Glassner=-=[Glass84]-=- and improved in other papers[Arvo88, Samet89, Endl94]. This yields a simpler method. The following sections describe these two steps in detail. The second step is carried out by using a parametric DD... |

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Citation Context ...mputing time. With respect to the movements between neighbour voxels with the same parent voxel, we use an algorithm which is also based on the ray parameter, as the algorithm described by Amanatides =-=[Amana87]-=-. Sung [Sung91] presented an octree traversal algorithm which has the same theoretical basis as the 3DDDA traversal algorithm [Amana87] for uniform spatial subdivision, however, for unbalanced octrees... |

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Citation Context ...ed version of the algorithm for quadtrees. The extension for octrees is detailed in section 3. A comparison in terms of efficiency with other methods, such as the bottom-up method introduced by Samet =-=[Samet89]-=-, two extensions of it proposed by Endl [Endl94], and a recursive top-down method [Garga93], is also included. We use the same software system for all the algorithms. Results show that the new algorit... |

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Citation Context ...th respect to the movements between neighbour voxels with the same parent voxel, we use an algorithm which is also based on the ray parameter, as the algorithm described by Amanatides [Amana87]. Sung =-=[Sung91]-=- presented an octree traversal algorithm which has the same theoretical basis as the 3DDDA traversal algorithm [Amana87] for uniform spatial subdivision, however, for unbalanced octrees, efficiency de... |

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Citation Context ...ency decreases. This is due to the fact that Sung’s algorithm uses the smallest octree leaf as traversal base unit. Moreover, we must refer a significant work presented by J. Spackman and P.J. Willi=-=s [Spack91]-=-. The authors presented a very efficient algorithm to traverse an octree that only employed operations with integer arithmetic throughout the traversal. That algorithm is outlined into the paper and i... |

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Citation Context ...tension for octrees is detailed in section 3. A comparison in terms of efficiency with other methods, such as the bottom-up method introduced by Samet [Samet89], two extensions of it proposed by Endl =-=[Endl94]-=-, and a recursive top-down method [Garga93], is also included. We use the same software system for all the algorithms. Results show that the new algorithm is more efficient than these other methods ex... |

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Citation Context ...re computed incrementally, by using additions and divisions by two. In essence, this algorithm is related to other parametric top-down algorithms, such as the one introduced by Jansen [Janse85], Arvo =-=[Arvo88], -=-and Agate [Agate91]. Afterward, Sung and Shirley [Sung92] proposed a version on a BSP tree of Jansen’s work. Authors of these papers pointed out that the cost of traversing an octree and a BSP tree ... |

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Citation Context ... 3. A comparison in terms of efficiency with other methods, such as the bottom-up method introduced by Samet [Samet89], two extensions of it proposed by Endl [Endl94], and a recursive top-down method =-=[Garga93]-=-, is also included. We use the same software system for all the algorithms. Results show that the new algorithm is more efficient than these other methods except on the algorithm presented by Spackman... |

3 |
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Citation Context ...tally, by using additions and divisions by two. In essence, this algorithm is related to other parametric top-down algorithms, such as the one introduced by Jansen [Janse85], Arvo [Arvo88], and Agate =-=[Agate91]. -=-Afterward, Sung and Shirley [Sung92] proposed a version on a BSP tree of Jansen’s work. Authors of these papers pointed out that the cost of traversing an octree and a BSP tree are similar, (these r... |

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Citation Context ... by two. In essence, this algorithm is related to other parametric top-down algorithms, such as the one introduced by Jansen [Janse85], Arvo [Arvo88], and Agate [Agate91]. Afterward, Sung and Shirley =-=[Sung92] p-=-roposed a version on a BSP tree of Jansen’s work. Authors of these papers pointed out that the cost of traversing an octree and a BSP tree are similar, (these results have been formally presented by... |

2 |
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Citation Context .... These values are computed incrementally, by using additions and divisions by two. In essence, this algorithm is related to other parametric top-down algorithms, such as the one introduced by Jansen =-=[Janse85], -=-Arvo [Arvo88], and Agate [Agate91]. Afterward, Sung and Shirley [Sung92] proposed a version on a BSP tree of Jansen’s work. Authors of these papers pointed out that the cost of traversing an octree ... |