Ray Tracing an Octree: Numerical Evaluation of the First Intersection

Abstract

An algorithm is presented which finds the first intersection of a directed semi‐infinite straight‐line (called ray) with an octree, without resorting to the evaluation of neighbouring nodes. Given a pointer‐based region octree, intersections of the ray with a node's bisecting planes are first evaluated to determine in which sub‐octants the ray‐node intersections may lie; a local ordering then determines the sequence in which these sub‐octants should be examined so that the intersection closest to the ray's origin can be selected. This idea is applied recursively starting from the root of the octree; the novelty of the approach consists of the fact that the choice of each node's child in the octree is directly derived from the intersection of the ray‐segment within the tested sub‐octant, thus avoiding searching for any neighbouring nodes. The problem of selecting the correct octant while using the commonly available floating‐point arithmetic is also addressed in a ray tracing environment. Comparisons of this approach with the method given by Samet17 are carried out in a variety of cases involving millions of voxels. The improvement ranged from 32% to 62% in terms of execution time.

Interactive Isosurface Ray Tracing of Large Octree Volumes

“…Sung [19] proposed a DDA traversal similar to a hierarchical grid. Finally, Gargantini and Atkinson [5] implemented a traversal similar to a kd-tree where the ray intersection with each octant mid-plane is ordered.…”

“…After experimenting with the methods of Sung [19] and Samet [17], the fastest traversal that emerged most resembled the technique of Gargantini and Atkinson [5]. The traversal is similar to that of a kd-tree, with splits along the X,Y and Z mid-planes of each node.…”

Arbitrary 3D Resolution Discrete Ray Tracing of Implicit Surfaces

“…Once a certain level is reached the octant is considered a leaf node or voxel and stored in an octree. During rendering time, the basic idea is to traverse each ray through the octree to find the first voxel containing a part of an object in the scene, which is in appearance similar to the work of Glassner [4] or Gargantini [6]. The fundamental difference between their approaches is that Glassner uses a linear octree, while Gargantini uses a hierarchical pointer octree.…”

“…Nonetheless, the ray traversal itself might rely on intersections between rays and bounding volumes [2,3] or between rays and discrete subspaces where the scene was previously voxelized [4,5,6,7]. Octrees [8,4,6,5,7,9] have been proved to have great advantages for space decomposition in these techniques, since empty regions can be efficiently skipped. However, their advantages have been considerably hindered by the fact that the intersection calculations between rays and the boundaries of the regions traversed are not only inefficient but also unreliable [6].…”

“…Octrees [8,4,6,5,7,9] have been proved to have great advantages for space decomposition in these techniques, since empty regions can be efficiently skipped. However, their advantages have been considerably hindered by the fact that the intersection calculations between rays and the boundaries of the regions traversed are not only inefficient but also unreliable [6]. Sometimes, these intersection calculations were implicitly or exclusively accomplished by incremental algorithms [8,10,7,9].…”