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

Figure 1: Large volume data ray-traced at 512 2 using octrees for compression and acceleration. From left to right: (1) LLNL Richtmyer-Meshkov instability field (shown at timestep 270, with an isovalue of 100). (2) Closer view of the previous scene. (3) Utah CSAFE heptane simulation (timestep 152, isovalue 42). Data is losslessly compressed into an octree volume to occupy less than one quarter the size of the original 3D array. Our approach permits storage of large data such as the LLNL simulation, and full sequences of medium-size data such as the heptane, in main memory of consumer machines. Frame rates on an Intel Core Duo 2.16 GHz laptop with 2 GB RAM are 2.4, 1.3, and 3.3 fps respectively. On a 16-node NUMA 2.4 GHz Opteron workstation, these images render at 17.9, 9.8, and 22.0 fps. We present a technique for ray tracing isosurfaces of large compressed structured volumes. Data is first converted into a losslesscompression octree representation that occupies a fraction of the original memory footprint. An isosurface is then dynamically rendered by tracing rays through a min/max hierarchy inside interior octree nodes. By embedding the acceleration tree and scalar data in a single structure and employing optimized octree hash schemes, we achieve competitive frame rates on common multicore architectures, and render large time-variant data that could not otherwise be accomodated.

This article suggests a new approach to visualize implicit surfaces by using discrete Ray-Tracing. A preprocessing phase to rasterize the implicit surface is necessary to make use of this kind of Ray-Tracing. Several methods were proposed to subdivide an implicit surface. We extend their ideas to visualize this kind of surface directly into the voxel space.

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