A technique for rendering images of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.

Volume rendering

Volume rendering is a technique for visualizing sampled scalar or vector fields of three spatial dimensions without fitting geometric primitives to the data. A subset of these techniques generates images by computing 2-D projections of a colored semitransparent volume, where the color and opacity at each point are derived from the data using local operators. Since all voxels participate in the generation of each image, rendering time grows linearly with the size of the dataset. This paper presents a front-to-back image-order volume-rendering algorithm and discusses two techniques for improving its performance. The first technique employs a pyramid of binary volumes to encode spatial coherence present in the data, and the second technique uses an opacity threshold to adaptively terminate ray tracing. Although the actual time saved depends on the data, speedups of an order of magnitude have been observed for datasets of useful size and complexity. Examples from two applications are given: medical imaging and molecular graphics.

/pdf/efficient-ray-tracing-of-volume-data-4l5b7uzhr8.pdf

Efficient ray tracing of volume data

A fast and simple voxel traversal algorithm through a 3D space partition is introduced. Going from one voxel to its neighbour requires only two floating point comparisons and one floating point addition. Also, multiple ray intersections with objects that are in more than one voxel are eliminated. Introduction In recent years, ray tracing has become the algorithm of choice for generating high fidelity images. Its simplicity and elegance allows one to easily model reflection, refraction and shadows. Unfortunately, it has a major drawback: computational expense. The prime reason for this is that the heart of ray tracing, intersecting an object with a ray, is expensive and can easily take up to 95% of the rendering time. Unless some sort of intersection culling is performed, each ray must intersect all the objects in the scene, a very expensive proposition. There are two general strategies for intersection culling: hierarchical bounding volumes 2, 3, 4 and space partitioning. 6, 7, 8 The general idea of the first approach is to envelop complicated objects that take a long time to intersect with simpler bounding volumes that are much easier to intersect, such as spheres or boxes. Before intersecting the complicated object, the bounding volume is first intersected. (Actually, it is not a full intersection test; all we care about is if the ray hits the bounding volume, not where). If there is no intersection with the bounding volume, there is no need to intersect the complicated object, thus saving time. For a complicated scene made up of many objects, a bounding volume is placed around the entire scene with each object also containing a bounding volume. If an object is made up of several parts each of these parts can also have a bounding volume. We thus can built a tree of bounding volumes, with each node containing a bounding volume that envelops its children. Objects within a subtree are intersected only if their parent node bounding volume is intersected by the ray. In this manner, the amount of actual intersections are significantly reduced. Of course, we now hav e to spent time intersecting bounding volumes but this is more than offset by the reduced total intersections. The second approach of reducing intersections is to partition space itself into regions or voxels. Each voxel has a list of objects that are in that voxel. If an object spans several voxels it is in more than one list. When a ray is shot, we first look into the voxel in which it originates. If it hits any objects in the starting voxel’s list, the intersections are sorted and the closest one is retained. If the intersection is in the current voxel there is no need to intersect any other objects as we have found the closest intersection. If no intersection is found in the current voxel or the object list is empty, we follow the ray into a neighbouring voxel and check its object list. We continue until either we find an intersection or we completely traverse the space partition. Since we intersect objects roughly in the order as they occur along the ray and trivially reject objects far from the ray, the number of intersections that need to be performed is vastly reduced. There are two popular space partition schemes: octrees by Glassner, where voxels are of different sizes, and constant size voxel partitioning (hereafter called a grid partition) by Fujimoto et. al. 8 The first conserves space but makes traversal difficult while the latter allows for simpler traversal at the expense of more voxels. In this paper, we introduce a fast and simple incremental grid traversal algorithm. Like Fujimoto et. al., 8 it is a variant of the DDA line algorithm. However, instead of basing it on the simple DDA (Fujimoto et. al.), in which an unconditional step along one axis is required, ours has no preferred axis. This considerably simplifies the inner loop and allows for easy testing of an intersection point to see if it is in the current voxel. Along with the the new traversal algorithm, we introduce a technique to eliminate multiple intersections when an object spans several voxels. This technique can be used with all space subdivision algorithms with minimum modifications. The New Traversal Algorithm Let us derive the new traversal algorithm. We consider the two dimensional case first; the extension to three dimensions is straightforward. Consider figure 1:

/pdf/a-fast-voxel-traversal-algorithm-for-ray-tracing-4ds478v575.pdf

A Fast Voxel Traversal Algorithm for Ray Tracing

A new algorithm for speeding up ray-object intersection calculations is presented. Objects are bounded by a new type of extent, which can be made to fit convex hulls arbitrarily tightly. The objects are placed into a hierarchy. A new hierarchy traversal algorithm is presented which is efficient in the sense that objects along the ray are queried in an efficient order.Results are presented which demonstrate that our technique is several times faster than other published algorithms. Furthermore, we demonstrate that it is currently possible to ray trace scenes containing hundreds of thousands of objects.

Ray tracing complex scenes

In this article we propose algorithms that address the two basic problems encountered in generating continuous-tone images by ray tracing: speed and aliasing. We examine previous approaches to the problem and then propose a scheme based on the coherency of an auxiliary data structure imposed on the original object domain. After investigating both simple spatial enumeration and a hybrid octree approach, we developed 3DDDA, a 3D line generator for efficient traversing of both structures. 3DDDA provides an order of magnitude improvement in processing speed compared to other known ray-tracing methods. Processing time is found to be virtually independent of the number of objects involved in the scene. For large numbers of objects, this method actully becomes faster than scan-line methods. To remove jags from edges, a scheme for identifying edge orientation and distance from pixel center to true edge has been implemented. The time required for antialiasing depends on the total length of the edges encountered, but it is normally only a fractional addition to the time needed to produce the scene without antialiasing.

ARTS: accelerated ray-tracing system

This paper proposes algorithms for dealing with two essential problems encountered in generating continuous-tone images by the ray tracing method: speed and aliasing These two factors are considered an Achilles’ heel of the method and have been the main cause preventing the method from being widely used The paper examines previous approaches to the problem and finally proposes a scheme based on the coherency of an auxiliary data structure imposed on the original object domain Both simple spatial enumeration and a hybrid octree approach were investigated 3DDDA (3D line generator) was developed for efficient traversing of both structures It constitutes the essential factor providing a dramatic improvement (order of magnitude) in processing speed in comparison to other known ray tracing methods In particular, processing time is found to be virtually independent of the number of objects involved in the scene For a larger number of objects (around 1500), this method actually becomes faster than scan-line methods In order to remove jags from edges, a scheme for identifying the edge orientation and the distance from a pixel center to the true edge has been implemented The additional time required for antialiasing depends on the total length of the edges encountered in the scene, but is normally only a fractional addition to the time required to produce such a scene without antialiasing

Accelerated Ray Tracing

A subpixel addressability feature allows this algorithm to address vector end points between pixel centers and helps it eliminate the Achilles' heel of raster displays?jaggies.

Jag-Free Images on Raster Displays

Capable of displaying 10,000 polygons per second, this interactive terminal produces smooth, color-shaded surfaces quickly for applications in science, engineering, training simulation, and animation.

A 3-D Graphics Display System With Depth Buffer and Pipeline Processor

This paper presents an algorithm for removing all kinds of jags (staircase-like effects) due to the aliasing phenomenon which is intrinsic in all synthesized wire frame and continuous-tone images displayed on raster CRT’s.

Jag Free Images on a Raster CRT

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