Overview

Almost eighteen years ago, Frieder, Gordon, and Reynolds published a paper on the back-to-front display of voxel-based objects.

The idea can be explained in parallel to raycasting. Instead of casting rays originating from the eye point and intersecting it with the volume data for color calculations, rays are projected from behind the data set and onto the screen.

So, this cell projection technique can be thought of as reverse-ray integration, and can produce accurate renderings that parallel the quality of ray-casted images.

In cell projection, the rendering is done in object space. That means, regardless of the image size, the rendering time will be essentially the same. This may be an advantage if high-resolution renderings are desired. But it is not difficult to see that even for moderately sized data sets, say, sixty-four cubed, millions of polygons will have to be drawn for each frame.

Although cell projection is not purposed towards real-time rendering, it has many desirable properties. Because the data set is voxelated, the voxels can be manipulated to produce colorful visual effects. For example, different techniques that subdivide each voxel for display will produce different artifacts.

Our project is motivated by the different artifacts produced by different tetrahedralation techniques. "Simplicial Subdivisions and Sampling Artifacts" by Hamish Carr and Torsten Moeller describes many such techniques. By setting some of them up for the Cartesian grid now, it will be possible to transfer them onto the BCC grid later. At that time, differences due to of the two grids can be compared and studied.
With that overview, we will now discuss our approach to the project.
Original Goals

I had already worked on the project for some time this past summer. When Ian and I started working on the project again, it was able to subdivide voxels via the minimal five-fold scheme and project voxels in back to front order. A synthetic sphere was hardcoded along with its transfer function, and color calculations for each triangulated tetrahedron was done without considering the thickness of the tetrahedron.

The original plan was two-fold. Ian was going to work on regular and curvilinear file reading and I was going to work on tetrahedralation techniques and on re-implementing the color calculations for the triangulation of tetrahedra. I said in our initial proposal that if I don't manage to re-implement the color calculations, I will at least produce demos that will help me implement them later.