The goal of this dissertation is to improve the state of the art in unstructured mesh volume rendering. Over the past decade, there has been research to perform volume rendering that is either fast [86,98,102,110] or accurate [92,105], but not both. This dissertation presented algorithms that are as fast as the former but as accurate as the latter.
I started with the View Independent Cell Projection algorithm [98,100]. The speed of the algorithm was obtained by taking advantage of recent improvements in accelerated graphics hardware. I have made several improvements to this algorithm and demonstrated their effectiveness.
The original View Independent Cell Projection implementation used Pre-Integration [81] to perform its color computations. Pre-Integration had many advantages. Because the heavy ray integrations were done off line, Pre-Integration could yield high frame rates. Given a large enough table, Pre-Integration eliminated errors from sampling the transfer function. In addition, Pre-Integration could potentially support any type of ray integration method.
However, Pre-Integration had several design limitations. The pre-integration table was built specifically for a given transfer function. Thus, the table had to be rebuilt every time the transfer function changed, which, during a practical application, was often. Furthermore, the accuracy of Pre-Integration relied heavily on the size of the table used and ray integrations performed. However, larger tables and more accurate ray-integration methods would slow down the table building. Pre-Integration worked only with 1D transfer functions, whereas higher dimensional transfer functions could more effectively highlight features in the volume [46,47,50,94]. Pre-Integration was incapable also of performing many non-photorealistic feature highlighting techniques [21,43,44]. For these reasons, my algorithms did not rely on Pre-Integration.
To avoid aliasing without Pre-Integration, I implemented Adaptive Transfer Function Sampling. Although it improved image quality, the Adaptive Transfer Function Sampling negatively affected the rendering speed. However, even with Adaptive Transfer Function Sampling, my algorithm ran at about the same speed as View Independent Cell Projection.
My algorithms performed ray integration in the graphics card during rendering. To do this, I devised new ray-integration methods that were both fast and accurate. These ray-integration methods are for linearly varying volume parameters. I provided methods for both linearly varying volume density, which has a closed form, and linearly varying observable opacity, which does not have a closed form. I have shown that these ray-integration methods are competitive with both the speed of previous fast approximations [86,102] and the accuracy of slow approximations [105].
Sandia National Laboratories is currently using the algorithms introduced in this dissertation for its scientific visualization needs. Furthermore, the code is integrated into the Visualization Toolkit (VTK) [84] and will soon be incorporated into ParaView [57], a fully featured, open-source scientific visualization package.
The work in this dissertation may take several directions. First, although I have contrasted the ray integrations presented in this dissertation with the approach of Pre-Integration, the two approaches could be complementary. The entries in the pre-integration table are filled with values computed with ray integration. We could use the ray-integration methods presented in this dissertation to increase both the accuracy of the entries in the table and the speed with which they are calculated.
Second, although my volume rendering implementations currently support only 1D transfer functions, there are no fundamental limitations preventing the use of transfer functions of two or more dimensions so long as they are still piecewise linear. However, the representation of a piecewise linear function in two or more dimensions can be problematic, and tools for building multidimensional transfer functions are still being developed.
Third, although the ray integration methods introduced in this dissertation are valid only for piecewise linear approximations, we can approximate higher orders of color variation along the ray with a piecewise linear function without any noticeable visual artifacts. However, for maximal speed, we need to minimize the number of segments used in the piecewise linear approximation. The minimal segmentation needs to be investigated.