Introduction

Figure 1.1: A photorealistic scene with translucent volumes (clouds). The image is courtesy of Mark Harris [37].

Even though we call them three-dimensional graphics cards, commodity graphics hardware directly supports only zero-, one-, and two-dimensional primitives (points, lines, and polygons). The reason is simple. An opaque solid object is visually indistinguishable from just its surface when viewed from the outside. However, a photorealistic scene may involve any number of translucent volumetric objects such as clouds, dust, steam, fog, or jiggly food products [38]. We describe the synthesis of such elements as volume rendering. Figure 1.1 shows an example usage of translucent objects in a photorealistic scene.

In addition, direct volume visualization has become a popular technique for visualizing volumetric data from sources such as scientific simulations, analytic functions, and medical scanners such as MRI, CT, and ultrasound. All these data comprise samples, voxels, or cells distributed in a three dimensional volume. Visualizing these types of data can be problematic. A human being is capable of perceiving only the two dimensional projection of an object on the retina in the back of his eye, and the majority of objects a person sees in day to day life is opaque. Opaque surfaces, therefore, drive many visualization techniques, but the consequence is that interesting features of volumetric data could be lost if embedded in the middle, hidden by outer surfaces such as those demonstrated in Figure 1.2.

Figure 1.2: Visualization of a rotational x-ray scan of a human foot. The dataset is courtesy of Philips Research, Hamburg Germany.

Surface Rendering	Volume Rendering

Unfortunately, equations describing all but the simplest and approximate optical models are difficult to solve in real time. Many volume-rendering applications use drastic simplifications such as constant light emission or absorption (or both) through discrete segments. A scarce few use linear interpolation of both. Meanwhile, many organizations, including Sandia National Laboratories, have a continuing interest in unstructured meshes, volumetric models that can, and often do, vary wildly in cell size, shape, and connectivity. Although most of these models have linear cells, cells that vary linearly in both position and parameter, there is also a growing interest in models with nonlinear cells, cells with nonlinear parametric functions defining their shape and parameters [42]. Currently no interactive direct volume visualization systems can render such elements correctly.

This dissertation seeks to improve the current state of the art of volume rendering. In it, I demonstrate how to render a model consisting of linear cells (or, equivalently, a first order (linear) approximation). My method for volume rendering will be fast enough for interactive applications, whereas other systems may take minutes for a single rendered image. My method performs calculations close to those defined by the volumetric model I use, whereas others make brash approximations. Furthermore, unlike other systems, my method does not require any preprocessing, which will allow for fast changes in volume rendering parameters such as the transfer function.