In part one of this dissertation, we present a scheme for rendering higher-order isosurfaces. Animation and visualization of rectilinear data require interpolation schemes for smooth image generation. Piecewise trilinear interpolation, the de facto standard for interpolating rectilinear data, usually leads to significant visual artifacts in the resulting imagery. These artifacts reduce the fidelity of the resulting visualization, and may even lead to false interpretations of the data. This part is concerned with the generation of smooth isosurface image sequences, obtained by casting rays through the image plane and computing their intersections with an isosurface. We describe a novel solution to this problem: We replace trilinear interpolation by tricubic interpolation, smoothing out the artifacts in the images; and we simplify the ray-isosurface intersection calculations by rotating and resampling the original rectilinear data onto a second rectilinear grid- a grid with one family of grid planes parallel to the image plane.
In part two of this dissertation, we discuss multiresolution techniques for hardware-accelerated, texture-based visualization of very large data sets. We discuss both volume visualization and cutting-planes techinques and how we have implemented them. In general, these methods use an adaptive scheme that renders the volume in a region-of-interest at a high resolution and the volume away from this region at progressively lower resolutions. The developed algorithm is based on the segmentation of texture space into an octree, where the leaves of the tree define the original data and the internal nodes define lower-resolution approximations. Rendering is done adaptively by selecting high-resolution cells close to a center of attention and low-resolution cells away from this area. We discuss four items particular to multiresolution volume visualization: (a) the special attention that must be paid to the transfer functions; (b) the proxy geometry; (c) indexed texture maps to allow for quick changes to the tranfer function; and (d) error evalutation in the context of index texture maps. We discuss a method for removing artifacts in multiresolution cutting planes.