Implicit surfaces are useful representations of geometry in visualization. Since geometric data are nearly always discrete, it is typically desirable to pair them with a continuous reconstruction filter. An isosurface is a manifestation of that filter in implicit form. Traditionally, the preferred methods for rendering isosurfaces have been to extract and rasterize a triangle mesh, or to resample the implicit as simpler proxy geometry such as splats. Ray casting allows for direct and pixel-exact rendering of an implicit surface by root-solving for the intersection. Full ray tracing methods pair this intersection process with a spatial acceleration structure, such as a bounding volume hierarchy or octree. While traditionally slow compared to rasterization, this approach has several advantages. It enables multiple-bounce effects such as shadows and reflections, and allows for dynamic changes in the implicit without offline processing. More significantly for visualization, acceleration structures are traversed in logarithmic time, allowing for graceful scaling to large data. This dissertation presents several advancements in ray tracing implicit surfaces and its applications, namely single-ray and coherent multiresolution methods for isosurface ray tracing of octree-compressed large structured data, a coherent method for isosurface rendering of tetrahedral meshes, and algorithms for rendering arbitrary implicit forms robustly using interval and affine arithmetic. While computationally costly, techniques such as these map well to modern multicore CPUs and thread-parallel GPUs, and will continue to improve in efficiency and applicability as parallel hardware trends evolve.
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