Figure 1: Overview of our construction for a voxelized Lucy model, colored by mapping x, y, and z coordinates to red, green, and blue respectively (far left). The 3.5 million voxels (left) are input as 32-bit keys and placed into buckets of ≤ 512 items, averaging 409 each (center). Each bucket then builds a cuckoo hash with three sub-tables and stores them in a larger structure with 5 million entries (right). Close-ups follow the progress of a single bucket, showing the keys allocated to it (center; the bucket is linear and wraps around left to right) and each of its completed cuckoo sub-tables (right). Finding any key requires checking only three possible locations. We demonstrate an efficient data-parallel algorithm for building large hash tables of millions of elements in real-time. We consider two parallel algorithms for the construction: a classical sparse perfect hashing approach, and cuckoo hashing, which packs elements densely by allowing an element to be stored in one of multiple possible locations. Our construction is a hybrid approach that uses both algorithms. We measure the construction time, access time, and memory usage of our implementations and demonstrate real-time performance on large datasets: for 5 million key-value pairs, we construct a hash table in 35.7 ms using 1.42 times as much memory as the input data itself, and we can access all the elements in that hash table in 15.3 ms. For comparison, sorting the same data requires 36.6 ms, but accessing all the elements via binary search requires 79.5 ms. Furthermore, we show how our hashing methods can be applied to two graphics applications: 3D surface intersection for moving data and geometric hashing for image matching.

Figure 1: A scene using several vector textures with some closeups showing embossing and transparency. Vector graphics representations of images are resolution independent. Direct use of vector images for real-time texture mapping would be desirable to avoid sampling artifacts such as blurring common with raster images. Scalable Vector Graphics (SVG) files are typical of vector graphics image representations. Such representations composite images from layers of paths and strokes defined with lines, elliptical arcs, and quadratic and cubic parametric splines. High-quality texture mapping requires both random access and anisotropic antialiasing. For vector images, these goals can be achieved by computing the distance to the closest primitives from a sample point and then mapping this distance through a soft threshold function. Representing transparency masks in this way is especially useful, since vector mattes can be used to render complex curvilinear geometry as textures on simple geometric primitives. Unfortunately, computing the exact minimum distance to the parametric curves used in vector images is difficult. Previous work has used approximations, but an accurate minimum distance is desirable in order to enable wide strokes and special effects such as embossing. In this paper, a simple algorithm is presented that can efficiently and accurately compute the minimum distance to a parametric curve when the sample point is within its radius of curvature and the curve can be segmented into monotonic regions. This technique can be used in a GPU shader to render antialiased vector images exactly as defined by SVG files.

graphics rule!

Because of the resolution independent nature of vector graphics images, it is useful to consider using them directly as textures in 3D rendering. Spline curves are used to represent boundaries in standard vector graphics representations. Antialiased rendering of such content can be obtained by soft thresholding an implicit representation of these boundary features. The distance function is an especially useful implicit representation, and an accurate distance can also be used for special effects such as embossing and stroke texturing. Unfortunately, computation of the true distance to a spline curve is expensive. Therefore, normally either the distance is approximated or the spline curves are approximated with simpler primitives for which an accurate distance can be computed. Approximation with line segments gives only C 0 continuity. We approximate spline curves using circular arcs instead. This approximation has C 1 continuity, and computing the distance to a circular arc is nearly equivalent in expense to computing the distance to a line segment. 1.

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Algorithms are presented that enable the use of vector graphics representations of images in texture maps for 3D real time rendering. Vector graphics images are resolution inde-pendent and can be zoomed arbitrarily without losing detail or crispness. Many important types of images, including text and other symbolic information, are best represented in vector form. Vector graphics textures can also be used as transparency mattes to augment geometric detail in models via trim curves. Spline curves are used to represent boundaries around regions in standard vector graphics representations, such as PDF and SVG. Antialiased rendering of such content can be obtained by thresholding implicit representations of these curves. The distance function is an especially useful implicit representation. Accurate distance function com-