In this article we propose algorithms that address the two basic problems encountered in generating continuous-tone images by ray tracing: speed and aliasing. We examine previous approaches to the problem and then propose a scheme based on the coherency of an auxiliary data structure imposed on the original object domain. After investigating both simple spatial enumeration and a hybrid octree approach, we developed 3DDDA, a 3D line generator for efficient traversing of both structures. 3DDDA provides an order of magnitude improvement in processing speed compared to other known ray-tracing methods. Processing time is found to be virtually independent of the number of objects involved in the scene. For large numbers of objects, this method actully becomes faster than scan-line methods. To remove jags from edges, a scheme for identifying edge orientation and distance from pixel center to true edge has been implemented. The time required for antialiasing depends on the total length of the edges encountered, but it is normally only a fractional addition to the time needed to produce the scene without antialiasing.

ARTS: accelerated ray-tracing system

Spreadsheet languages, which include commercial spreadsheets and various research systems, have had a substantial impact on end-user computing. Research shows, however, that spreadsheets often contain faults; thus, we would like to provide at least some of the benefits of formal testing methodologies to the creators of spreadsheets. This article presents a testing methodology that adapts data flow adequacy criteria and coverage monitoring to the task of testing spreadsheets. To accommodate the evaluation model used with spreadsheets, and the interactive process by which they are created, our methodology is incremental. To accommodate the users of spreadsheet languages, we provide an interface to our methodology that does not require an understanding of testing theory. We have implemented our testing methodology in the context of the Forms/3 visual spreadsheet language. We report on the methodology, its time and space costs, and the mapping from the testing strategy to the user interface. In an empirical study, we found that test suites created according to our methodology detected, on average, 81% of the faults in a set of faulty spreadsheets, significantly outperforming randomly generated test suites.

A methodology for testing spreadsheets

The present invention provides a unified image and graphics processing system that provides both image and graphics processing at high speeds. The system includes a parallel vector processing unit, a graphics subsystem, a shared memory and a set of high-speed data buses for connecting all of the other components. Generally, the parallel vector processing unit includes a series of vector processors. Each processor includes a vector address generator for efficient generation of memory addresses for regular address sequences. In order to synchronize and control the vector processors' accesses to shared memory, the parallel vector processing unit includes shared memory access logic. The logic is incorporated into each vector processor. The graphics subsystem includes a series of polygon processors in a pipelined configuration. Each processor is connected in the pipeline by a first-in-first-out (FIFO) buffer for passing data results. Additionally, each polygon processor is connected to a local shared memory in which programm instructions and data are stored. The graphics subsystem also includes a device addressing mechanism for identifying a destination device using a tagged address. The shared memory, the parallel vector processor and the graphics subsystem also incorporate an abbreviated addressing scheme, which reduces the amount of information required to request sequential addresses from the shared memory.

Imaging and graphics processing system

A procedure for computing shaded pictures of curved surfaces is presented. The surface is approximated by small polygons in order to solve easily the hidden-parts problem, but the shading of each polygon is computed so that the discontinuities of shade are eliminated across the surface and a smooth appearance is obtained. In order to achieve speed efficiency, the technique developed by Watkins is used which makes possible a hardware implementation of this algorithm.

Continuous shading of curved surfaces

A method, using a filter function, generates an anti-aliased discrete image from a continuous image including an edge. The method defines a line sample. A progressive convolution is derived from the filter function and the line sample. A pixel at a predetermined location in the discrete image is selected, and the line sample is oriented with respect to the selected pixel. A distance is measured from a point in the continuous image corresponding to the selected pixel to the edge along the oriented the line sample. The progressive convolution is evaluated at the measured distance to produce a weighted coverage value, and the weighted coverage value is associated with the pixel to anti-alias the pixel in the discrete image.

/pdf/antialiasing-with-line-samples-28r70xysn7.pdf

Antialiasing with Line Samples

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A 3-D Graphics Display System With Depth Buffer and Pipeline Processor