Jack Goldfeather

Pixel-planes 5: a heterogeneous multiprocessor graphics system using processor-enhanced memories

This paper introduces the architecture and initial algorithms for Pixel-Planes 5, a heterogeneous multi-computer designed both for high-speed polygon and sphere rendering (1M Phong-shaded triangles/second) and for supporting algorithm and application research in interactive 3D graphics. Techniques are described for volume rendering at multiple frames per second, font generation directly from conic spline descriptions, and rapid calculation of radiosity form-factors. The hardware consists of up to 32 math-oriented processors, up to 16 rendering units, and a conventional 1280 × 1024-pixel frame buffer, interconnected by a 5 gigabit ring network. Each rendering unit consists of a 128 × 128-pixel array of processors-with-memory with parallel quadratic expression evaluation for every pixel. Implemented on 1.6 micron CMOS chips designed to run at 40MHz, this array has 208 bits/pixel on-chip and is connected to a video RAM memory system that provides 4,096 bits of off-chip memory. Rendering units can be independently reasigned to any part of the screen or to non-screen-oriented computation. As of April 1989, both hardware and software are still under construction, with initial system operation scheduled for fall 1989.

A novel cubic-order algorithm for approximating principal direction vectors

There are a number of applications in computer graphics that require as a first step the accurate estimation of principal direction vectors at arbitrary vertices on a triangulated surface. Although several methods for calculating principal directions over such models have been previously proposed, we have found in practice that all exhibit unexplained large errors in some cases. In this article, we describe our theoretical and experimental investigations into possible sources of errors in the approximation of principal direction vectors from triangular meshes, and suggest a new method for estimating principal directions that can yield better results under some circumstances.

Fast spheres, shadows, textures, transparencies, and imgage enhancements in pixel-planes

Pixel-planes is a logic-enhanced memory system for raster graphics and imaging. Although each pixel-memory is enhanced with a one-bit ALU, the systems real power comes from a tree of one-bit adders that can evaluate linear expressions Ax+By+C for every pixel (x,y) simultaneously, as fast as the ALUs and the memory circuits can accept the results. We and others have begun to develop a variety of algorithms that exploit this fast linear expression evaluation capability. In this paper we report some of those results. Illustrated in this paper is a sample image from a small working prototype of the Pixel-planes hardware and a variety of images from simulations of a full-scale system. Timing estimates indicate that 30,000 smooth shaded triangles can be generated per second, or 21,000 smooth-shaded and shadowed triangles can be generated per second, or over 25,000 shaded spheres can be generated per second. Image-enhancement by adaptive histogram equalization can be performed within 4 seconds on a 512x512 image.

Near real-time CSG rendering using tree normalization and geometric pruning

A description is given of a set of algorithms for efficiently rendering an object defined by constructive solid geometry (CSG) directly onto a frame buffer without converting first to a boundary representation. This method requires only that the frame buffer contain sufficient memory to hold two color values, two depth values, and three one-bit flags. The algorithm first converts the CSG tree to a normalized form that is analogous to the sum-of-products form for Boolean switching functions. The following are developed: dynamic interleaving of Boolean tree normalization with bounding-box pruning, allowing efficient rendering for most CSG objects; a method for extending the technique to nonconvex primitives; and implementation of these ideas in an interactive CSG design system on the Pixel-planes 4 solid modeling system. In the design system the designer directly manipulates the CSG structure while continuously viewing the color rendering of the object being designed.<<ETX>>

Fast constructive-solid geometry display in the pixel-powers graphics system

We present two algorithms for the display of CSG-defined objects on Pixel-Powers, an extension of the Pixel-Planes logic-enhanced memory architecture, which calculates for each and every pixel on the screen (in parallel) the value of any quadratic function in the screen coordinates (x,y). The first algorithm restructures any CSG tree into an equivalent, but possibly larger, tree whose display can be achieved by the second algorithm. The second algorithm traverses the restructured tree and generates quadratic coefficients and opcodes for Pixel-Powers. These opcodes instruct Pixel-Powers to generate the boundaries of primitives and perform set operations using the standard Z-buffer algorithm.Several externally-supplied CSG data sets have been processed with the new tree-traversal algorithm and an associated Pixel-Powers simulator. The resulting images indicate that good results can be obtained very rapidly with the new system. For example, the commonly used MBB test part (at right) with 24 primitives is translated into approximately 1900 quadratic equations. On a Pixel-Powers system running at 10MHz (the speed at which our current Pixel-Planes memories run), the image should be rendered in about 7.5 milliseconds.

Quadratic Surface Rendering on a Logic-Enhanced Frame-Buffer Memory

A new system, Pixel-powers, has been designed for the rapid rendering of curved surfaces. This system is a generalization of the design of our logic-enhanced framed buffer memory system, Pixel-planes. Our new design can directly evaluate quadratic expressions of the form Ax2 + Bxy + Cy2 + Dx + Ey + F for every pixel (x,y) in the image in parallel. Sample images generated by a high-level simulation of the new system are shown.

Adaptive redirected walking in a virtual world

Redirected walking enables the physical exploration of large virtual environments within the confines of more limited physical spaces. In this paper, we present a novel method for adaptively determining an appropriate mapping from a linear path in a larger virtual environment into a curved path in a smaller tracked space that simultaneously integrates the use of both rotational and translational offsets. We evaluate the method using a software simulator that redirects a user walking on random paths between 16 randomly selected target locations in a virtual environment that is twice as wide as the available tracked space. We find that our controller has a 77% success rate using an average rotational offset of 0.5 degrees per step and an average translational gain of 1.5.

Methods to identify individual eddy structures in turbulent flow

Turbulent flows are intrinsic to many processes in science and engineering, and efforts to elucidate the physics of turbulence are of critical importance to many fields. However, ongoing efforts to achieve a fundamental understanding of the mechanisms of turbulent flow are hindered by the difficulty of quantifying the complex, non- linear interactions between individual eddies in these flows. The difficulty of this task is compounded by the lack of robust methods for accurately identifying individual eddy structures and characterizing their dynamic evolution and organization across multiple scales. In this paper we address this problem by proposing several novel approaches for more accurately segmenting individual eddy structures in turbulent flows.

Tracking in Virtual Reality

I magine you are standing in an empty room wearing a pair of goggles, the lenses of which are tiny computer screens capable of displaying sophisticated computer graphics images. Imagine also that an object, say a chair, is stored as data in a computer. For example, the geometry of the chair might be defined in terms of vertices, edges and faces, with the vertices defined relative to a fixed world coordinate system in the room. The question is: