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.

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.

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.

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 system's 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.