Jerry R. Van Aken

Curve-drawing algorithms for Raster displays

The midpoint method for deriving efficient scan-conversion algorithms to draw geometric curves on raster displays in described. The method is general and is used to transform the nonparametric equation f(x,y) = 0, which describes the curve, into an algorithms that draws the curve. Floating point arithmetic and time-consuming operations such as multiplies are avoided. The maximum error of the digital approximation produced by the algorithm is one-half the distance between two adjacent pixels on the display grid. The midpoint method is compared with the two-point method used by Bresenham, and is seen to be more accurate (in terms of the linear error) in the general case, without increasing the amount of computation required. The use of the midpoint method is illustrated with examples of lines, circles, and ellipses. The considerzations involved in using the method to derive algorithms for drawing more general classes of curves are discussed.

Requirements for a VLSI Graphics Processor

This article will discuss issues that must be considered in the design of a VLSI (very large scale integration) 32-bit microprocessor specialized for graphics applications. With a properly chosen architecture, a single-chip graphics processor should provide a cost-effective means for achieving high performance in color bit-mapped graphics displays for PCs and workstations. The goal in selecting an architecture is to reduce the components required for a medium-to high-resolution display so they fit easily on a single, small, printed-circuit card. At the same time the processing speed must result in screen updates that occur without perceptible delay. These improvements should enable bit-mapped graphics displays to replace the text-only displays that have seen wide-spread use in cost-sensitive applications.

A parametric elliptical arc algorithm

Publisher Summary Sometimes an arc of a circle or of an ellipse is a better choice than a cubic spline for representing a particular curved shape. Circles and ellipses are inherently simpler curves than cubics, so the algorithms for generating them should also be simpler. This is chiefly why conic splines are popular in applications such as the generation of font outlines, where drawing speed is of critical importance. This chapter describes an algorithm for generating points along an elliptical arc. The points are separated by a fixed angular increment specified in radians of elliptical arc. The algorithm is based on a parametric representation of the ellipse. It is particularly inexpensive in terms of the amount of computation required. Only a few integer shifts, additions, and subtractions are needed to generate each point—without compromising accuracy. Defining an ellipse in terms of its conjugate diameters is equivalent to defining the ellipse in terms of an enclosing parallelogram. The chapter illustrates affine transformation of a unit circle inscribed in a square into an ellipse inscribed in a parallelogram.