Curves in Computer Graphics

The only primitive geometric objects that computer graphics hardware typically can draw are points, lines and polygons. Usually there are special mechanisms to draw images, text characters, et cetera, but these are not commonly considered “geometric” since they are not usually transformed by geometric operations like rotation and perspective projection. Obviously it is important that graphics programs be able to draw more complex geometric forms from simple circles to complex surfaces in three dimensions. In real computer hardware, curves are usually drawn as a series of short straight line segments, and surfaces as meshes of polygons, usually triangles or quadrilaterals. A major problem in the design of graphics libraries is to provide a high level interface to the hardware that allows users to draw curves and surfaces from higher level descriptions rather than to require them to reduce curves and surfaces to line segments and polygons themselves. In this paper we will discuss some methods that are used to draw curves; many surface generating techniques are similar, but needless to say, the situation there is often far more complicated.