Fundamental Algorithms for Computer Graphics pp 289-301 | Cite as

# A Review of Curve Drawing Algorithms

## Abstract

A variety of curve drawing methods have now been devised for computer graphics and CAD. These range from simple, piecewise interpolating curves through a set of points in a plane, to complex, smoothing curves for CAD, and approximation curves which allow error bounds on individual points to be specified and incorporated in the curve definition.

- (i)
Single-valued or multi-valued in either coordinate

- (ii)
Shape and axis-independence on transformation (e.g. rotational invariance)

- (iii)
Smoothness and fairness — mathematical, aesthetic, or model-based

- (iv)
Global and local control of shape

- (v)
Approximation functions

The importance of a particular characteristic is often related to the requirements of the application area under consideration, so it is possible to select an approach which satisfies the prime requirement. However, there are advantages and disadvantages to the different methods.

The interface between curve generation and curve display necessitates a consideration of how best to translate curve specifications into drawn curves (e.g. by some optimal vector sequence) and also what primitive functions it is desirable for graphical output devices to accommodate or emulate, in order to facilitate specification of this interface at a high level.

The development of curve drawing algorithms from the early ad hoc approaches in the 1960’s to the sophisticated polynomials of the 1980’s will be reviewed, concentrating on those methods and algorithms which are believed to be fundamental, and the basis for future development.

### Keywords

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