Page "Bézier curve" Paragraph 8

The simplest method for scan converting ( rasterizing ) a Bézier curve is to evaluate it at many closely spaced points and scan convert the approximating sequence of line segments.

However, this does not guarantee that the rasterized output looks sufficiently smooth, because the points may be spaced too far apart.

Conversely it may generate too many points in areas where the curve is close to linear.

A common adaptive method is recursive subdivision, in which a curve's control points are checked to see if the curve approximates a line segment to within a small tolerance.

If not, the curve is subdivided parametrically into two segments, 0 ≤ t ≤ 0. 5 and 0. 5 ≤ t ≤ 1, and the same procedure is applied recursively to each half.

There are also forward differencing methods, but great care must be taken to analyse error propagation.

Analytical methods where a spline is intersected with each scan line involve finding roots of cubic polynomials ( for cubic splines ) and dealing with multiple roots, so they are not often used in practice.