10.1.5.5 Subdivision

When Limn cannot fit a bitmap curve within the `error-threshold' (see the previous section), it must subdivide the curve into two pieces and fit each independently, applying the fitting algorithm recursively.

As a strategy to improve the fit, subdivision is inferior to reparameterization, because it increases the number of splines in the character definition. This increases the memory required to store the character, and also the time to render it. However, subdivision is unavoidable in some circumstances: for example, the outlines on an `o' cannot be fit by a single spline.

For the initial guess of the point at which to subdivide, Limn chooses the point of worst error--the point where the fitted spline is farthest from the bitmap curve. Although this is usually a good choice, minimizing the chance that further subdivision will be necessary, occasionally it is not the best: in order to preserve straight lines, it is better to subdivide at the point where a straight becomes a curve if that point is close to the worst point. For example, this happens where a serif joins the stem.

Limn has three options to control this process:

1. `-subdivide-search percent' specifies how far away from the worst point to search for a better subdivision point, as a percentage of the total number of points in the curve; the default is 10. If you find Limn missing a join as a subdivision point, resulting in a straight line becoming a curve, you probably need to increase this.

2. `-subdivide-threshold real': if the distance between a point p (within the search range) and a straight line is less than this, subdivide at p; default is .03 pixels.

3. `-subdivide-surround unsigned': when calculating the linearity of the curve surrounding a potential subdivision, use this many points; default is 4.

Because fitting a shorter curve is easier, this process will always terminate. (Eventually the curve will be short enough to fit with a straight line (see section 10.1.5 Fitting the bitmap curve), if nothing else.)