[ft-devel] Re: preliminary analysis of the problem with cubic spline optimisation

[Graham Asher]

Correction: it's not monotonicity that matters, but having the two 
control points on different sides of the straight line.

Graham Asher wrote:
> The aim is to draw a straight line between the start end end of a 
> cubic spline, instead of rendering the curve correctly, if the curve 
> deviates by less than a certain value from the straight line. The code 
> in gray_render_cubic in ftgrays.c checks only the midpoint of the 
> curve. However, this is not necessarily the furthest point from the 
> straight line. If the sequence start, control1, control2, end is not 
> monotonic in one of the dimensions x, y, an s-shaped curve is produced 
> with points further from the line than the midpoint, which may even 
> lie on the line. This situation occurs in 's' for the sample font.
>
> With this information I can easily produce a fix, simply by testing 
> for non-monotonicity and disabling the optimisation in such 
> circumstances, but I shall see if I can up with something slightly 
> better.
>
> Graham