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

[Graham Asher]

No, in nearly all cases the midpoint is the point on the curve furthest 
from the straight line when both control points are on the same side. It 
can happen, though. I'm now working on a fix depending on finding how 
far the furthest control point is from the straight line. No point on 
the curve can be further from the straight line than both control points.

Graham

James Cloos wrote:
> > > > > > "GA" == Graham Asher <address@hidden> writes:
> > > > > >             
>
> GA> Correction: it's not monotonicity that matters, but having the two
> GA> control points on different sides of the straight line.
>
> Wouldn't the midpoint also fail to be the furthest point from the line
> whenever the two off-curve control points are on the same side of the
> midpoint?
>
> -JimC
>