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

2010-09-01 Thread David Bevan
-Original Message- From: freetype-devel-bounces+david.bevan=pb@nongnu.org [mailto:freetype-devel-bounces+david.bevan=pb@nongnu.org] On Behalf Of Graham Asher Sent: 29 August 2010 20:01 To: James Cloos Cc: freetype-devel Subject: Re: [ft-devel] Re: preliminary analysis

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

2010-08-29 Thread 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

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

2010-08-29 Thread James Cloos
GA == Graham Asher graham.as...@btinternet.com 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

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

2010-08-29 Thread Graham Asher
It can happen, though. In fact I now don't think it can happen. If there are any good mathematicians out there (better than me at this, which sets quite a low bar), please confirm that no point on a cubic spline curve with both control points on the same side of the straight line from start to