From: Ken Starks <ken@la...>  20080812 10:51:08

Ken Starks wrote: > I've only just subscribed to this mailing list, so I expect this thread > is dead. > > Dan Reinholz <xaenn@...>  20080717 18:07 wrote: > > > As long as I'm on the subject, could anybody help me > > actually figure out how to shade the regions required > > for Simpson's rule? In each region I will want to > > connect three straight lines, with a parabola on top, > > and then fill the total area with a solid color. > > > Hi Dan, > > An ordinary cubic Bezier includes parabolas as a special case. > Unlike f(x) = quadratic, their axis need not be vertical. > > You don't need four points, you just need three. it doesn't much > matter but you may as well merge the two control points. > > Instead of using Bezier segment A .. B .. C .. D > > Use A .. P .. P .. D > > To get your parabola through A and B, set point P to > the point where the tangents at A and B intersect. > > I meant : "To get your parabola through A and D, set point P ... " > (For the special case where the 'parabola' is actually a straight line, > just use the midpoint instead, but anywhere on segment AD will do) > > When a straight segment AD is replaced by a cubic Bezier, most software actually chooses A .. B .. C .. D where B and C are onethird and twothirds of the way along AD. >  > This SF.Net email is sponsored by the Moblin Your Move Developer's challenge > Build the coolest Linux based applications with Moblin SDK & win great prizes > Grand prize is a trip for two to an Open Source event anywhere in the world > http://moblincontest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > PyXuser mailing list > PyXuser@... > https://lists.sourceforge.net/lists/listinfo/pyxuser > > > 