## Re: [PyX-user] Simpson's rule

 Re: [PyX-user] Simpson's rule From: Ken Starks - 2008-08-12 10:19:15 ```I've only just subscribed to this mailing list, so I expect this thread is dead. Dan Reinholz - 2008-07-17 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. (For the special case where the 'parabola' is actually a straight line, just use the midpoint instead, but anywhere on segment AD will do) ```

 Re: [PyX-user] Simpson's rule From: Ken Starks - 2008-08-12 10:19:15 ```I've only just subscribed to this mailing list, so I expect this thread is dead. Dan Reinholz - 2008-07-17 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. (For the special case where the 'parabola' is actually a straight line, just use the midpoint instead, but anywhere on segment AD will do) ```
 Re: [PyX-user] Simpson's rule From: Ken Starks - 2008-08-12 10:51:08 ```Ken Starks wrote: > I've only just subscribed to this mailing list, so I expect this thread > is dead. > > Dan Reinholz - 2008-07-17 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 one-third and two-thirds 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://moblin-contest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > PyX-user mailing list > PyX-user@... > https://lists.sourceforge.net/lists/listinfo/pyx-user > > > ```