Re: [PyX-user] Simpson's rule

[Ken S. <ke...@la...>]

I've only just subscribed to this mailing list, so I expect this thread 
is dead.

Dan Reinholz <xaenn@ya...> - 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)