Hello Keith

>> is there a way to calculate a point midway along the curve?
> private function findPointOnCurve(p1x:Number, p1y:Number, cx:Number,

- this method can return midway along the curve if
bezier curve is symmetrical only.

finding point on curve by time iterator is very different thing than finding
point by distance along the curve. It is difficult calculation using bisection
of Newton algorithm:
http://bezier.googlecode.com/svn/trunk/bezier/src/flash/geom/Bezier.as
look at getTimeByDistance

possible way using Bezier class:

var myBezier:Bezier = new Bezier(.....);
var midwayTime:Number = myBezier.getTimeByDistance(myBezier.length/2);
var midwayPoint:Point = myBezier.getPoint(midwayTime);

also analog of findPointOnCurve is presented in Bezier class as
getPoint method.


good luck!

-- 
iv
http://www.bezier.ru
http://bezier.googlecode.com
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