There are two easy ways to find the points on a curve:
1 — use the parametric equations to find x and y over the parameter range [0 <= t <= 1.0]. These equations are shown in the SEG_QUADTO and SEG_CUBICTO field details of the PathIterator api.
2 — use a PathIterator with a flatness appropriate for the curve/parent size (0.01 to 0.001 range ballpark) and iterate along the curve to retrieve the x, y coordinates.
[url=http://forum.java.sun.com/thread.jspa?threadID=724953]This example[/url] shows the basic techniques.