There are two fairly straightforward ways:
1 — use a FlatteningPathIterator with a suitably small flatness, say 0.01 to start, to get the coordinates along the curve. You can get a PathIterator from both the QuadCurve2D and CubicCurve2D classes.
2 — use the parametric form of the curve to get (x,y) for [0<= t <= 1.0]
These equations are given in the Field Detail section of the PathIterator interface for the SEG_QUADTO and SEG_CUBICTO fields.
I would try to get points closer together than the distance increment along the curve that you want for your animation. Then you can move along the curve and collect points that are close to your desired distance increment.
In the example here it looks like the parametric form is more amenable to this.
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