There are mathematical techniques for determing such points, but they require access to the mathematical definition of the curve involved. Qt doesn't make this information available, and doesn't provide such a function as part of QPainterPath.
If the paths involved are always simple (circles, for instance, or straight line segments) you should be able to come up with a solution independently. If the curve is arbitrary, however, you are probably out of luck short of a brute-force approach of some sort.
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