CGAL users discussion list

[Tapadi <>]

If you are still searching for a solution :

- Distance [point , circle] = Distance [point, circle center] - circle
radius

- For the Distance [point, bezier curve], there is no close form as far as I
know. CG algorithms may get a good approximation, but I did not find a web
page talking precisely about point-curve distance queries. Here is the
solution I implemented myself a while ago, not perfect for precision nor for
computation time:

1. Discretize the Bezier curve into a polyline (using De Casteljau
algorithm, or more basically computing the points P(t) for many values of
t).
2. Optional: Store the polyline into a space partition structure (I used a
grid, but one can use a spatial tree, etc).
3. Look for the polyline segment nearest to the query point.
4. Return the distance between the point and the selected segment.

This is a quick-and-dirty solution, but it does the job. I hope it will help
you.

Then, there is *another question* I add to the topic: what CGAL package
should we use for replacing this temporary solution? Thanks in advance for
any hint :o)

Best regards,
Hugo Loi
PhD student at Inria - Maverick team
http://maverick.inria.fr/



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