# how can one calculate the minimum and maximum distance between two given circular arcs?

how can one calculate the minimum and maximum distance between two given circular arcs?

I know everything of each arc: startangle, endangle, center, radius of arc. The only thing I don't know how to calculate is the min and max distance.

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you can set it up as a variational problem –  yoyo Dec 29 '11 at 19:04
I think it would be better if we knew the equations of the arcs. However if they have a point of intersection, the of course the minimum distance between them will be zero. –  smanoos Dec 29 '11 at 19:06
Are the arcs coplanar? –  Mark Bennet Dec 29 '11 at 19:18
@MarkBennet yes. –  Mig Dec 29 '11 at 19:34

There are four cases to consider:

1) Endpoints of both arcs

2) An endpoint of one and an interior point of the other, which is on the line through that endpoint and the centre of the other arc.

3) Interior points of both arcs, which are on the line through the centres of the two arcs.

4) Intersections of the two arcs (thanks for pointing that out, Lopsy)

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"4) Intersections of the two arcs" too, surely? –  Lopsy Dec 29 '11 at 20:14
@Lopsy - that looks right But other than that Robert gave the answer I was just about to post. –  Mark Bennet Dec 29 '11 at 20:29
Thanks @robert-israel –  Mig Jan 2 '12 at 20:06