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From: hallett@shoreland.uucp (Jeff Hallett x4-6328)
Newsgroups: comp.graphics,sci.math
Subject: Re: Curve normal to two circles
Message-ID: <962@mrsvr.UUCP>
Date: 1 Sep 89 16:20:00 GMT
References: <439@ncis.tis.llnl.gov>
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Reply-To: hallett@shoreland.UUCP (Jeff Hallett x4-6328)
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Organization: GE Medical Systems, Milwaukee,  WI
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In article <439@ncis.tis.llnl.gov> carlson@lance.tis.llnl.gov (John Carlson) writes:
>
>Given:
>	A, B circles in R2 and an two points P & Q, one on
>each circle (P on A, Q on B).
>
>Construct a curve C with endpoints P & Q such that the curve is
>normal to A & B at P & Q.  C only intersects A & B at P & Q.  The
>function describing the curve should be differentiable at all
>points on the curve except P & Q.  C is made up of at most 2
>segments (3 parametric quadratics won't do! :-).
>
>
>Remember, C only intersects A & B at P & Q (Otherwise the
>problem is cake).

The problem needs some more definition, I think.  Of what form should
C be, quadratic, transcendental, etc.?  If we don't determine the
curve format, there are potentially an infinite number of solutions.
Maybe another bound would be to minimize the length of C in R2?

Also, I'll make the assumption that the curve should be right or left
differentiable at P & Q (even though it isn't fully differentiable, by
its termination)


Good problem.  I like it.

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--
                Jeffrey A. Hallett, PET Software Engineering
                    GE Medical Systems, W641, PO Box 414
                            Milwaukee, WI  53201
          (414) 548-5163 : EMAIL -  hallett@positron.gemed.ge.com