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If this has been covered before then mea culpa, but I have searched the
links collection and the internet at large to no avail.
Does anyone possess a macro for calculating the points defining the
shortest path between two circles (not discs, circles) given the normal,
centre and radius of each circle, or some algorithm/formula from which
such a macro may be easily derived?
I am led to believe that the calculations involved in solving this
problem are reasonably difficult, so don't knock yourselves out trying
to work out a solution for me, unless you enjoy that kind of thing :?)
I'm really just hoping that someone happens to have the appropriate
information just lying around.
Thanks, Ed.
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To get the vector for spheres:
#declare centerA=<10,5.0,-5.50>;
#declare radiusA=3.1415;
#declare centerB=<1.0,-45.0,15.50>;
#declare radiusB=0.1415;
#declare 1stpoint= centerA+ radiusA*vnormalize(centerB-centerA);
#declare 2ndpoint= centerB+ radiusB*vnormalize(centerA-centerB);
Then the vector in question is between 1stpoint and 2ndpoint.
A treatment for "circles" is the same as that for spheres with coplanar
centers.
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Greg M. Johnson wrote:
> To get the vector for spheres:
>
> #declare centerA=<10,5.0,-5.50>;
> #declare radiusA=3.1415;
> #declare centerB=<1.0,-45.0,15.50>;
> #declare radiusB=0.1415;
>
> #declare 1stpoint= centerA+ radiusA*vnormalize(centerB-centerA);
> #declare 2ndpoint= centerB+ radiusB*vnormalize(centerA-centerB);
>
> Then the vector in question is between 1stpoint and 2ndpoint.
> A treatment for "circles" is the same as that for spheres with coplanar
> centers.
Thanks, but my purpose requires a solution for pairs of circles with any
orientation and position relative to one another, not just coplanar circles.
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To find the closest points on any pair of circles, simply draw a line from
center to center. Then locate the points on each circle that the line passes
through.
Cheers!
Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip
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On Tue, 25 Mar 2003 08:47:08 -0500, "Greg M. Johnson" <gregj:-)565### [at] aol com>
wrote:
> To get the vector for spheres:
>
> #declare centerA=<10,5.0,-5.50>;
> #declare radiusA=3.1415;
> #declare centerB=<1.0,-45.0,15.50>;
> #declare radiusB=0.1415;
>
> #declare 1stpoint= centerA+ radiusA*vnormalize(centerB-centerA);
> #declare 2ndpoint= centerB+ radiusB*vnormalize(centerA-centerB);
>
> Then the vector in question is between 1stpoint and 2ndpoint.
No. Being in 2D consider circle located at <0,0> with radius 2 and circle
located at <3,0> with the same radius 2. Closest points between circles are
located in intersections which are not between centers.
ABX
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Sir Charles W. Shults III wrote:
> To find the closest points on any pair of circles, simply draw a line from
> center to center. Then locate the points on each circle that the line passes
> through.
This only works when both your circles are sitting on the same plane,
not when they may take any orientation in 3D space.
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ABX wrote:
> No. Being in 2D consider circle located at <0,0> with radius 2 and circle
> located at <3,0> with the same radius 2. Closest points between circles are
> located in intersections which are not between centers.
>
> ABX
Quite so, and furthermore my circles are not in 2D space, they are in 3D
space. However I'm happy enough not to consider cases where they
intersect one another.
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On Wed, 26 Mar 2003 01:14:02 +1100, Edward Coffey <eco### [at] alphalinkcomau>
wrote:
> This only works when both your circles are sitting on the same plane,
> not when they may take any orientation in 3D space.
You have to define distance as function and then find where it has minimum.
http://mathworld.wolfram.com/Minimum.html
ABX
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Edward Coffey wrote:
...
> Does anyone possess a macro for calculating the points defining the
> shortest path between two circles (not discs, circles)
...
Sorry, I should have been more clear - when I specified that I was
dealing with circles not discs I did not mean to imply that I was
working in a 2D space, only that the path had to connect to the
circumference, not to any point within a disc.
My circles exist in 3D space and may take any position or orientation
relative to one another.
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ABX wrote:
...
> You have to define distance as function and then find where it has minimum.
...
Yes, but as I stated in my original post, the mathematics of this is
quite complex, it's not as though you're finding the minimum of a
quadratic equation with one variable. Certainly the mathematics of it is
quite beyond my abilities, which is why I haven't asked anyone to solve
it, simply that if they happen to have access to a solution (or if
they're math mad and really want to create their own solution) to post
it here.
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