Subject:
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Re: Tangent between two circles in 3D space?
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Newsgroups:
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lugnet.cad.dev
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Date:
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Tue, 21 Jan 2003 16:45:54 GMT
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Viewed:
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875 times
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In lugnet.cad.dev, Kevin Clague writes:
> In lugnet.cad.dev, Steven Combs writes:
> > In lugnet.cad.dev, Kevin Clague writes:
> > > Anyone know how to find out the tangent between two cicles in 3D space?
> >
> > Wouldn't they have to be on the same plane in order to find the tangency? Or
> > did you mean the tangency of two spheres?
>
> With two circles in the same plane you can have four possible tangent lines.
> LSynthcp uses this to calculate straight line segments of rubber bands
> around pulleys.
>
> In 3D space you can have circles that are tangent along one line. Imagine a
> vertical bar that has a circle attached tangentially, but can turn around
> the bar, and slide up and down the bar. Attach another circle to the bar
> with the same capabilities. You can hold one circle fixed, and place the
> other circle an infinite number of places and orientations and still be
> tangent to the line.
>
> So, given two pulleys in a rubber band synthesis specification, I need to be
> able to tell if there is a common tangent between the two of them in 3D
> space, and if so, what the parameters for the line are. This will allow me
> to synthesize non-planar rubber bands.
It sounds like you want the intersection point of the 2nd circle with
the plane of the first circle. I guess that should be exactly one point
unless they're in the same plane. However, I don't see how the rubber
band gets back to the first circle without violating your rules. Is
there another pulley/circle you're not telling us about?
Don
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Message has 2 Replies:
 | | Re: Tangent between two circles in 3D space?
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| Don, I'm assuming four pulleys in this case. Two are parallel to each other where the rubber band bends to be non-planar, and two others that pull the band around the two parallel pulleys. Kevin (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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Message is in Reply To:
| | Re: Tangent between two circles in 3D space?
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| (...) With two circles in the same plane you can have four possible tangent lines. LSynthcp uses this to calculate straight line segments of rubber bands around pulleys. In 3D space you can have circles that are tangent along one line. Imagine a (...) (22 years ago, 21-Jan-03, to lugnet.cad.dev)
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