On 6/30/2013 7:08 AM, Henry Baker wrote:
In 3D, take a pipe (not-necessarily of round cross-section) & bend it to form an 'elbow'.
The interesting (to me) points of the elbow lie on the angle bisector _plane_ for the elbow.
Are there names for the innermost & outermost points on this bisector plane?
(I've been calling them the 'inner' and 'outer' elbow points.)
Now comes the hard part.
Consider a joint formed by _three_ pipes coming together at arbitrary (but fixed) angles.
Is there a name for such an object? I'll call it a '3lbow', after the hacker use of the digit '3' as a reversed letter 'e'; I have no idea how to pronounce '3lbow'.
I think you should call is a Ybow (the "L" is pictographic); then you could pronounce it. Brent Meeker
We can still define 'inner' and 'outer' for a '3lbow'.
The interesting (to me) points now lie on the _line_ going through the point of intersection of the 3 pipes and the _circumcenter_ of the 3 normalized vectors emanating from that point of intersection.
I call this line the 'groin line', with the inner point along this line being the 'groin' point, and the outer point being the 'tip of the elbow' (??). Is there a more standard name for this line? It is also the central line of the right circular cone whose tip is the intersection point of the 3lbow.
The technical reason why I choose the line of circumcenters is that in the limiting case where two of the pipes converge to one another, this circumcenter line will lie on the angle bisector line and hence the 3lbow becomes an 'elbow'.
I'm happy to use pre-existing names for these objects and points, but I wouldn't know where to start to find them.
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