From: steve@hcrlgw (Steven Collins)
Subject: Sphere from 4 points
Organization: Central Research Lab. Hitachi, Ltd.
Lines: 24
Nntp-Posting-Host: hcrlgw

>
>Another method is to first find the center of the circle defined by 2 sets
>of 3 points, and intersecting the normals from there.  This would also define
>the circle center.  However, small numerical imprecisions would make the
>lines not intersect.  Supposedly 3 planes HAVE to intersect in a unique
>point if they are not parallel.
>

Having thought about this, why don't you project the 2 lines onto the 2d
plane formed by the lines.  Do an intersection calculation in the plane in
2D, where you're guaranteed a unique solution (unless they're parallel which
won't happen in this case), and then use parametric distance along the lines
from the circle centres to determine the exact point of interest.  This
bypasses the messy error propogation required to do the calculation in 3d.

Hope I haven't put my foot in it again!

steve
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+---------------------------------------+--------------------------------+
| Steven Collins			| email: steve@crl.hitachi.co.jp |
| Visiting Computer Graphics Researcher	| phone: (0423)-23-1111 	 |
| Hitachi Central Research Lab. Tokyo.	| fax:   (0423)-27-7742		 |
