## RE: [Algorithms] Bounding cones.

 RE: [Algorithms] Bounding cones. From: Johnson, James - 2004-01-28 01:33:14 You're correct. I should have tested the obvious first. James -----Original Message----- From: gdalgorithms-list-admin@... [mailto:gdalgorithms-list-admin@...] On Behalf Of Nick Carter Sent: Tuesday, January 27, 2004 4:45 PM To: 'gdalgorithms-list@...' Subject: RE: [Algorithms] Bounding cones. I don't think that this iterative technique will always generate the smallest cone -- it doesn't seem to work in the case of 2D circles. Consider three small circles of equal radius whose centers are mutually equidistant (i.e., in the pattern of an equilateral triangle). Then the minimum bounding circle of any two of the small circles will not be fully contained in the minimum bounding circle of all three of the small circles. So there's no way to "build up" a minimum bounding circle in the iterative way that James suggests. This counterexample is easily extended from circles to cones: consider three cones, of small theta, whose centerlines, pairwise, are at equal angles to one another. I'm very curious about bounds on optimality of like iterative techniques, in either the 2D-circle or 3D-cone (which is still 2 dof) cases. Does anyone know? - nick carter ---------------------------------------------------- Vivendi Universal Games- <>:=0D The information transmitted is intended only for the=0D person or entity to which it is addressed and may=0D contain confidential and/or privileged material of=0D Vivendi Universal Games which is for the exclusive=0D use of the individual designated above as the=0D recipient. Any review, retransmission, dissemination=0D or other use of, or taking of any action in reliance=0D upon, this information by persons or entities other=0D than the intended recipient is prohibited. If you=0D received this in error, please contact immediately=0D the sender by returning e-mail and delete the=0D material from any computer. If you are not the=0D specified recipient, you are hereby notified that=0D all disclosure, reproduction, distribution or action taken on the basis of this message is prohibited.