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Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 10 Jul, 2011 22:30:12 Message: 1 of 16 
I have a ellipsoid "defined" at a point E. I have its shape information stored: 
Subject: Shortest distance from point to ellipsoid surface From: ImageAnalyst Date: 10 Jul, 2011 23:03:37 Message: 2 of 16 
Define "massive"  are we talking about tens of millions of voxels 
Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 11 Jul, 2011 00:38:09 Message: 3 of 16 
Thank you for replying, 
Subject: Shortest distance from point to ellipsoid surface From: ImageAnalyst Date: 11 Jul, 2011 01:27:35 Message: 4 of 16 
Robert: 
Subject: Shortest distance from point to ellipsoid surface From: Bruno Luong Date: 11 Jul, 2011 05:52:09 Message: 5 of 16 
"Robert Phillips" <phillir1@my.erau.edu> wrote in message <ivd95k$6h2$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Roger Stafford Date: 11 Jul, 2011 05:56:09 Message: 6 of 16 
"Robert Phillips" <phillir1@my.erau.edu> wrote in message <ivd95k$6h2$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: John D'Errico Date: 11 Jul, 2011 12:09:09 Message: 7 of 16 
"Robert Phillips" <phillir1@my.erau.edu> wrote in message <ivd95k$6h2$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Roger Stafford Date: 11 Jul, 2011 17:18:10 Message: 8 of 16 
"John D'Errico" <woodchips@rochester.rr.com> wrote in message <ivep55$3b$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Bruno Luong Date: 11 Jul, 2011 17:49:09 Message: 9 of 16 
"Roger Stafford" wrote in message <ivfb8h$rmv$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 16 Jul, 2011 23:51:09 Message: 10 of 16 
Thank you all for the overwhelming amount of help! I'll be reading through all of this and your recommended threads and resources. I will report back with my findings and solutions soon. 
Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 22 Sep, 2011 00:45:31 Message: 11 of 16 
I've finally had the time to work more on this. I've gone through stepbystep and obtained the polynomial equation and its seven coefficients (although it seems my coefficients are the negatives of the ones provided by Roger Stafford). I wasn't familiar with how Lagrange multipliers work so it took a bit to absorb it. 
Subject: Shortest distance from point to ellipsoid surface From: Steven_Lord Date: 22 Sep, 2011 13:49:25 Message: 12 of 16 

Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 24 Sep, 2011 20:02:14 Message: 13 of 16 
Thank you for the help; I ended up defining the coefficients as calculated numeric values and then using a forloop to take ROOTS for each point (I'm calculating minimum distances from points in a Nx3 matrix to the ellipsoid surface). 
Subject: Shortest distance from point to ellipsoid surface From: Bruno Luong Date: 24 Sep, 2011 20:29:11 Message: 14 of 16 
"Robert Phillips" <roll24dive7@gmail.com> wrote in message <j5ld06$blu$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Robert Phillips Date: 25 Sep, 2011 00:30:29 Message: 15 of 16 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <j5lein$gmf$1@newscl01ah.mathworks.com>... 
Subject: Shortest distance from point to ellipsoid surface From: Sebahattin bekta? Date: 16 Apr, 2014 19:27:12 Message: 16 of 16 
Hello 
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