Sphere Center of four point

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  02 February 2009
Sphere Center of four point

I have 4 particles randomly.

I wantto get a point that distance are all same with these each of four point .

by another way to describe :
I have 4 points.And I need a sphere center coordinates that these 4 points are on these sphere surface.(thus each these 4 point to center point distance are all same)

is there a fast way to do this ?
or I have to code hundreds of codes
 
  02 February 2009
If you have four points generated randomly there's a chance (even bigger chance in 2d) that it's impossible to draw a 'circle'/'sphere' through all these points.. Like when the points are in 'one' line. Or when three points are in one line..

This is important to remember and understand.
 
  02 February 2009
if three point of them, position in one line, you can not get result in theory ,
I would rather do it like this
create a sphere,
create four point on sphere surface,then rand them position on surface
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  02 February 2009
and my problem starts here.
because there is no sphere.
there is 4 points (randomly) waits me to built a sphere by using all of them.
(a point as a sphere center that each distance of these 4 points must be same)
 
  02 February 2009
got my solution via this page....sorry unable to share. But all you have to do is form the cofactor matrices and solve for their determinant.......

http://local.wasp.uwa.edu.au/~pbour...ry/spherefrom4/

Last edited by tbaypaul : 02 February 2009 at 05:18 PM.
 
  02 February 2009
useful link .thanks
 
  02 February 2009
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