1## Copyright (C) 2021 David Legland
2## All rights reserved.
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27
28function sphere = createSphere(varargin)
29%CREATESPHERE Create a sphere containing 4 points.
30%
31%   s = createSphere(p1, p2, p3, p4);
32%   return in s the sphere common to the 4 pointsp1, p2, p3 and p4.
33%
34%   Ref: P. Bourke
35%   http://astronomy.swin.edu.au/~pbourke/geometry/spherefrom4/
36%
37%   See also
38%   spheres, circles3d
39%
40%   ---------
41%   author : David Legland
42%   INRA - TPV URPOI - BIA IMASTE
43%   created the 22/03/2005.
44%
45
46
47if length(varargin)==4
48    pts = [varargin{1};varargin{2};varargin{3};varargin{4}];
49elseif length(varargin)==1
50    pts = varargin{1};
51else
52    error('wrong number of arguments in createSphere');
53end
54
55
56m1 = det([pts ones(4,1)]);
57s2 = sum(pts.*pts, 2);
58m2 = det([s2 pts(:,2) pts(:,3) ones(4,1)]);
59m3 = det([pts(:,1) s2 pts(:,3) ones(4,1)]);
60m4 = det([pts(:,1) pts(:,2) s2 ones(4,1)]);
61
62m5 = det([s2 pts]);
63
64x0 = m2*.5/m1;
65y0 = m3*.5/m1;
66z0 = m4*.5/m1;
67r  = sqrt(x0*x0 + y0*y0 + z0*z0 - m5/m1);
68
69sphere = [x0 y0 z0 r];
70