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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function sphere = createSphere(varargin)
%CREATESPHERE Create a sphere containing 4 points.
%
% s = createSphere(p1, p2, p3, p4);
% return in s the sphere common to the 4 pointsp1, p2, p3 and p4.
%
% Ref: P. Bourke
% http://astronomy.swin.edu.au/~pbourke/geometry/spherefrom4/
%
% See also
% spheres, circles3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-03-22
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
if length(varargin)==4
pts = [varargin{1};varargin{2};varargin{3};varargin{4}];
elseif length(varargin)==1
pts = varargin{1};
else
error('wrong number of arguments in createSphere');
end
m1 = det([pts ones(4,1)]);
s2 = sum(pts.*pts, 2);
m2 = det([s2 pts(:,2) pts(:,3) ones(4,1)]);
m3 = det([pts(:,1) s2 pts(:,3) ones(4,1)]);
m4 = det([pts(:,1) pts(:,2) s2 ones(4,1)]);
m5 = det([s2 pts]);
x0 = m2*.5/m1;
y0 = m3*.5/m1;
z0 = m4*.5/m1;
r = sqrt(x0*x0 + y0*y0 + z0*z0 - m5/m1);
sphere = [x0 y0 z0 r];
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