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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 circle = createDirectedCircle(varargin)
%CREATEDIRECTEDCIRCLE Create a directed circle.
%
% C = createDirectedCircle(P1, P2, P3);
% Creates a circle going through the given points.
% C is a 1*4 array of the form: [XC YC R INV].
% The last parameter is set to 1 if the points are located in clockwise
% order on the circle.
%
% C = createDirectedCircle(P1, P2);
% Creates the circle whith center P1 and passing throuh the point P2.
%
% Works also when input are point arrays the same size, in this case the
% result has as many lines as the point arrays.
%
% See also
% circles2d, createCircle
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-01-12
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
if nargin == 2
% inputs are the center and a point on the circle
p1 = varargin{1};
p2 = varargin{2};
x0 = (p1(:,1) + p2(:,1))/2;
y0 = (p1(:,2) + p2(:,2))/2;
r = hypot((p2(:,1)-p1(:,1)), (p2(:,2)-p1(:,2)))/2;
% circle is direct by default
d = 0;
elseif nargin == 3
% inputs are three points on the circle
p1 = varargin{1};
p2 = varargin{2};
p3 = varargin{3};
% compute circle center
line1 = medianLine(p1, p2);
line2 = medianLine(p1, p3);
center = intersectLines(line1, line2);
x0 = center(:, 1);
y0 = center(:, 2);
% circle radius
r = hypot((p1(:,1)-x0), (p1(:,2)-y0));
% compute circle orientation
angle = angle3Points(p1, center, p2) + angle3Points(p2, center, p3);
d = angle>2*pi;
end
circle = [x0 y0 r d];
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