/usr/share/octave/packages/geometry-1.7.0/geom2d/createDirectedCircle.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## 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
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## 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,
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{circle} = } createDirectedCircle (@var{p1}, @var{p2}, @var{p3})
## @deftypefnx {Function File} {@var{circle} = } createDirectedCircle (@var{p1}, @var{p2})
## Create a circle from 2 or 3 points.
##
## Creates the circle passing through the 3 given points.
## C is a 1x4 array of the form: [XC YX R INV].
##
## When two points are given, creates the circle whith center @var{p1} and passing
## throuh the point @var{p2}.
##
## Works also when input are point arrays the same size, in this case the
## result has as many lines as the point arrays.
##
## Example
##
##
## @seealso{circles2d, createCircle}
## @end deftypefn
function circle = createDirectedCircle(varargin)
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];
endfunction
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