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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 elli = createEllipse(type, varargin)
%CREATEELLIPSE Create an ellipse, from various input types.
%
% ELLI = createEllipse('CartesianCoefficients', COEFFS)
% ELLI = createEllipse(COEFFS)
% Where COEFFS are the cartesian coefficients of the ellipse:
% COEFFS = [A B C D E F]
% such that the points on the ellipse follow:
% A*X^2 + B*X*Y + C*Y^2 + D*X + E*Y + F = 0
%
%
% Example
% elli = [30 20 40 20 30];
% coeffs = ellipseCartesianCoefficients(elli)
% elli2 = createEllipse(coeffs)
% elli2 =
% 30.0000 20.0000 40.0000 20.0000 30.0000
%
%
% References
% https://en.wikipedia.org/wiki/Ellipse#Standard_parametric_representation
%
% See also
% ellipses2d, equivalentEllipse, fitEllipse,
% ellipseCartesianCoefficients
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2022-09-05, using Matlab 9.12.0.1884302 (R2022a)
% Copyright 2022-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
if nargin == 1 && isnumeric(type)
varargin = {type};
type = 'CartesianCoefficients';
end
if strcmpi(type, 'CartesianCoefficients')
% retrieve coefficients
coeffs = varargin{1};
if ~isnumeric(coeffs) || any(size(coeffs) ~= [1 6])
error('Conversion from cartesian coefficients expects a 1-by-6 numeric array');
end
% call coefficients with their usual names
A = coeffs(1); B = coeffs(2); C = coeffs(3);
D = coeffs(4); E = coeffs(5); F = coeffs(6);
% retrieve center
delta = B * B - 4 * A * C;
xc = (2 * C * D - B * E) / delta;
yc = (2 * A * E - B * D) / delta;
% find orientation
theta = 0.5 * atan(B / (A - C));
% retrieve length of semi-axes
common = 2 * (A * E^2 + C * D^2 - B * D * E + delta * F);
root = sqrt((A - C)^2 + B^2);
a1 = -sqrt(common * ((A + C) + root)) / delta;
a2 = -sqrt(common * ((A + C) - root)) / delta;
elli = [xc yc a1 a2 rad2deg(theta)];
else
error('Unknown representation type: ' + type);
end
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