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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 perim = ellipsePerimeter(ellipse, varargin)
%ELLIPSEPERIMETER Perimeter of an ellipse.
%
% P = ellipsePerimeter(ELLI)
% Computes the perimeter of an ellipse, using numerical integration.
% ELLI is an ellipse, given using one of the following formats:
% * a 1-by-5 row vector containing coordinates of center, length of
% semi-axes, and orientation in degrees
% * a 1-by-2 row vector containing only the lengths of the semi-axes.
% The result
%
% P = ellipsePerimeter(ELLI, TOL)
% Specify the relative tolerance for numerical integration.
%
%
% Example
% P = ellipsePerimeter([30 40 30 10 15])
% P =
% 133.6489
%
% See also
% ellipses2d, ellipseArea, ellipseToPolygon, drawEllipse
%
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-02-20, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
%% Parse input argument
if size(ellipse, 2) == 5
ra = ellipse(:, 3);
rb = ellipse(:, 4);
elseif size(ellipse, 2) == 2
ra = ellipse(:, 1);
rb = ellipse(:, 2);
elseif size(ellipse, 2) == 1
ra = ellipse;
rb = varargin{1};
varargin(1) = [];
end
% relative tolerance
tol = 1e-10;
if ~isempty(varargin)
tol = varargin{1};
end
%% Numerical integration
n = length(ra);
perim = zeros(n, 1);
for i = 1:n
% function to integrate
f = @(t) sqrt(ra(i) .^ 2 .* cos(t) .^ 2 + rb(i) .^ 2 .* sin(t) .^ 2) ;
% absolute tolerance from relative tolerance
eps = tol * max(ra(i), rb(i));
% integrate on first quadrant
if verLessThan('matlab', '7.14')
perim(i) = 4 * quad(f, 0, pi/2, eps); %#ok<DQUAD>
else
perim(i) = 4 * integral(f, 0, pi/2, 'AbsTol', eps);
end
end
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