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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 point = ellipsePoint(elli, pos)
%ELLIPSEPOINT Coordinates of a point on an ellipse from parametric equation.
%
% POINT = ellipsePoint(ELLI, POS)
% Computes the coordinates of the point with parameter value POS on the
% ellipse. POS is contained within [0, 2*PI].
%
% Example
% elli = [50 50 40 20 30];
% pts = ellipsePoint(elli, linspace(0, pi, 12));
% figure; drawEllipse(elli, 'b'); hold on;
% axis equal; axis([0 100 0 100]);
% drawPoint(pts, 'bo');
%
% See also
% ellipses2d, drawEllipse, projPointOnEllipse, ellipseToPolygon
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2022-09-09, using Matlab 9.12.0.1884302 (R2022a)
% Copyright 2022-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
% make sure pos is column vector
pos = pos(:);
% pre-compute rotation angles (given in degrees)
theta = elli(:,5);
cot = cosd(theta);
sit = sind(theta);
% compute position of points used to draw current ellipse
a = elli(:,3);
b = elli(:,4);
xt = elli(:,1) + a * cos(pos) * cot - b * sin(pos) * sit;
yt = elli(:,2) + a * cos(pos) * sit + b * sin(pos) * cot;
% concatenate
point = [xt yt];
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