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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 varargout = angleSort3d(pts, varargin)
%ANGLESORT3D Sort 3D coplanar points according to their angles in plane.
%
% PTS2 = angleSort3d(PTS);
% Considers all points are located on the same plane, and sort them
% according to the angle on plane. PTS is a [Nx2] array. Note that the
% result depends on the plane orientation: points can be in reverse order
% compared to expected. The reference plane is computed based on the
% first three points.
%
% PTS2 = angleSort3d(PTS, PTS0);
% Computes angles between each point of PTS and PT0. By default, uses
% centroid of points.
%
% PTS2 = angleSort3d(PTS, PTS0, PTS1);
% Specifies the point which will be used as a start.
%
% [PTS2, I] = angleSort3d(...);
% Also return in I the indices of PTS, such that PTS2 = PTS(I, :);
%
% See also
% points3d, angles3d, angleSort
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-24
% Copyright 2005-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% default values
pt0 = mean(pts, 1);
pt1 = pts(1,:);
if length(varargin)==1
pt0 = varargin{1};
elseif length(varargin)==2
pt0 = varargin{1};
pt1 = varargin{2};
end
% create support plane
plane = createPlane(pts(1:3, :));
% project points onto the plane
pts2d = planePosition(pts, plane);
pt0 = planePosition(pt0, plane);
pt1 = planePosition(pt1, plane);
% compute origin angle
theta0 = atan2(pt1(2)-pt0(2), pt1(1)-pt0(1));
theta0 = mod(theta0 + 2*pi, 2*pi);
% translate to reference point
n = size(pts, 1);
pts2d = pts2d - repmat(pt0, [n 1]);
% compute angles
angle = atan2(pts2d(:,2), pts2d(:,1));
angle = mod(angle - theta0 + 4*pi, 2*pi);
% sort points according to angles
[angle, I] = sort(angle); %#ok<ASGLU>
% format output
if nargout<2
varargout{1} = pts(I, :);
elseif nargout==2
varargout{1} = pts(I, :);
varargout{2} = I;
end
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