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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 theta = polygonNormalAngle(poly, inds)
%POLYGONNORMALANGLE Normal angle at each vertex of a polygon.
%
% THETA = polygonNormalAngle(POLY);
% where POLY is a N-by-2 array representing vertex coordinates, computes
% the normal angle at each vertex of the polygon. THETA is a N-by-1 array
% containing numeric values between -PI and +PI. The result depends on
% the orientation of the polygon (counter-clockwise or clockwise).
%
% THETA = polygonNormalAngle(POLY, IND);
% Computes the normal angle for each vertex specified by IND. If IND is a
% vector of vertex indices.
%
%
% Example
% % Normal angles at vertices of an isosceles right triangle are pi/2 at
% % right angle-vertex and 3*pi/4 for the two remaining vertices.
% poly = [0 0 ; 1 0 ; 0 1];
% polygonNormalAngle(poly)
% ans =
% 1.5708
% 2.3562
% 2.3562
%
% % Compute normal angles for a slightly more complicated polygon
% poly = [0 0;0 1;-1 1;0 -1;1 0];
% % compute normal angle at each vertex
% theta = polygonNormalAngle(poly);
% % sum of all normal angle of a non-intersecting polygon equals 2*pi
% % (can be -2*pi if polygon is oriented clockwise)
% sum(theta)
% ans =
% 6.2832
%
% See also
% polygons2d, polygonOuterNormal, normalizeAngle
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-30
% Copyright 2005-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% number of polygon vertices
np = size(poly, 1);
if nargin == 1
inds = 1:np;
end
% number of angles to compute
nv = length(inds);
theta = zeros(nv, 1);
for i = 1:nv
% current vertex
curr = poly(inds(i), :);
% previous and next vertices
prev = poly(mod(inds(i)-2, np)+1, :);
next = poly(mod(inds(i), np)+1, :);
theta(i) = angle3Points(prev, curr, next) - pi;
end
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