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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 vect = polygonOuterNormal(poly, iVertex)
%POLYGONOUTERNORMAL Outer normal vector for a given vertex(ices).
%
% NV = polygonOuterNormal(POLY, VIND)
% Where POLY is a polygon and VIND is the index of a vertex, returns the
% outer normal vector of the specified vertex.
% The normal is computed by averaging the tangent vectors of the two
% neighbor edges, i.e. by computing a finite difference of the neighbor
% vertices.
%
% NV = polygonOuterNormal(POLY)
% Returns an array with as many vectors as the number of vertices of the
% input polygon, containing the outer normal of each vertex.
%
%
% Example
% % compute outer normals to an ellipse
% elli = [50 50 40 20 30];
% poly = ellipseToPolygon(elli, 200);
% figure; hold on;
% drawPolygon(poly, 'b'); axis equal; axis([0 100 10 90]);
% inds = 1:10:200; pts = poly(inds, :); drawPoint(pts, 'bo')
% vect = polygonOuterNormal(poly, inds);
% drawVector(pts, vect*10, 'b');
%
% See also
% polygons2d, polygonPoint, polygonNormalAngle
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2017-11-23, using Matlab 8.6.0.267246 (R2015b)
% Copyright 2017-2023 INRA - Cepia Software Platform
% number of vertices
nv = size(poly, 1);
% if indices not specified, compute for all vertices
if nargin == 1
iVertex = 1:nv;
end
% allocate memory
vect = zeros(length(iVertex), 2);
% compute normal vector of each result vertex
for i = 1:length(iVertex)
iNext = mod(iVertex(i), nv) + 1;
iPrev = mod(iVertex(i)-2, nv) + 1;
tangent = (poly(iNext,:) - poly(iPrev,:)) / 2;
vect(i,:) = [tangent(2) -tangent(1)];
end
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