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

0001 function vect = polygonOuterNormal(poly, iVertex)
0002 % Outer normal vector for a given vertex(ices).
0003 %
0004 %   NV = polygonOuterNormal(POLY, VIND)
0005 %   Where POLY is a polygon and VIND is the index of a vertex, returns the
0006 %   outer normal vector of the specified vertex.
0007 %   The normal is computed by averaging the tangent vectors of the two
0008 %   neighbor edges, i.e. by computing a finite difference of the neighbor
0009 %   vertices.
0010 %
0011 %   NV = polygonOuterNormal(POLY)
0012 %   Returns an array with as many vectors as the number of vertices of the
0013 %   input polygon, containing the outer normal of each vertex.
0014 %
0015 %
0016 %   Example
0017 %     % compute outer normals to an ellipse
0018 %     elli = [50 50 40 20 30];
0019 %     poly = ellipseToPolygon(elli, 200);
0020 %     figure; hold on;
0021 %     drawPolygon(poly, 'b'); axis equal; axis([0 100 10 90]);
0022 %     inds = 1:10:200; pts = poly(inds, :); drawPoint(pts, 'bo')
0023 %     vect = polygonOuterNormal(poly, inds);
0024 %     drawVector(pts, vect*10, 'b');
0025 %
0026 %   See also
0027 %     polygons2d, polygonPoint, polygonNormalAngle
0028 %
0029  
0030 % ------
0031 % Author: David Legland
0032 % e-mail: david.legland@inrae.fr
0033 % Created: 2017-11-23,    using Matlab 8.6.0.267246 (R2015b)
0034 % Copyright 2017 INRA - Cepia Software Platform.
0035 
0036 % number of vertices
0037 nv = size(poly, 1);
0038 
0039 % if indices not specified, compute for all vertices
0040 if nargin == 1
0041     iVertex = 1:nv;
0042 end
0043 
0044 % allocate memory
0045 vect = zeros(length(iVertex), 2);
0046 
0047 % compute normal vector of each result vertex
0048 for i = 1:length(iVertex)
0049     iNext = mod(iVertex(i), nv) + 1;
0050     iPrev = mod(iVertex(i)-2, nv) + 1;
0051     tangent = (poly(iNext,:) - poly(iPrev,:)) / 2;
0052     vect(i,:) = [tangent(2) -tangent(1)];
0053 end