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

0001 function theta = polygonNormalAngle(poly, inds)
0002 % Normal angle at each vertex of a polygon.
0003 %
0004 %   THETA = polygonNormalAngle(POLY);
0005 %   where POLY is a N-by-2 array representing vertex coordinates, computes
0006 %   the normal angle at each vertex of the polygon. THETA is a N-by-1 array
0007 %   containing numeric values between -PI and +PI. The result depends on
0008 %   the orientation of the polygon (counter-clockwise or clockwise).
0009 %
0010 %   THETA = polygonNormalAngle(POLY, IND);
0011 %   Computes the normal angle for each vertex specified by IND. If IND is a
0012 %   vector of vertex indices.
0013 %
0014 %
0015 %   Example
0016 %   % Normal angles at vertices of an isosceles right triangle are pi/2 at
0017 %   % right angle-vertex and 3*pi/4 for the two remaining vertices.
0018 %     poly = [0 0 ; 1 0 ; 0 1];
0019 %     polygonNormalAngle(poly)
0020 %     ans =
0021 %         1.5708
0022 %         2.3562
0023 %         2.3562
0024 %
0025 %   % Compute normal angles for a slightly more complicated polygon
0026 %     poly = [0 0;0 1;-1 1;0 -1;1 0];
0027 %     % compute normal angle at each vertex
0028 %     theta = polygonNormalAngle(poly);
0029 %     % sum of all normal angle of a non-intersecting polygon equals 2*pi
0030 %     % (can be -2*pi if polygon is oriented clockwise)
0031 %     sum(theta)
0032 %     ans =
0033 %         6.2832
0034 %
0035 %   See also:
0036 %     polygons2d, polygonOuterNormal, normalizeAngle
0037 %
0038 
0039 % ------
0040 % Author: David Legland
0041 % e-mail: david.legland@inra.fr
0042 % Created: 2005-11-30
0043 % Copyright 2005 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).
0044 
0045 % number of polygon  vertices
0046 np = size(poly, 1);
0047 
0048 if nargin == 1
0049     inds = 1:np;
0050 end
0051 
0052 % number of angles to compute
0053 nv = length(inds);
0054 
0055 theta = zeros(nv, 1);
0056 
0057 for i = 1:nv
0058     % current vertex
0059     curr = poly(inds(i), :);
0060     
0061     % previous and next vertices
0062     prev = poly(mod(inds(i)-2, np)+1, :);
0063     next = poly(mod(inds(i), np)+1, :);
0064     
0065     theta(i) = angle3Points(prev, curr, next) - pi;
0066 end