polygon3dNormalAngle

POLYGON3DNORMALANGLE Normal angle at a vertex of the 3D polygon.

   THETA = polygon3DNormalAngle(POLYGON, IND)
   where POLYGON is a set of points, and IND is index of a point in
   polygon. The function compute the angle of the normal cone localized at
   this vertex.
   If IND is a vector of indices, normal angle is computed for each vertex
   specified by IND.

   Example
   % create an equilateral triangle in space
   poly3d = [1 1 0;-1 0 1;0 -1 -1];
   % compute each normal angle
   theta = polygon3dNormalAngle(poly3d, 1:size(poly3d, 1));
   % sum of normal angles must be equal to 2*PI for simple polygons
   sum(theta)

   IMPORTANT NOTE: works only for convex angles ! ! ! !

   See also
   polygons3d, faceNormalAngle

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2005-11-30
 Copyright 2005 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).

0001 function theta = polygon3dNormalAngle(points, ind)
0002 %POLYGON3DNORMALANGLE Normal angle at a vertex of the 3D polygon.
0003 %
0004 %   THETA = polygon3DNormalAngle(POLYGON, IND)
0005 %   where POLYGON is a set of points, and IND is index of a point in
0006 %   polygon. The function compute the angle of the normal cone localized at
0007 %   this vertex.
0008 %   If IND is a vector of indices, normal angle is computed for each vertex
0009 %   specified by IND.
0010 %
0011 %   Example
0012 %   % create an equilateral triangle in space
0013 %   poly3d = [1 1 0;-1 0 1;0 -1 -1];
0014 %   % compute each normal angle
0015 %   theta = polygon3dNormalAngle(poly3d, 1:size(poly3d, 1));
0016 %   % sum of normal angles must be equal to 2*PI for simple polygons
0017 %   sum(theta)
0018 %
0019 %   IMPORTANT NOTE: works only for convex angles ! ! ! !
0020 %
0021 %   See also
0022 %   polygons3d, faceNormalAngle
0023 %
0024 % ------
0025 % Author: David Legland
0026 % e-mail: david.legland@grignon.inra.fr
0027 % Created: 2005-11-30
0028 % Copyright 2005 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).
0029 
0030 
0031 % number of points
0032 np = size(points, 1);
0033 
0034 % number of angles to compute
0035 nv = length(ind);
0036 
0037 theta = zeros(nv, 1);
0038 
0039 for i=1:nv
0040     p0 = points(ind(i), :);
0041     
0042     if ind(i)==1
0043         p1 = points(np, :);
0044     else
0045         p1 = points(ind(i)-1, :);
0046     end
0047     
0048     if ind(i)==np
0049         p2 = points(1, :);
0050     else
0051         p2 = points(ind(i)+1, :);
0052     end
0053     
0054     theta(i) = pi - anglePoints3d(p1, p0, p2);
0055 end