supportFunction

SUPPORTFUNCTION Compute support function of a polygon.
 
   H = supportFunction(POLYGON, N)
   uses N points for suport function approximation

   H = supportFunction(POLYGON)
   assume 24 points for approximation

   H = supportFunction(POLYGON, V)
   where V is a vector, uses vector V of angles to compute support
   function.
   
   See also:
   polygons2d, convexification

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 20/12/2004.

0001 function h = supportFunction(polygon, varargin)
0002 %SUPPORTFUNCTION Compute support function of a polygon.
0003 %
0004 %   H = supportFunction(POLYGON, N)
0005 %   uses N points for suport function approximation
0006 %
0007 %   H = supportFunction(POLYGON)
0008 %   assume 24 points for approximation
0009 %
0010 %   H = supportFunction(POLYGON, V)
0011 %   where V is a vector, uses vector V of angles to compute support
0012 %   function.
0013 %
0014 %   See also:
0015 %   polygons2d, convexification
0016 %
0017 %   ---------
0018 %   author : David Legland
0019 %   INRA - TPV URPOI - BIA IMASTE
0020 %   created the 20/12/2004.
0021 %
0022 
0023 N = 24;
0024 u = 0:2*pi/N:2*pi*(1-1/N);
0025     
0026 if length(varargin)==1
0027     var = varargin{1};
0028     if length(var)==1
0029         N = var;
0030         u = 0:2*pi/N:2*pi*(1-1/N);
0031     else
0032         u = var;
0033     end
0034 end
0035 
0036 % ensure u vertical vector
0037 if size(u, 1)==1
0038     u=u';
0039 end
0040 
0041 
0042 h = zeros(size(u));
0043 
0044 for i=1:length(u)
0045     
0046     v = repmat([cos(u(i)) sin(u(i))], [size(polygon, 1), 1]);
0047 
0048     h(i) = max(dot(polygon, v, 2));
0049 end