triangleArea

TRIANGLEAREA Signed area of a triangle.

   AREA = triangleArea(P1, P2, P3)
   Computes area of the triangle whose vertices are given by P1, P2 and
   P3. Each vertex is a 1-by-2 row vector. 

   AREA = triangleArea(PTS)
   Concatenates vertex coordinates in a 3-by-2 array. Each row of the
   array contains coordinates of one vertex.


   Example
   % Compute area of a Counter-Clockwise (CCW) oriented triangle
     triangleArea([10 10], [30 10], [10 40])
     ans = 
         300

   % Compute area of a Clockwise (CW) oriented triangle
     triangleArea([10 40], [30 10], [10 10])
     ans = 
         -300

   See also
   polygonArea, triangleArea3d

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2011-08-23,    using Matlab 7.9.0.529 (R2009b)
 Copyright 2011 INRA - Cepia Software Platform.

0001 function area = triangleArea(pt1, pt2, pt3)
0002 %TRIANGLEAREA Signed area of a triangle.
0003 %
0004 %   AREA = triangleArea(P1, P2, P3)
0005 %   Computes area of the triangle whose vertices are given by P1, P2 and
0006 %   P3. Each vertex is a 1-by-2 row vector.
0007 %
0008 %   AREA = triangleArea(PTS)
0009 %   Concatenates vertex coordinates in a 3-by-2 array. Each row of the
0010 %   array contains coordinates of one vertex.
0011 %
0012 %
0013 %   Example
0014 %   % Compute area of a Counter-Clockwise (CCW) oriented triangle
0015 %     triangleArea([10 10], [30 10], [10 40])
0016 %     ans =
0017 %         300
0018 %
0019 %   % Compute area of a Clockwise (CW) oriented triangle
0020 %     triangleArea([10 40], [30 10], [10 10])
0021 %     ans =
0022 %         -300
0023 %
0024 %   See also
0025 %   polygonArea, triangleArea3d
0026 %
0027 % ------
0028 % Author: David Legland
0029 % e-mail: david.legland@grignon.inra.fr
0030 % Created: 2011-08-23,    using Matlab 7.9.0.529 (R2009b)
0031 % Copyright 2011 INRA - Cepia Software Platform.
0032 
0033 % if data is given as one array, split vertices
0034 if nargin == 1
0035     pt2 = pt1(2,:);
0036     pt3 = pt1(3,:);
0037     pt1 = pt1(1,:);
0038 end
0039 
0040 % compute individual vectors
0041 v12 = bsxfun(@minus, pt2, pt1);
0042 v13 = bsxfun(@minus, pt3, pt1);
0043 
0044 % compute area from cross product
0045 area = (v13(:,2) .* v12(:,1) - v13(:,1) .* v12(:,2)) / 2;