function area = triangleArea3d(pt1, pt2, pt3)
%TRIANGLEAREA3D Area of a 3D triangle
% AREA = triangleArea3d(P1, P2, P3)
% Computes area of the 3D triangle whose vertices are given by P1, P2 and
% P3. Each vertex is either a 1-by-3 row vector, or an array with 3
% columns, each column representing coordinate of a vertex.
% The result AREA has as many rows as the number of rows of the largest
% input array.
% Compared to polygonArea3d, this function is assumed to be faster, as it
% does not requires iteration over vertices. Moreover, it can be used to
% computes the area of several triangles simultaneously.
% AREA = triangleArea3d(PTS)
% Concatenates vertex coordinates in a 3-by-3 array. Each row of the
% array contains coordinates of one vertex.
% triangleArea3d([10 10 10], [30 10 10], [10 40 10])
% ans =
% See also
% polygons3d, polygonArea3d
% Author: David Legland
% e-mail: firstname.lastname@example.org
% Created: 2011-08-23, using Matlab 220.127.116.119 (R2009b)
% Copyright 2011 INRA - Cepia Software Platform.
% if data is given as one array, split vertices
if nargin == 1
pt2 = pt1(2,:);
pt3 = pt1(3,:);
pt1 = pt1(1,:);
% compute individual vectors
v12 = bsxfun(@minus, pt2, pt1);
v13 = bsxfun(@minus, pt3, pt1);
% compute area from cross product
area = vectorNorm3d(cross(v12, v13, 2)) / 2;