function area = triangle_area ( t ) %*****************************************************************************80 % %% TRIANGLE_AREA computes the area of a triangle in 2D. % % Discussion: % % If the triangle's vertices are given in counterclockwise order, % the area will be positive. If the triangle's vertices are given % in clockwise order, the area will be negative! % % An earlier version of this routine always returned the absolute % value of the computed area. I am convinced now that that is % a less useful result! For instance, by returning the signed % area of a triangle, it is possible to easily compute the area % of a nonconvex polygon as the sum of the (possibly negative) % areas of triangles formed by node 1 and successive pairs of vertices. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 17 October 2005 % % Author: % % John Burkardt % % Parameters: % % Input, real T(2,3), the triangle vertices. % % Output, real AREA, the area of the triangle. % area = 0.5 * ( ... t(1,1) * ( t(2,2) - t(2,3) ) ... + t(1,2) * ( t(2,3) - t(2,1) ) ... + t(1,3) * ( t(2,1) - t(2,2) ) ); return end