/usr/share/octave/packages/geometry-1.7.0/geom3d/polygonArea3d.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{area} =} polygonArea3d(@var{poly})
## Area of a 3D polygon
##
## @var{poly} is given as a N-by-3 array of vertex coordinates. The resulting
## area is positive.
##
## Example
## @example
## poly = [10 30 20;20 30 20;20 40 20;10 40 20];
## polygonArea3d(poly)
## ans =
## 100
## @end example
##
## @seealso{polygons3d, triangleArea3d, polygonArea, polygonCentroid3d}
## @end deftypefn
function area = polygonArea3d(poly)
# put the first vertex at origin (reducing computation errors for polygons
# far from origin)
v0 = poly (1, :);
poly -= v0;
# indices of next vertices
N = size (poly, 1);
iNext = [2:N 1];
# compute area (vectorized version)
# need to compute the sign explicitely, as the norm of the cross product
# does not keep orientation within supporting plane.
cp = cross (poly, poly(iNext,:), 2);
sign_i = sign (cp*cp(2,:)');
area_i = vectorNorm(cp) .* sign_i;
# sum up individual triangles area
area = sum(area_i) / 2;
endfunction
%!demo
%! poly = [10 30 20;20 30 20;20 40 20;10 40 20];
%! polygonArea3d(poly)
%!demo
%! l=0.25;
%! # Corner Triangle with a wedge
%! poly = [1 0 0; ...
%! ([1 0 0]+l*[-1 1 0]); ...
%! mean(eye(3)); ...
%! ([1 0 0]+(1-l)*[-1 1 0]); ...
%! 0 1 0; ...
%! 0 0 1];
%!
%! polygonArea3d(poly)
%!
%! # Is the same as
%! p1 = [1 0 0; 0 1 0; 0 0 1]; # Corner
%! p2 = [([1 0 0]+l*[-1 1 0]); ([1 0 0]+(1-l)*[-1 1 0]); mean(eye(3))]; # Wedge
%!
%! polygonArea3d(p1)-polygonArea3d(p2)
|