AREA3D Computes the area of a 3D closed polygon.

src/area3d.m

+function area = area3d( p )
+%AREA3D Computes the area of a 3D closed polygon.
+%   p must be a Nx3 matrix.
+
+    n_vertices = size( p, 1 );
+
+    % Put all vertex coordinates with respect to center.
+    center = mean( p );
+    center = repmat( center, [ n_vertices, 1 ] );
+    p = p - center;
+    
+    % Build small triangles.
+    index = [ 2 : n_vertices 1 ];
+    p1 = p;
+    p2 = p( index, : );
+    
+    % Cross product.
+    cp = cross( p1, p2 );
+    
+    % Norm of each vector.
+    vn = euclidean_norm( cp );
+    
+    % Positive area.
+    area_triangle = abs( vn );
+
+    % Total positive area.
+    area = sum( area_triangle ) / 2;
+        
+    function n = euclidean_norm( v )
+        n = sqrt( sum( v .* v, ndims( v ) ) );
+    end
+
+end
+