mesharea()

            --> mesharea

Computes the area of any 3D surface mapped with a {X,Y,Z} lattice of 4-vertices
cells.

 SYNTAX
 ------
        mesharea  // Displays this help
 area = mesharea(X, Y, Z)

 PARAMETERS
 ----------
 X,Y,Z : 3 matrices of real decimal numbers, with same sizes:
         Cartesian coordinates of the nodes of the lattice mapping the surface.
         {X(i,j), Y(i,j), Z(i,j)} locates the node (i,j).
         Each node (not on a border or a corner) is linked to 4 neighboors.
         Each cell of the lattice has 4 vertices set to nodes.
         For a closed surface, the first and last rows of X|Y|Z must be equal,
         as well as their first and last columns.
         Nan values are accepted. Each node having at least one of its x|y|z
         coordinates set to %nan is canceled. This allows for instance to make
         holes in the surface.
         Folded surfaces are possible, when X, Y, and/or Z are not regular
         nor monotonic grids.

 area : single positive decimal number. The area of the mesh.
        Each 4-vertices cell is split into 2 plan triangles. The area of the
        cell is the sum of both triangles areas. The area of the mesh is the
        sum of all cells areas.
        When a vertice is Nan, the area of the 4 triangles (half cells)
        touching it is ignored and not taken into account.

 REFERENCE
 ---------
  Comments, scoring and bug reports are welcome at the bottom of this page.

 SEE ALSO
 --------
  polygonmetrics : https://fileexchange.scilab.org/toolboxes/445000

 EXAMPLE
 -------
// Area of a sphere: Study of the error versus the surface sampling
n = 4;
for i = 1:8
    long = linspace(0, 2*%pi, 2*n+1);     // sampling longitudes
    lat  = linspace(-%pi/2, %pi/2, n+1)'; // sampling latitudes
    X = cos(lat)*cos(long);
    Y = cos(lat)*sin(long);
    Z = sin(lat)*ones(long);
    err(i) = mesharea(X, Y, Z)/(4*%pi) - 1;
    dAngle(i) = 180/n;  // angular step [°]
    n = n*2;
end
clf, plot2d("ll", dAngle, -err)
xtitle('mesharea() accuracy for a sphere', 'Angular sampling [°]', ..
       'Relative error on sphere''s area')
// => The relative error goes as the sampling step^2