Finding the surface area of a 3-D plot?

If I have the following topography:

%Heights

y=0:5:80; % Width Length measurement increments (m) 

x=0:5:180; % Length measurement increments (m)

z=xlsread('Truncated_Pyramid_Topography.xlsx', 'B24:Al40');

Is there a function or method I can use to find the surface area?

Answer 1

[Roger Stafford]

To get the surface area you need to first determine the surface normal for each point in your mesh of x-y points, as you would to use 'surf'. Use 'meshgrid' to convert your vectors to 2D matrices. Then use 'surfnorm' to determine the surface normal vectors. Next, normalize that normal vector and then use the reciprocal of its z component as the integrand of a numerical double integral taken over your x-y area. This reciprocal is the secant of the angle the normal makes with the z-axis which is the needed factor for conversion from horizontal area to your surface's area.

 [X,Y] = meshgrid(x,y);
 % Get the corresponding Z values for each pair in X and Y
 [Nx,Ny,Nz] = surfnorm(X,Y,Z);
 S = sqrt(Nx.^2+Ny.^2+Nz.^2)./Nz; % Secant of angle normal makes with z-axis
 % Now S is to be your integrand in the double integral

For this last you can use 'trapz' twice for this purpose, as explained in Walter's reference to my part of Newsreader thread 308496.

[宇哲]

Thanks

[Bret Jarod Sean Ordono]

do you have any reference for this? thank you! This really helped me a lot so I really need a book that contains this formula, if you dont mind.

Answer 2

[Walter Roberson]

http://www.mathworks.com/matlabcentral/newsreader/view_thread/308496

http://www.mathworks.com/support/solutions/en/data/1-18CK7/index.html