MATLAB: Finding the surface area of a 3-D plot

plot surface area 3-d

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?

Best Answer

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.

Related Solutions

MATLAB: How i can solve this problem? Pleas!

Your ‘T’ matrix must become a cell array. See my sample of ‘T’ for an example.

Once you do that, I would do something like this:

Y = [12.004
    13.1573 
    11.1665  
    11.8082    
    12.2129   
    12.8075   
    12.4167  
    11.5708   
    12.5798    
    13.7489];
T={'cluster2'; 'cluster1'; 'cluster3'; 'cluster9'; 'cluster0'; 'cluster7'; 'cluster4'}; % Sample Of Cell Array
[UnqClust,~,idx] = unique(T);                                                           % Unique Values & Locations
Out = Y(idx);                                                                           % Mapped Output
for k1 = 1:length(idx)
    fprintf(1, '\t%s\t%.4f\n', T{k1}, Out(k1))              % Demonstration Output (Delete Loop)
end
  cluster2  11.1665
  cluster1  13.1573
  cluster3  11.8082
  cluster9  12.4167
  cluster0  12.0040
  cluster7  12.8075
  cluster4  12.2129

MATLAB: How to calculate the angle between two surfaces

The command

[Nx,Ny,Nz] = surfnorm(Z)

will return surface normals to surface Z. See:

https://www.mathworks.com/help/matlab/ref/surfnorm.html

However these normals will change from point to point. You need the equation of the best fit plane to obtain a single over-all normal to your points. For a plane with equation

a*x+b*y+c*z+d = 0

its normal is the vector v = [a,b,c]. To make it of unit length do:

v = v/norm(v);

As I think you are aware, the angle between the normals to two planes is the same as the angle between those planes. The angle between two 3D vectors v1 and v2 is:

   ang = atan2(norm(cross(v1,v2)),dot(v1,v2));

Best Answer

Related Solutions

MATLAB: How i can solve this problem? Pleas!

MATLAB: How to calculate the angle between two surfaces

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