Surface Roughness of 3D Scatter Plot

I have 3 huge matrices (353600 x 1). The first represents an x coordinate, the second a y, and the third a z. When these are plotted in a scatter plot together, they create what resembles a surface.

The goal of these coordinates is to see how rough the given surface is. I have tried creating a mesh grid with the x and y coordinates and then using a power law power specteral density function on the height, but ran into issues with the size of my matrices and the fact that my height is represented my spatial data cords and not a mathematical function.

Basically my goal is to quantify the surface roughness of the data points so that I can then compare it to other surfaces to see how the roughness changes based on outside conditions.

If anyone knows any easy way of representing the roughness given many (x,y,z) coordinates, please let me know!

[Paul C]

Have you progressed on this?

Answer 1

[John D'Errico]

Despite the little information you have given us, conspicuous in its absence is what we are not told. So while KSSV MIGHT be on target, pointing you to a Delaunay triangulation in the (x,y) plane, every time I make an assumption about what someone has based on such sparse information, I find out I am wrong.

Does your data represent some surface, of the form z(x,y)?

Are the points essentially know in x and y, with noise in z only? Or is there noise in your measurement of each of x, y, and z?

Does your data represent a closed surface in some form? Say the surface of a sphere (or something isomorphic to one), with points randomly scattered on that surface?

Does your data only fall on the surface, subject to some noise? Or do some pints lie inside the object, whole you are mainly interested in surface roughness?

Is the domain of interest a convex one? Convexity is important, since even if it might be appropriate to use a triangulation, the boundaries of a delaunay triangulation are often composed of long, thin triangles. That will cause serious problems in trying to generate any surface roughness estimates. So an alpha shape might be more appropriate.

I can probably think of some other issues. Answers to the above questions would impact the direction you might want to proceed.

Answer 2

[KSSV]

Read about delaunayTriangulation. This will help you to get what you want. Check the below example code.

N = 100 ;
x = rand(N,1) ; % a randoms data 
y = rand(N,1) ;
z = rand(N,1) ;
dt = delaunayTriangulation(x,y) ;   % delaunay triangulation 
tri =dt.ConnectivityList ;

trisurf(tri,x,y,z) ;
shading interp 
view(2)