Find the upper surface of a 3d object.

As the title suggests, I would like to find the points that correlate only to the upper surface of a 3d object.

I have a matrix containing thousands of points (x,y,z coordinates). The shape is that of a slightly bent, rectangular plate. The coordinates pertain to a molecular structure, so the volume of the structure is filled with points.

I used following to approximate the the shape and then find the outer perimeter:

mymatrix;      %mymatrix(:,1) corresponds to x coordinates, mymatrix(:,2) corresponds to y, and mymatrix(:,3) corresponds to z

%The following creates a bounding volume and provides xyz coordinates of that bounding volume
shp = alsphashape(x,y,z, 0.1); 
[tri, xyz] = boundaryFacets(shp);
trisurf(tri,xyz(:,1),xyz(:,2),xyz(:,3), 'FaceColor','cyan','FaceAlpha',0.3) ; %This plots that outer perimeter and also yields the xyz matrix of that bounding box

I would like to extract the points correlating only to the upper surface of this matrix so that I can then later take the gradient of that surface.

I think I'm just missing something simple here. Any help is greatly appreciated.

Answer 1

[Image Analyst]

Try using scatteredInterpolant() to get a z value for every combination of x and y. See attached demo.

[Casey Ricks]

Maybe I'm misunderstanding. I don't see how to specify the upper or lower range within that function.

I have an fcc lattice in the shape of a plate with width (x), depth (y), and thickness (z), where every 'atom' is has an x, y, and z coordinate, as well as a radius. I'm trying to find the uppermost atoms that define the top surface of this plate.

I'm not understanding how to extract that with scatteredinterpolant.

[Image Analyst]

For some assortment of (x,y) locations, you have a value -- your z value. I assume that z is is the center of the atom so we now need to add the radius to it to get a new height to train the interpolant with.

This is just like the National Weather Service which has temperatures for a bunch of scattered cities, but not everywhere. Now you can turn that into a matrix where you DO have the value everywhere by using scatteredInterpolant. You have your x,y,height values, then you get the interpolant. Then you create a grid using meshgrid which will give you the coordinates for every possible (x,y) location - not just ones you have but ALL of them over your entire range of x and y. Then you just feed that into the interpolant to get the estimated height (z+radius) values everywhere. Not just at your training points, but everywhere in the possible range. This is how the NWS can turn a bunch of scattered temperatures for a limited number of discrete city locations into temperature values for anywhere in the country. Does that explain it better?

[Casey Ricks]

Yea, thank you for your in-depth responses. This is actually what I ended up doing last night, though I used griddata instead of scatteredinterpolant, but I think it is a very similar idea.

Answer 2

[Matt J]

Perhaps you can obtain the facet normals like in this example,

https://www.mathworks.com/help/matlab/ref/triangulation.facenormal.html#mw_629258bd-bf7e-4d1d-ab5f-6a9495067aa2

and classify any facet whose normal has a positive z-component as belonging to the upper surface.