Interpolate Points of a 3D Point Cloud?

I am trying to interpolate data points (x, y, z) to get a point cloud with higher density.

I have triangulation points (x-y-z coordinates) and faces from a .stl-file (imported with stlread()) that I can work with. (DATA is attached).

In the attached image you can see the given data points (BLUE) and indicated the points I want to create (RED) - but for the whole geometry and in larger numbers.

Any ideas?

[darova]

Please attach your data as file. It's annoying

[newbie]

I´m sorry, attached as file.

Answer 1

[darova]

• Use griddata to create surface
• Use contour3 to create crossection

clc,clear
load data.txt
x = data(:,1);
y = data(:,2);
z = data(:,3);
[t,r] = cart2pol(x,y);
rr = linspace(min(r),max(r),20);
tt = linspace(0,2*pi,20);
[T,R] = meshgrid(tt,rr);            % new mesh
[X,Y] = pol2cart(T,R);              % convert new mesh to cartesian
Z = griddata(x,y,z,X,Y);            % according Z coordinates
plot3(x,y,z,'.b')
hold on
surf(X,Y,Z,'faceColor','none','edgecolor',[1 1 1]*0.8)
contour3(X,Y,Z,[34 38])
hold off
axis equal

Result

[newbie]

Thank you! That helps me a lot!

My example with the cone was pretty simple, as it has a circular crosssection. Later on, the objects will be various forms of a polygon. I´ll try to adapt your approach ...

[Diego Hens]

Thanks, this is going to be useful. I don't know how exactly, but it will :D

Answer 2

[Daniel Vieira]

try the scatteredInterpolant, should work fine with these points (not so much if you had a closed surface)

[newbie]

I`ve read about scatteredInterpolant, but it doesn´t really makes sense to me, as it needs a function v (but I only have the given data points that I added to my question).

[Daniel Vieira]

Actually it doesn't need any function, it does exactly the same thing as griddata (others posted solutions above using it). The difference is griddata creates the interpolation over the given points and that's it, while scatteredInterpolant creates a reusable interpolator for you to use in any points you want how many times you need.