How do I plot interpolated grid data and original datapoint set in the same plot?

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NP on 16 Sep 2019
Commented: NP on 18 Sep 2019
Hi,
After creating a grid data series (Data Terrain Model) from interpolating contour lines, I would like to plot everything on the same layer, but I am not sure if it is possible in matlab. Here is the gist of what I've done:
[xi,yi] = meshgrid(Xmin:res:Xmax, Ymin:res:Ymax);
f = scatteredInterpolant(contour_grid.X,contour_grid.Y,contour_grid.Z);
zi= f(xi,yi)
Xi=[xi(:); contour_grid.X];
Yi=[yi(:); contour_grid.Y];
Zi=[zi(:); contour_grid.Z];
Is there a way to plot Xi, Yi, and Zi? I'd have to turn these arrays back into grids to be able to use mesh(X,Y,Z) but I am struggling to write how to do that.
Has anyone ever had to do that?
Thanks,

Bjorn Gustavsson on 17 Sep 2019
You can always simply plot all your points:
plot3(Xi,Yi,Zi,'r.')
Or with scatter:
scatter(Xi,Yi,32,Zi,'filled')
But to me this seems to be more interesting:
pcolor(xi,yi,zi),
hold on
plot(xi,yi,'k.','markersize',6)
scatter(contour_grid.X,contour_grid.Y,23,contour_grid.Z,'filled')
Or you could compare contour-plots:
Levels = linspace(min(Zi(:)),max(Zi),10);
contour(Xi,Yi,Zi,Levels,'k')
hold on
tri=delaunay(contour_grid.X,contour_grid.Y);
[c,h]=tricontour(tri,contour_grid.X,contour_grid.Y,contour_grid.Z,Levels);
plot(contour_grid.X,contour_grid.Y,'k.')
You can find the tricontour function on the file exchange: TRICONTOUR
HTH

NP on 17 Sep 2019
Thanks for this elaborate answer. I had a go at the different functions and they give interesting results. Ploting all the points is a bit taxing for the computer though. Ideally, I'd like to plot Xi, Yi and Zi that include the interpolated points and the original contour line points in a mesh, but can a mesh function even do that? Not sure.
Bjorn Gustavsson on 18 Sep 2019
This whish of yours confuse me. First you say that "plotting all the points" are too taxing, then you say that you want to plot Xi, Yi and Zi - that are explicitly all points you have.
The terse answer is: matlab's mesh function cannot do what you want. It requires, just as its plot-function siblings pcolor, surf et al., points in 2-D arrays (you have such for xi, yi and zi, but your contour_grid.X, contour_grid.Y, and contour_grid.Z are in 1-D arrays. It is not straightfor (impossible) ward to merge these into 1 set of regular 2-D arrays).
You might get what you request with the trimesh function. That would give you a mesh-plot of all points if you call it with something like:
tri=delaunay(Xi,Yi);
trimesh(tri,Xi,Yi,Zi);