# If I take 10 points in a high resolution rectangular grid is there some code or some function in matlab that displays volumetric object.?

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Rashi Mehrotra on 18 Aug 2020
Commented: Rashi Mehrotra on 6 Oct 2020
I have a 3D binary matrix in spherical coordinates. I have to from a high resolution rectangular grid .
Does Matlab itself has something that lets suppose if we give 5 or 10 points does it itself intelligently smooths it out and displays the object?

Walter Roberson on 18 Aug 2020
Do you mean something like, "given about 10 points on the surface of something that might be a sphere or rotated cuboid or conic section or polyhedron, figure out what shape it is and figure out its size and other key characteristics, and output a high resolution extrapolation of the shape"?
If so then the answer is NO, MATLAB does not have anything like that built in.
There are functions available in the file exchange to fit a sphere to a number of points, and I think I have seen fitting an ellipsoid as well.
Rotated cuboid could perhaps be done with a bit of pca to derive rotation angle.
Rashi Mehrotra on 22 Sep 2020
Walter, can you please tell how the conformal mapping works in this case,
I have a poor resolution image and I want to smooth it out.

John D'Errico on 7 Sep 2020
Is there some code that can automatically take some small set of points (worse, possibly with some noise? You did mention smoothing) and know what volumetric object they came from? Of course not.
Conside 8 points that form the vertices of a cube. Oh. Wait. Are these just 8 points in a specific configuration on the surface of a sphere? You cannot know which object they came from, as it is completely ambiguous.
You might consider computing the convex hull, or perhaps a delaunay tessellation, then ask if the triangulation is topologically equivelent to that of a dissection of a cube. (Note there are two distinct ways to dissect a 3-cube into simplexes, one with 6 pieces, one with 5., and then we would also have rotations thereof.) You could build in some pattern recognition intelligence that would recognize a tessellation as conformable to a cube/hyper-rectangle. But all of this would take some serious understanding of pattern recognition techniques. And it still would be unable to understand the points really just came from a sphere or ellipsoid anyway.
The human eye/brain is great at recognizing things from scattered data. In fact, we see this every night when we look at the night sky and see constellations. But must I point out that even those constellations are highly ambiguous? Two different people can look at the same configuarations and see totally different objects. And they both might be correct! Where is my MC Escher print when I need it?
Rashi Mehrotra on 6 Oct 2020
how to include high resolution in x, y and z coordinates in this if the poor image has resolution of 2.5 cm in x direction.