Constructing a 3D matrix out of single column coordinate data with a corresponding value

Hi,

I need to analyze a 3d velocity field from tecplot. I could transfer the data into a 4 column matrix consisting of 6644672 rows. The first three columns represent that XYZ respectively, and the fourth column is the velocity data at that coordinate.

Since I want to filter this field in the future, I for now need to construct a 3d Matrix out of this imported data. It is important that no coordinates get lost, that the velocity value stays at the right coordinate and that the coordinates are oriented in the right way to eachother.

The challenging thing for me was that the coordinates in the 4 column matrix are not ordered in some logical way.

Can someone help me?

[Catalytic]

What would the voxels of the 3D matrix contain, and how would those contents be related to the imported data?

[Emil Litjens]

Each voxel would contain a velocity value at a certain coordinate.

Answer 1

[Matt J]

Let's call your Nx4 matrix XYZV.

xyzv=num2cell(sortrows(XYZV,[3,2,1]) ,1);

[I,J,K,V] =deal(xyzv{:});

I=findgroups(I);
J=findgroups(J);
K=findgroups(K);


matrix3D=accumarray([I,J,K], V);  %the result

[Emil Litjens]

Hi thanks for your help,

But this Matrix3D returns like 763x763x763, but expect it to be 188^3, since the length of the columns are also 188^3, and the coordinates are retracted from a perfect cube. Besides that, when i select some random parts of this creacted matrix and i analayze them, i find only zeros, which cannot be the case. I will display a part of "xyzv" matrix below.:

-0.000520000001000000 0.00228000013000000 -0.00444000028000000 0.0914448053000000

-0.000520000001000000 0.00228000013000000 -0.00435999967000000 0.0867100433000000

-0.000520000001000000 0.00236000004000000 -0.00444000028000000 0.0901703462000000

-0.000520000001000000 0.00236000004000000 -0.00435999967000000 0.0832454637000000

-0.000600000028000000 0.00228000013000000 -0.00427999999000000 0.0638148636000000

-0.000600000028000000 0.00228000013000000 -0.00420000032000000 0.0449321158000000

-0.000600000028000000 0.00236000004000000 -0.00427999999000000 0.0659241527000000

-0.000600000028000000 0.00236000004000000 -0.00420000032000000 0.0842402205000000

-0.000520000001000000 0.00228000013000000 -0.00427999999000000 0.0794742778000000

-0.000520000001000000 0.00228000013000000 -0.00420000032000000 0.0790982544000000

[Matt J]

It means your (x,y,z) data do not sweep over a cube exactly. You could try the modification below, which allows the (x,y,z) to deviate from the nodes of a cube with a tolerance, but I don't/can't know what the appropriate TOL for your data would be.

TOL=1e-4; %example

I=findgroupstol(I,TOL);
J=findgroupstol(J,TOL);
K=findgroupstol(K,TOL);


function G=findgroupstol(U,tol)

  [~,~,G]=uniquetol(U,tol);

end

[Emil Litjens]

You are a hero! It works, thanks a lot.

Answer 2

[Matt J]

If you are trying to query velocity values at arbitrary 3D locations, do not use a 3D array. Instead, use scatteredInterpolant or griddata.

[Emil Litjens]

I don't want the data to be interpolated before filtering yet. And the output of the scatteredinterpolant does not return a 3d matrix with x times y times z.

[Matt J]

But you don't possess velocity values at all points in a 3D lattice, only at some scattered cloud of (x,y,z) coordinates around them. How will you define values at the lattice points if not by interpolation?

[Emil Litjens]

But I do have all the points in a 3D lattice I believe.