Interpolation using Excel Data

Hello. Newb here. I have a set of data in Excel (attached) that I would like to plot and interpolate and show the below and after plots (before interpolation and after). I have tried to follow various examples on interpolation, but am having a hard time understanding how to use my data in the code itself since I have an array of various answers. Right now my table is in 10s, and I want to interpolate the values between 10 and 20, 20 and 30,etc for inclination, and 300 and 310, etc for each.

I tried to see if I can figure out how to just interpret between the each and then manually enter into excel, but I'm having trouble here too.

What I'd REALLY love is all the values interpolated based on the data I have an plot the before (not interpolated) and after (after interpolation) on a 2D meshgrid.

Help??

thanks!

Veronica

Answer 1

[Star Strider]

One approach —

% C1 = readcell('FluxData.xlsx')

T1 = readtable('FluxData.xlsx')

T1 = 92×20 table
        Var1        Var2      Var3         Var4          Var5         Var6         Var7         Var8         Var9         Var10        Var11        Var12        Var13        Var14        Var15        Var16        Var17        Var18        Var19         Var20  
    ____________    ____    _________    _________    __________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    __________    _________

    {0×0 char  }    NaN            10           20            30           40           50           60           70           80           90           98          100          110          120          130          140          150           160          170
    {'Altitude'}    300     3.421e-08    4.059e-08     5.242e-08    4.567e-08    4.147e-08    4.287e-08    3.951e-08    5.478e-08    6.376e-08      5.2e-08    4.925e-08    5.238e-08    6.125e-08    8.317e-08    7.686e-08    9.879e-08     8.283e-08    1.058e-07
    {0×0 char  }    310     4.252e-08    4.075e-08     3.614e-08    3.472e-08    3.756e-08    4.766e-08    5.917e-08    9.377e-08    8.392e-08    6.897e-08    7.078e-08     6.61e-08    6.631e-08    6.824e-08    7.123e-08    7.971e-08     7.926e-08    1.074e-07
    {0×0 char  }    320     7.164e-08    5.049e-08     5.291e-08    5.516e-08    5.649e-08    5.612e-08    7.005e-08    9.938e-08    1.056e-07     7.96e-08     8.31e-08    7.555e-08    7.661e-08    8.905e-08     9.13e-08    9.877e-08     9.812e-08    1.451e-08
    {0×0 char  }    330      6.99e-08    6.738e-08     6.263e-08    6.359e-08    7.276e-08    7.841e-08     9.61e-08    1.328e-07    1.195e-07     1.03e-07     8.31e-08    9.903e-08    1.084e-07     1.45e-07    1.176e-07    1.195e-07     1.273e-07     1.55e-07
    {0×0 char  }    340     8.915e-08    9.009e-08     8.952e-08    9.115e-08    1.041e-07    1.155e-07    1.155e-07    1.383e-07    1.521e-07    1.588e-07     1.49e-07    1.401e-07    1.601e-07    1.576e-07    1.398e-07    1.505e-07     1.517e-07    1.806e-07
    {0×0 char  }    350     6.648e-08    6.913e-08    7.1654e-08    8.288e-08    9.692e-08    9.374e-08    1.076e-07    1.449e-07    1.487e-07    1.495e-07    1.557e-07     1.37e-07    1.464e-07     1.74e-07    1.494e-07    1.228e-07     1.298e-07    1.342e-07
    {0×0 char  }    360     3.693e-08    3.502e-08      3.39e-08    5.745e-08    5.058e-08    4.978e-08    5.355e-08    5.868e-08    5.487e-08    6.224e-08    6.003e-08    6.538e-08    6.881e-08    7.896e-08    8.467e-08    7.157e-08     8.227e-08    1.002e-07
    {0×0 char  }    370     5.007e-08    4.519e-08     6.075e-08    5.858e-08    7.319e-08    7.767e-08    8.992e-08    1.312e-07      1.2e-07    1.082e-07    1.036e-07    9.134e-08     8.91e-08    1.035e-07    8.078e-08    9.484e-08     8.471e-08    1.128e-07
    {0×0 char  }    380     1.015e-07    1.218e-07      1.18e-07    1.095e-07    1.225e-07    1.182e-07     1.43e-07    1.751e-07     1.67e-07    1.949e-07    1.854e-07    1.649e-07    1.544e-07    1.816e-07    1.681e-07    1.639e-07     2.052e-07    1.928e-07
    {0×0 char  }    390     1.736e-07    1.719e-07     1.778e-07    1.762e-07    1.878e-07    2.038e-07    2.198e-07     2.71e-07    2.676e-07    2.728e-07    2.714e-07    2.668e-07    2.832e-07     3.08e-07      3.1e-07     3.63e-07     3.356e-07    3.484e-07
    {0×0 char  }    400     2.332e-07    2.047e-07     1.974e-07    2.229e-07    2.276e-07    2.164e-07    2.279e-07    2.537e-07    2.677e-07    2.801e-07    2.875e-07    2.813e-07    3.398e-07    5.263e-07    4.309e-07    4.082e-07     4.348e-07    4.333e-07
    {0×0 char  }    410     2.381e-07    2.241e-07     2.334e-07    2.295e-07    2.518e-07    2.828e-07    3.154e-07    3.751e-07    4.007e-07    3.984e-07    4.108e-07    4.561e-07    5.326e-07    6.362e-07    4.896e-07    4.367e-07      4.64e-07    3.828e-07
    {0×0 char  }    420     1.659e-07    1.775e-07     1.725e-07    1.807e-07    1.963e-07    2.064e-07    2.414e-07    3.832e-07    3.569e-07    3.665e-07    3.226e-07    2.415e-07    2.383e-07    2.505e-07    2.408e-07    2.306e-07    1.2265e-07    2.262e-07
    {0×0 char  }    430      2.06e-07    2.134e-07     2.252e-07    2.396e-07    2.562e-07    2.745e-07    2.848e-07    3.262e-07    3.018e-07    2.898e-07    2.913e-07     3.03e-07    3.328e-07    3.469e-07    3.256e-07    2.855e-07     2.664e-07    2.707e-07
    {0×0 char  }    440     2.179e-07    2.418e-07     2.155e-07    2.035e-07    2.293e-07    2.359e-07    2.696e-07    3.338e-07    3.318e-07    3.271e-07    3.321e-07    3.001e-07     2.99e-07    3.114e-07    2.979e-07    2.859e-07     3.131e-07    2.735e-07

xvar = T1{1,3:end};
yvar = T1{2:end,2};
A = T1{2:end,3:end};

figure
surf(xvar, yvar, A)
colormap(turbo)
colorbar
xlabel('Inclination')
ylabel('Altitude')
zlabel('Flux')

[Xu,Yu] = meshgrid(xvar, yvar);

interpv = 5;
xq = linspace(min(xvar), max(xvar), numel(xvar)*interpv);
yq = linspace(min(yvar), max(yvar), numel(yvar)*interpv);
[Xi,Yi] = meshgrid(xq,yq);

Ai = interp2(Xu,Yu,A,Xi,Yi);

figure
surf(Xi, Yi, Ai)
colormap(turbo)
colorbar
xlabel('Inclination')
ylabel('Altitude')
zlabel('Flux')

Experiment with idfferent interp2 interpolation methods to get the desired result.

.

[Veronica Vigil]

Star - this is what I needed. Now, last question. If I wanted the raw data behind the plot, how do I pull that data? So it would include my original values for the 10s, and now include the 1s (hope that last part makes sense

[Star Strider]

Thank you!

The data that created the original plot are in the ‘xvar’, ‘yvar’, and‘A’ variables. The corresponding values for the interpolated plot are ‘xq’, ‘yq’, and ‘Ai’ variables.

The interpolation value (the scaling value) is the ‘interpv’ variable (and its assigned value). It controls the interpolation density, so here that is 5 times the original density. It can be set to any value you want (within reason). If the reulting surf plot is so dense that it appears black (because of the edge density), you can set the 'EdgeColor' to either 'interp' or 'off'. There are other options as well. See the surf documentation for those details.

.

[Veronica Vigil]

Is there a way I could write a code such that it also pulls these values into a table?

[Veronica Vigil]

I figured out how to get the values I want, but Now to figure out how to extract it into a table. I set it to 10 times the original density and will play with the colors as you mentioned.

Any idea how to pull them out? I know if I type just "Ai", it will display all of the data, but it's so much it gets cut off. I know there's a way to, for lack of a better term "export" the data into a table. Do you know how to do that?

[Star Strider]

Creating the matrix to write to the file requires a bit of creativity.

This approximately corresponds to the format of the original file —

% C1 = readcell('FluxData.xlsx')

T1 = readtable('FluxData.xlsx')

T1 = 92×20 table
        Var1        Var2      Var3         Var4          Var5         Var6         Var7         Var8         Var9         Var10        Var11        Var12        Var13        Var14        Var15        Var16        Var17        Var18        Var19         Var20  
    ____________    ____    _________    _________    __________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    _________    __________    _________

    {0×0 char  }    NaN            10           20            30           40           50           60           70           80           90           98          100          110          120          130          140          150           160          170
    {'Altitude'}    300     3.421e-08    4.059e-08     5.242e-08    4.567e-08    4.147e-08    4.287e-08    3.951e-08    5.478e-08    6.376e-08      5.2e-08    4.925e-08    5.238e-08    6.125e-08    8.317e-08    7.686e-08    9.879e-08     8.283e-08    1.058e-07
    {0×0 char  }    310     4.252e-08    4.075e-08     3.614e-08    3.472e-08    3.756e-08    4.766e-08    5.917e-08    9.377e-08    8.392e-08    6.897e-08    7.078e-08     6.61e-08    6.631e-08    6.824e-08    7.123e-08    7.971e-08     7.926e-08    1.074e-07
    {0×0 char  }    320     7.164e-08    5.049e-08     5.291e-08    5.516e-08    5.649e-08    5.612e-08    7.005e-08    9.938e-08    1.056e-07     7.96e-08     8.31e-08    7.555e-08    7.661e-08    8.905e-08     9.13e-08    9.877e-08     9.812e-08    1.451e-08
    {0×0 char  }    330      6.99e-08    6.738e-08     6.263e-08    6.359e-08    7.276e-08    7.841e-08     9.61e-08    1.328e-07    1.195e-07     1.03e-07     8.31e-08    9.903e-08    1.084e-07     1.45e-07    1.176e-07    1.195e-07     1.273e-07     1.55e-07
    {0×0 char  }    340     8.915e-08    9.009e-08     8.952e-08    9.115e-08    1.041e-07    1.155e-07    1.155e-07    1.383e-07    1.521e-07    1.588e-07     1.49e-07    1.401e-07    1.601e-07    1.576e-07    1.398e-07    1.505e-07     1.517e-07    1.806e-07
    {0×0 char  }    350     6.648e-08    6.913e-08    7.1654e-08    8.288e-08    9.692e-08    9.374e-08    1.076e-07    1.449e-07    1.487e-07    1.495e-07    1.557e-07     1.37e-07    1.464e-07     1.74e-07    1.494e-07    1.228e-07     1.298e-07    1.342e-07
    {0×0 char  }    360     3.693e-08    3.502e-08      3.39e-08    5.745e-08    5.058e-08    4.978e-08    5.355e-08    5.868e-08    5.487e-08    6.224e-08    6.003e-08    6.538e-08    6.881e-08    7.896e-08    8.467e-08    7.157e-08     8.227e-08    1.002e-07
    {0×0 char  }    370     5.007e-08    4.519e-08     6.075e-08    5.858e-08    7.319e-08    7.767e-08    8.992e-08    1.312e-07      1.2e-07    1.082e-07    1.036e-07    9.134e-08     8.91e-08    1.035e-07    8.078e-08    9.484e-08     8.471e-08    1.128e-07
    {0×0 char  }    380     1.015e-07    1.218e-07      1.18e-07    1.095e-07    1.225e-07    1.182e-07     1.43e-07    1.751e-07     1.67e-07    1.949e-07    1.854e-07    1.649e-07    1.544e-07    1.816e-07    1.681e-07    1.639e-07     2.052e-07    1.928e-07
    {0×0 char  }    390     1.736e-07    1.719e-07     1.778e-07    1.762e-07    1.878e-07    2.038e-07    2.198e-07     2.71e-07    2.676e-07    2.728e-07    2.714e-07    2.668e-07    2.832e-07     3.08e-07      3.1e-07     3.63e-07     3.356e-07    3.484e-07
    {0×0 char  }    400     2.332e-07    2.047e-07     1.974e-07    2.229e-07    2.276e-07    2.164e-07    2.279e-07    2.537e-07    2.677e-07    2.801e-07    2.875e-07    2.813e-07    3.398e-07    5.263e-07    4.309e-07    4.082e-07     4.348e-07    4.333e-07
    {0×0 char  }    410     2.381e-07    2.241e-07     2.334e-07    2.295e-07    2.518e-07    2.828e-07    3.154e-07    3.751e-07    4.007e-07    3.984e-07    4.108e-07    4.561e-07    5.326e-07    6.362e-07    4.896e-07    4.367e-07      4.64e-07    3.828e-07
    {0×0 char  }    420     1.659e-07    1.775e-07     1.725e-07    1.807e-07    1.963e-07    2.064e-07    2.414e-07    3.832e-07    3.569e-07    3.665e-07    3.226e-07    2.415e-07    2.383e-07    2.505e-07    2.408e-07    2.306e-07    1.2265e-07    2.262e-07
    {0×0 char  }    430      2.06e-07    2.134e-07     2.252e-07    2.396e-07    2.562e-07    2.745e-07    2.848e-07    3.262e-07    3.018e-07    2.898e-07    2.913e-07     3.03e-07    3.328e-07    3.469e-07    3.256e-07    2.855e-07     2.664e-07    2.707e-07
    {0×0 char  }    440     2.179e-07    2.418e-07     2.155e-07    2.035e-07    2.293e-07    2.359e-07    2.696e-07    3.338e-07    3.318e-07    3.271e-07    3.321e-07    3.001e-07     2.99e-07    3.114e-07    2.979e-07    2.859e-07     3.131e-07    2.735e-07

xvar = T1{1,3:end};
yvar = T1{2:end,2};
A = T1{2:end,3:end};

% figure
% surf(xvar, yvar, A)
% colormap(turbo)
% colorbar
% xlabel('Inclination')
% ylabel('Altitude')
% zlabel('Flux')

[Xu,Yu] = meshgrid(xvar, yvar);

interpv = 5;
xq = linspace(min(xvar), max(xvar), numel(xvar)*interpv);
yq = linspace(min(yvar), max(yvar), numel(yvar)*interpv);
[Xi,Yi] = meshgrid(xq,yq);

Ai = interp2(Xu,Yu,A,Xi,Yi);

% figure
% surf(Xi, Yi, Ai)
% colormap(turbo)
% colorbar
% xlabel('Inclination')
% ylabel('Altitude')
% zlabel('Flux')

[r,c] = size(Ai);                                               % Create Matrix To Write
M = NaN(r+1,c+1);
M(2:r+1, 2:c+1) = Ai;
M(1,2:end) = xq;
M(2:end,1) = yq;

M                                                               % Display Matrix

M = 456×91

NaN 10.0000 11.7978 13.5955 15.3933 17.1910 18.9888 20.7865 22.5843 24.3820 26.1798 27.9775 29.7753 31.5730 33.3708 35.1685 36.9663 38.7640 40.5618 42.3596 44.1573 45.9551 47.7528 49.5506 51.3483 53.1461 54.9438 56.7416 58.5393 60.3371 300.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 301.9824 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 303.9648 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 305.9471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 307.9295 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 309.9119 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 311.8943 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 313.8767 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 315.8590 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

writematrix(M,'FluxDataInterp.xlsx')                            % Write Matrix To File

InterpFlux = readmatrix('FluxDataInterp.xlsx')                  % Check Written File

InterpFlux = 456×91

NaN 10.0000 11.7978 13.5955 15.3933 17.1910 18.9888 20.7865 22.5843 24.3820 26.1798 27.9775 29.7753 31.5730 33.3708 35.1685 36.9663 38.7640 40.5618 42.3596 44.1573 45.9551 47.7528 49.5506 51.3483 53.1461 54.9438 56.7416 58.5393 60.3371 300.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 301.9824 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 303.9648 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 305.9471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 307.9295 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 309.9119 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 311.8943 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 313.8767 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 315.8590 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

xq = InterpFlux(1,2:end)                                        % Retrieve Data

xq = 1×90

10.0000 11.7978 13.5955 15.3933 17.1910 18.9888 20.7865 22.5843 24.3820 26.1798 27.9775 29.7753 31.5730 33.3708 35.1685 36.9663 38.7640 40.5618 42.3596 44.1573 45.9551 47.7528 49.5506 51.3483 53.1461 54.9438 56.7416 58.5393 60.3371 62.1348

yq = InterpFlux(2:end,2)                                        % Retrieve Data

yq = 455×1

1.0e-05 * 0.0034 0.0036 0.0038 0.0039 0.0041 0.0042 0.0048 0.0054 0.0060 0.0065

Ai = InterpFlux(2:end,2:end)                                    % Retrieve Data

Ai = 455×90

1.0e-05 * 0.0034 0.0035 0.0037 0.0038 0.0039 0.0040 0.0042 0.0044 0.0046 0.0048 0.0050 0.0052 0.0051 0.0050 0.0049 0.0048 0.0047 0.0045 0.0045 0.0044 0.0043 0.0042 0.0042 0.0042 0.0042 0.0042 0.0042 0.0043 0.0043 0.0042 0.0036 0.0037 0.0038 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0046 0.0047 0.0049 0.0048 0.0047 0.0046 0.0045 0.0044 0.0043 0.0043 0.0042 0.0042 0.0041 0.0041 0.0041 0.0042 0.0042 0.0043 0.0043 0.0044 0.0044 0.0038 0.0038 0.0039 0.0039 0.0040 0.0040 0.0041 0.0042 0.0043 0.0044 0.0045 0.0046 0.0045 0.0044 0.0044 0.0043 0.0042 0.0041 0.0041 0.0041 0.0040 0.0040 0.0040 0.0041 0.0041 0.0042 0.0043 0.0044 0.0045 0.0045 0.0039 0.0039 0.0040 0.0040 0.0040 0.0041 0.0041 0.0041 0.0042 0.0042 0.0042 0.0043 0.0042 0.0042 0.0041 0.0040 0.0040 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0040 0.0041 0.0042 0.0044 0.0045 0.0046 0.0047 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0040 0.0040 0.0040 0.0040 0.0040 0.0039 0.0039 0.0038 0.0038 0.0037 0.0037 0.0037 0.0038 0.0038 0.0038 0.0038 0.0039 0.0041 0.0042 0.0044 0.0045 0.0047 0.0048 0.0042 0.0042 0.0042 0.0042 0.0041 0.0041 0.0040 0.0040 0.0039 0.0038 0.0037 0.0036 0.0036 0.0036 0.0036 0.0035 0.0035 0.0035 0.0035 0.0036 0.0036 0.0037 0.0037 0.0039 0.0041 0.0043 0.0044 0.0046 0.0048 0.0050 0.0048 0.0047 0.0046 0.0045 0.0044 0.0043 0.0042 0.0042 0.0041 0.0041 0.0040 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0040 0.0040 0.0041 0.0041 0.0042 0.0044 0.0045 0.0047 0.0048 0.0050 0.0052 0.0054 0.0052 0.0050 0.0049 0.0047 0.0045 0.0044 0.0044 0.0044 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 0.0044 0.0044 0.0044 0.0045 0.0046 0.0047 0.0048 0.0049 0.0050 0.0051 0.0054 0.0060 0.0057 0.0055 0.0053 0.0050 0.0048 0.0046 0.0046 0.0046 0.0046 0.0046 0.0046 0.0046 0.0046 0.0046 0.0046 0.0047 0.0047 0.0047 0.0048 0.0048 0.0048 0.0049 0.0049 0.0050 0.0051 0.0051 0.0052 0.0053 0.0055 0.0065 0.0062 0.0059 0.0056 0.0053 0.0050 0.0048 0.0049 0.0049 0.0049 0.0049 0.0049 0.0050 0.0050 0.0050 0.0050 0.0051 0.0051 0.0051 0.0051 0.0052 0.0052 0.0052 0.0053 0.0053 0.0053 0.0054 0.0054 0.0055 0.0057

This should do everything you want with the interpolated data.

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[Veronica Vigil]

This is awesome. Thank you, this helped me get to where I need to be.

[Star Strider]

As always, my pleasure!