3D plot to 2D plot

Question

I think someone should have asked this, but I could not find the answer. If anyone knows similar question, please let me know on the comment!

I want to convert 3D data to 2D cross section data.

For example, I have 3D data such as

Flatten[Table[{i, j, Sqrt[(i/2)^2 + j^2]}, {i, -100, 100}, {j, -100, 100}], 1]

Data looks like this.

I want to see the cross-sectional plot along the linear line. If I have any linear line on this 3D plot such as

I am expected to get 2D data like this along the linear cut that I made

Because I know how the function looks like so I can analytically calculate the 2d cross-section.

Assume that I do not know how the data looks like, can I do it numerically with Mathematica? Does it still work even if I have big data such as (2500x2500x2500)?

Answer 1

You can create an interpolating function that you can then call with a parametric equation representing cross sections. Try this:

    dat = Flatten[Table[{i, j, Sqrt[(i/2)^2 + j^2]}, {i, -100, 100}, {j, -100, 100}], 1];
    res = Interpolation[dat];
    Plot[{res[t, t/2], res[t, t], res[t, -t + 3]}, {t, -100, 100}]
    Show[{ListContourPlot[dat], ParametricPlot[{{t, t/2}, {t, t}, {t, -t + 3}}, {t, -100, 100}]}]