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Possible to check interpolation for 3D surface plot?

When I hover my mouse over a given point in a surface plot, I see black lines on the surface tracing along points where x,y, or z remain the same.

Is there a way I can extract/view what the equations of those lines are?

@tensor Yes, the equations of the three lines, that are parallel to the axes and pass through the displayed point

  1. x=0.888, y=0.33 (this one is || to Oz)
  2. y=0.33, z=0.0146 -the line || Ox
  3. z=0.0146, x=0.88 - the line || Oy

In the 3d space a line has two equations, because it is defined as the intersection of two planes.

@empet Maybe I’m missing something, but it seems like you’re referring to the straight axis-parallel lines. I am looking for the equations of the curved lines which trace along the 3d surface.

If this is what you were referring to, could you please clarify what you mean, e.g. with the line where z=.0146?