intersection between plane and 3d points

Hi

I have to compute the intersection between a plane and a surface (for testing I generated it with meshgrid but I will have scattered 3d points instead sampled with fixed step in both x and y axis). I computed the distance from the plane of all points and picked only those whose distance was lower than a threshold.

it is correct so far but I would like to compute a smooth profile (a point every sample step), I managed to do something as shown in the figure but it works only for particular orientation of the plane so it is not general. (Actually what I did was to compute the mean of blocks of N red points and then apply linear interpolation in the middle)

Any ideas? Thank you

[Are Mjaavatten]

A very good solution is given by the Matworks support team at: https://se.mathworks.com/matlabcentral/answers/93623-how-do-i-plot-the-line-of-intersection-between-two-surfaces