Plot the line of intersection between two surfaces with trisurf

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Referring to this thread:
Is there a possibility to plot the line of intersection, in case one of the surface is a trisurf?
In my use case, I'm not able to meshgrid one of the surfaces because of numerical quality. The amount of points is too big to pass to meshgrid. However, if I choose a random subset, the resulting surface does not reproduce the shape built up by my data points. What is possible is to use delauny and trisurf on the data.

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