It is hard to find the intersection of a surface and a plane (in general), as it is explained here by Patrikalakis et al. And it may be harder to obtain a smooth curve.
But if you can do with a number of points on the (branches of the) curve(s), you can:
- Find the scalar function d of the distance from the points on the surface to the plane
- Compute the contour lines of d of value 0, keeping the output of the function:
C = contour(x, y, d, [0 0]);
In C you can find all the points on the surface which belong to the intersection, see the documentation here: ContourMatrix property
