How do i find the intersection points between a surface and a patch?

Hello,

I am looking for a way to determine the intersection points between a surface and a patch as in the image. The result should be the (smooth) curve of these intersection points. Anybody who knows how to do this?

Greetings, Rudy

Answer 1

[Unai San Miguel]

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:

1. Find the scalar function d of the distance from the points on the surface to the plane
2. 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