MUPAD: plotting the intersection of two functions

Dear sirs,

the problem I would like to solve is related to representation of constrained optimization problems in MUPAD, but in broader terms, this could apply to a variety of cases.

To exemplify, my problem is to trace on the surface of a target function like, for instance, z = x^2+y^2 its intersection with, say, a plane (the constraint) that according to its inclination would result on the surface of the target function in an ellipse, a circle or a parabola.

Of course, in a more general setting, the constraint itself needs not be linear.

The natural choice would seem plot::curve3d, but I am unable to parametrize the constraint function, particularly when it is a quadratic function such as an ellipse or a circle.

Also, all my initial equations are expressed in Cartesian coordinates.

Thanks to anyone who would share any useful suggestion on the subject.

Answer 1

[Christopher Creutzig]

For the special case of intersecting with an axes-parallel plane, it may be worth checking out the second example in the documentation of plot::Scene3d. For the general case, I am afraid there is no generic ready solution.