Let $$X= \{x|a_j^Tx\leq b_j, j=1,...,m \}$$ be a polyhedron, and p is a point inside a polyhedron as shown below. I want to derive an expression for calculating an orthogonal plane from point p which intersect the polyhedron. The orthogonal plane is constructed perpendicular to the trajectory at the considered point, i.e., p
In other words, this is what I want "Intersection of a Convex Polyhedron and a Plane"
This figure was taken from here: https://demonstrations.wolfram.com/IntersectionOfAConvexPolyhedronAndAPlane/
Any help will be appreciated.