Home > mpt > extras > control > optmerge > mpt_intersectHP1.m

mpt_intersectHP1

PURPOSE ^

Tobias Geyer, 2003-2004

SYNOPSIS ^

function m = mpt_intersectHP1(H, K, a, b, lpsolver, tol);

DESCRIPTION ^

 Tobias Geyer, 2003-2004
 Does the hyperplane a*x=b intersect with the polyhedron H*x<=K?

 inputs:
 H, K: polyhedron: H*x <= K
 a, b: hyperplane: a*x = b, where the norm of a is equal to 1
 lpsolver
 tolerance
 
 output:
 m = 0: the hyperplane intersects with the polyhedron
    +1: the polyhedron lies on the + side of the hyperplane (and does not intersect)
    -1: the polyhedron lies on the - side of the hyperplane (and does not intersect)

 remarks:
 * The tolerance is used to relax the (distances in the) inequalities,
   i.e. we want to avoid, that the algorithm determines that the hyperplane 
   cuts the polyhedron, when the hyperplane is only touching it.
 * Relying on the fact, that the hyperplane a*x=b is normed allows us to
   calculate the distance to the Chebycheff center (this is new compared to ver. 0)
   speeding up the function

CROSS-REFERENCE INFORMATION ^

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