Re: Minimum distance from a point to a surface defined by constraints

From: The Qurqirish Dragon (qurqirishd_at_aol.com)
Date: 03/03/05 

Date: 3 Mar 2005 07:23:02 -0800

If the half-planes do not intersect, then there is no region (in more
than 2 dimensions no hypersurface) defined, and so you need to rephrase
the problem. For example, what if I choose P to be the origin, and give
the constraints x>1 and x<2.

What answer would you want to get here? By the way the problem is
phrased, there is no answer, as the restrictions leave you with an
empty set.
Note that since the vertices I look for are the solutions set of your
constraint equations (using equality, rather than inequality), the
assumption that the regions intersect is the same as assumingthat the
system of equations is consistant. If there is no intersection, then
this will be found before any distances are calculated.

Relevant Pages

  • Re: Minimum distance from a point to a surface defined by constraints
    ... If the half-planes do not intersect, then there is no region (in more ... than 2 dimensions no hypersurface) defined, and so you need to rephrase ... empty set. ... constraint equations, the ...
    (sci.math)
  • Re: Proposal: s1.intersects(s2)
    ... "these two sets intersect" is ... But you can't avoid treating the empty set as special, ... Of course if you exclude the empty set by definition, ... There's one, obvious, correct definition, as given above. ...
    (comp.lang.python)
  • Re: Proposal: s1.intersects(s2)
    ... def intersects: ... I'd rather see sets gain an method "isintersect" with the functionality ... "these two sets intersect" is ... -- the meaning of subset and superset with the empty set is ...
    (comp.lang.python)
  • Re: infinite sequence ring theory problem
    ... certainly false in some rings, so you must have some specific ring to ... >equal to J intersect S, show that IJ intersect S is not the empty set. ... --- Calvin ...
    (sci.math)