.. highlightlang:: us

.. _poly_hull:

poly_hull
=========

.. index:: poly_hull

.. us.tag  poly_hull NOTREADYENGLISH base_graph New363 Changed400

:ref:`poly_hull` calculates the convex hull in the x/y plane.

.. function::  rvIdx = poly_hull(x, y)
    rvIdx = poly_hull(x, y, opt)

.. us.return

**Return Value**

*rvIdx* are the hull indices. In case of an error *rvIdx* is a string vector
with two elements. The first element identifies the error, the second element is 
the error text.

.. us.params

**Parameters**

.. uparam:: x

   *x* is a vector with x coordinates. The vector must have the same number
   of elements as the vector *y*.

.. uparam:: y

   *y* is a vector with y coordinates. The vector must have the same number
   of elements as the vector *x*. At least 4 elements are necessary.

.. uparam:: opt

   If *opt* is set to 1, points on the edge of the hull will not be ignored.
   If set to 0 (default value) points on the edge of the hull will be ignored.

.. us.example

**Example**

::

   * poly_hull([0,1,1,0,0], [0,0,1,1,0])
       1.0000
       2.0000
       3.0000
       4.0000
       1.0000

::

   * poly_hull(rand(1,1000), rand(1,1000))
     443.0000
     970.0000
     939.0000
     591.0000
     526.0000
     776.0000
     584.0000
      92.0000
     536.0000
     877.0000
     580.0000
     238.0000
      50.0000
     875.0000
     338.0000
     230.0000
      44.0000
     288.0000
     243.0000
     443.0000

::

   * poly_hull([1,1,1],[1,1,1])
   2,x-poly-error
   Singular Input Data (e.g. Points form a line)

.. image:: S:/uniplot-obj/images/poly_hull.*

::

   idx = poly_hull(x = rand(1,1000), y = rand(1,1000))
   if (type(idx) == "string") {
      MessageBoxError("Error: " + idx[1] + "\n\n + idx[2]);
      return 0;
   }
   h = plot(x[idx], y[idx])
   h2 = plot(x, y, h[2])
   XYShowMarker(h2[3], TRUE)
   XYShowLine(h2[3], FALSE)
   LayerSetAxisMinMaxDelta(h2[2], "X", -0.1, 1.1, 0.1)
   LayerSetAxisMinMaxDelta(h2[2], "Y", -0.1, 1.1, 0.1)
   LayerShowGrid(h2[2], "X", FALSE, FALSE)
   LayerShowGrid(h2[2], "Y", FALSE, FALSE)
   LayerSetAxisTitle(h2[2], "X", "")
   LayerSetAxisTitle(h2[2], "Y", "")
   PageReplot(h2[1])

.. seealso::
   :ref:`poly_triangulate`

This function uses the qhull algorithm see:

Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., 
"The Quickhull algorithm for convex hulls," ACM Trans. on Mathematical
Software, Dec 1996. http://www.qhull.org/.

.. code-block:: none

                      Qhull, Copyright (c) 1993-2002

          The National Science and Technology Research Center for
           Computation and Visualization of Geometric Structures
                           (The Geometry Center)
                          University of Minnesota
                               400 Lind Hall
                           207 Church Street S.E.
                         Minneapolis, MN 55455  USA

                          email: qhull@geom.umn.edu

   This software includes Qhull from The Geometry Center.  Qhull is
   copyrighted as noted above.  Qhull is free software and may be obtained
   via http from www.geom.umn.edu.  It may be freely copied, modified,
   and redistributed under the following conditions:

   1. All copyright notices must remain intact in all files.

   2. A copy of this text file must be distributed along with any copies
      of Qhull that you redistribute; this includes copies that you have
      modified, or copies of programs or other software products that
      include Qhull.

   3. If you modify Qhull, you must include a notice giving the
      name of the person performing the modification, the date of
      modification, and the reason for such modification.

   4. When distributing modified versions of Qhull, or other software
      products that include Qhull, you must provide notice that the original
      source code may be obtained as noted above.

   5. There is no warranty or other guarantee of fitness for Qhull, it is
      provided solely "as is".  Bug reports or fixes may be sent to
      qhull_bug@geom.umn.edu; the authors may or may not act on them as
      they desire.

:sub:`id-749714`