<?xml version="1.0" encoding="ISO-8859-1"?><refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="pl_bb"><info><pubdate>04-Apr-2006</pubdate></info><refnamediv><refname>pl_bb</refname><refpurpose>Lower convex envelope/convex hull, Beneath-Beyond algorithm</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>[bbx,bby] = pl_bb (X,Y)</synopsis></refsynopsisdiv>

  
   <refsection><title>Parameters</title>
  
      <variablelist>

    
         <varlistentry>
    
            <term>X</term>
    
            <listitem>
       
               <para>column vector. A grid of points on which the function is sampled.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>Y</term>
    
            <listitem>
       
               <para>column vector. The value of the function on the grid X: usually Y(i)=f(X(i)) for some function f.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>bbx</term>
    
            <listitem>
       
               <para>column vector. X-coordinates of the vertices of the lower convex hull.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>bby</term>
    
            <listitem>
       
               <para>column vector. Y-coordinates of the vertices of the lower convex hull.
       </para>
    
            </listitem>
    
         </varlistentry>
  
      </variablelist>
  
   </refsection>
 
  
   <refsection><title>Description</title>

     
         <para>
        Compute numerically the lower convex envelope of the set of points (X(i), Y(i)) and returns the coordinates of the vertices of the lower convex hull.
     </para>
     
         <para>
	pl_bb implements the Beneath-Beyond algorithm to achieve a linear-time algorithm.
     </para>

  
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
    X=[-2:0.5:2]';
    Y=(X.^2-1)^2;
    [bbx,bby]=pl_bb(X,Y);
    plot2d(X,Y,2,rect=[-3,-1,3,5]);
    plot(X,Y,'squareblue');
    plot(bbx,bby,'*red');
    plot2d(bbx,bby,5);
  ]]></programlisting></refsection>

  
   <refsection><title>See Also</title><simplelist type="inline">
	  
      <member> 
         <link linkend="pl_lft_llt">pl_lft_llt</link> 
      </member>
  
   </simplelist></refsection>

  
   <refsection><title>Authors</title><para>
	  
      <literal>Yves Lucet</literal>, University of British Columbia, BC, Canada
  </para></refsection>

  
   <refsection><title>Bibliography</title>

   <itemizedlist>

     <listitem>F. P. Preparata and M. I. Shamos, Computational Geometry An Introduction, Series: Monographs in Computer Science, 1st ed. 1985. Corr. 5th printing 1993.</listitem>

   </itemizedlist>

   </refsection>

</refentry>
