orthProj
========

Computes the orthogonal projection of a point to a polyline in the
plane.



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [d,ptp,ind,c] = orthProj(data,pt)




Arguments
~~~~~~~~~

:data a n by 2 array. The first column contains the X coordinates of
  the poyline, while the second one contains the Y coordinates.
: :pt an array with 2 entries: the coordinates of the point
: :d The minimum distance between the given point and a polyline data
  point.
: :ptp an array with 2 entries: the coordinates of the point that
  realizes the minimum distance
: :ind The polyline closest point lies on the segment `[ind ind+1]`.
: :c The interpolation coefficient of the orthonal projection.
:



Description
~~~~~~~~~~~

Computes the orthogonal projection of a point to a polyline in the
plane.



Examples
~~~~~~~~


::

    x=`linspace`_(0,1,30)';
    y=`sin`_(4*x.^3)/2;
    `clf`_();a=`gca`_();a.isoview='on';
    `plot`_(x,y)
    pt=[0.7 0.3];
    `plot`_(pt(1),pt(2),'xb')
    [d,ptp,ind,c]=orthProj([x y],pt);
    `plot`_(x(ind:ind+1),y(ind:ind+1),'+r')
    `xpoly`_([pt(1);ptp(1)],[pt(2);ptp(2)])
    e=`gce`_();e.polyline_style=4;e.arrow_size_factor = 1.5;
    
    pt=[0.75 -0.3];
    `plot`_(pt(1),pt(2),'xb')
    [d,ptp,ind,c]=orthProj([x y],pt);
    `plot`_(x(ind:ind+1),y(ind:ind+1),'+r')
    `xpoly`_([pt(1);ptp(1)],[pt(2);ptp(2)])
    e=`gce`_();e.polyline_style=4;e.arrow_size_factor = 1.5;