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;