orthProj

Arguments

data

a n by 2 array. The first column contains the X coordinates of the polyline, 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 orthogonal 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(), isoview()
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;

See Also

• proj — projection
• householder — Householder orthogonal reflexion matrix. Symetrical wrt a plane
• scaling — affine transformation of a set of points