Re: perl module or code for calculating the shortest distance between a line and a point (vector linear algebra)

A general algorithm for calculating the closest distance between a line and a point is described, for example, at http://math.ucsd.edu/~wgarner/math4c/derivations/distance/distptline.htm. Here's a script that illustrates this:

use strict;
use warnings;
# line passes through (x1, y1) and (x2, y2)
my ($x1, $y1) = (0, 2);
my ($x2, $y2) = (-2, 2);
# put it into the form y = mx + b
my $m = ($y2 - $y1) / ($x2 - $x1);
my $b = ($y1 * $x2 - $y2 * $x1) / ($x2 - $x1);
# target point is (x0, y0)
my ($x0, $y0) = (8, 0);
# shortest distance from line to target point
my $d = abs( $y0 - $m * $x0 - $b) / sqrt($m * $m + 1);
print "The closest distance is $d\n";
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Re^2: perl module or code for calculating the shortest distance between a line and a point (vector linear algebra) by spx2 (Deacon) on Jan 01, 2010 at 09:15 UTC
hi randyk, yes, that's true, for the plane. in his code he seems to use `$z(point)` which suggests these lines and points are in 3D space. the shortest distance from a point to a line is a perpendicular on the line passing through that point. see here the development of a formula for the problem in question.	[reply] [d/l]
Re^2: perl module or code for calculating the shortest distance between a line and a point (vector linear algebra) by salva (Canon) on Jan 01, 2010 at 10:35 UTC
Your code can't handle the case where $x2 == $x1.	[reply]