I'm a little late to the party on this one, but wanted to share my solution anyway since it covers all cases.

The only trick to this problem is realizing that you need the following three equations:

Assuming you want a third point to be within a specified uncertainty that is either constant or relative to the segment length, than the following would work:

use Test::More tests => 3*(2*6 + 1); use strict; use warnings; local $" = ','; # Slope 1 { my $matcher = path_matcher({ p1 => [0,0], p2 => [100,100], }); # Points on edge of tolerance for ([0,20], [20,0], [40,60], [60,40], [80,100], [100,80]) { ok($matcher->(@$_), "slope 1: match [@$_]"); } # Out of bounds for ([0,21], [21,0], [40,61], [61,40], [80,101], [101,80], [-1,20] +) { ok(!$matcher->(@$_), "slope 1: not match [@$_]"); } } # Slope 0 { my $matcher = path_matcher({ p1 => [0,50], p2 => [100,50], }); # Boundary cases for ([0,60], [0,40], [50,60], [50,40], [100,60], [100,40]) { ok($matcher->(@$_), "slope 0: match [@$_]"); } # Out of bounds for ([0,61], [0,39], [50,61], [50,39], [100,61], [100,39], [-1,60] +) { ok(!$matcher->(@$_), "slope 0: not match [@$_]"); } } # Slope INF { my $matcher = path_matcher({ p1 => [50,0], p2 => [50,100], }); # Boundary cases for ([40,0], [60,0], [40,50], [60,50], [40,100], [60,100]) { ok($matcher->(@$_), "slope INF: match [@$_]"); } # Out of bounds for ([39,0], [61,0], [39,50], [61,50], [39,100], [61,100], [40,-1] +) { ok(!$matcher->(@$_), "slope INF: not match [@$_]"); } } ### ### Begin Actual functionality sub path_matcher { my ($args_ref) = @_; my $p1 = delete $args_ref->{p1} || [delete @$args_ref{qw(x1 y1)}]; my $p2 = delete $args_ref->{p2} || [delete @$args_ref{qw(x2 y2)}]; my $sigma = delete $args_ref->{sigma} // '10%'; die "Unknown parameters" if keys %$args_ref; die "Points must be defined" if grep {! defined} (@$p1, @$p2); # Order by x and y ($p1, $p2) = sort {$a->[0] <=> $b->[0] || $a->[1] <=> $b->[1]} ($p +1, $p2); my ($x1, $y1) = @$p1; my ($x2, $y2) = @$p2; # Solve y = m x + b my $dX = $x2 - $x1; my $dY = $y2 - $y1; my $m = $dX == 0 ? undef : $dY / $dX; my $b = $dX == 0 ? undef : $y1 - $m * $x1; # Sigma as a percentage of segment length if ($sigma =~ s/%//) { my $length = sqrt($dX ** 2 + $dY ** 2); $sigma *= $length / 100; } # Perpendicular M # M = -1 / m; # Y = M x + B my $M = ! defined $m ? 0 : $m == 0 ? undef : -1 / $m; # Anonymous sub to match multiple points. return sub { my ($x, $y) = @_; # Calculate [X,Y]: closest point on segment to [x,y] my ($X, $Y); # Vertical Line (constant x) if (! defined $m) { $X = $x1; $Y = $y; $Y = $y1 if $Y < $y1; $Y = $y2 if $Y > $y2; # Horizontal Line (constant y) } elsif ($m == 0) { $X = $x; $X = $x1 if $X < $x1; $X = $x2 if $X > $x2; $Y = $y1; # Regular line } else { my $B = $y - $M * $x; $X = ($B - $b) / ($m - $M); $Y = $m * $X + $b; ($X,$Y) = ($x1, $y1) if $X < $x1; ($X,$Y) = ($x2, $y2) if $X > $x2; } my $dist = sqrt(($x-$X) ** 2 + ($y-$Y) ** 2); return $dist <= $sigma; }; }

In reply to Re: Check if line is straight by wind
in thread Check if line is straight by Anonymous Monk

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