TL;DR

On with TASK #2 from the Perl Weekly Challenge #101. Enjoy!

# The challenge

You are given three points in the plane, as a list of six co-ordinates: A=(x1,y1)', B=(x2,y2) and C=(x3,y3). Write a script to find out if the triangle formed by the given three co-ordinates contain origin (0,0). Print 1 if found otherwise

# The questions

A few questions…

• is a point on the edge (or even a vertex) considered to be inside?
• the examples seems to imply that it is
• should we favour an integers-based solution?
• if not, what should our tolerance be?
• is inside a synonym for in the part of the plane delimited by the three segments and with a finite area?
• well, assume yes.

# The solution

I was thinking about a solution involving the vectors from the origin to the three points and how they revolve around the origin itself, then I thought that reinventing the wheel so late is moot and there’s surely some computational geometry article somewhere out there, just to surrender to the power of CPAN.

So… Math::Polygon.

First of all, it does indeed allow to solve the problem quite easily:

sub origin_containing_triangle ($A,$B, $C) { Math::Polygon->new($A, $B,$C, $A)->contains([0, 0]) ? 1 : 0; }  Then, it’s by Mark Overmeer, which I consider a warranty in terms of correctness and accuracy. So… by all means I’ll stick to this solution! #!/usr/bin/env perl use 5.024; use warnings; use experimental qw< postderef signatures >; no warnings qw< experimental::postderef experimental::signatures >; use Math::Polygon; sub origin_containing_triangle ($A, $B,$C) {
Math::Polygon->new($A,$B, $C,$A)->contains([0, 0]) ? 1 : 0;
}

my @pts;
push @pts, [splice @ARGV, 0, 2] while @ARGV;
say origin_containing_triangle(@pts[0..2]);
`

Stay safe!