# ETOOBUSY ðŸš€ minimal blogging for the impatient

# PWC101 - Origin-containing Triangle

**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 questionsâ€¦

- 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 thereâ€™s surely some computational geometry article somewhere out there, just to surrender to the power of CPAN.

Soâ€¦ 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, itâ€™s by Mark Overmeer, which I consider a warranty in terms of correctness and accuracy.

Soâ€¦ by all means Iâ€™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!