PWC101 - Origin-containing Triangle


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!

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