The code

map {$x += $$_[0]; $y += $$_[1];} @{$r{$k};};
is better written as:
for (@{ $r{$k} })   { $x += $_->[0]; $y += $_->[1]; }
(Using map statement in void context in lieu of for is confusing.)

The dereferences are used because the structure is populated with array references. In other words, you have a hash of arrays (HoA). See perldata, perldsc.

Specifically, look at the matching statements: 

push @{ $r{ ... } }, [ ... ];
...
for (@{ $r{ ... } })  { ... $_->[...] }

[download]
The first populates the HoA with necessary data. The second one uses this data further down. Why HoA, why the need for array [ constructors ] and dereferences? Because one scalar was not enough. The original programmer needed to track two values and used the small arrays as tuples.

In reply to Re: Code clarification - use of map and $$_ by Anonymous Monk
in thread Code clarification - use of map and $$_ by Anonymous Monk

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