++ed by:

2 PAUSE users

Kevin Ryde
and 1 contributors


Math::PlanePath::PentSpiralSkewed -- integer points in a pentagonal shape


 use Math::PlanePath::PentSpiralSkewed;
 my $path = Math::PlanePath::PentSpiralSkewed->new;
 my ($x, $y) = $path->n_to_xy (123);


This path makes a pentagonal (five-sided) spiral with points skewed so as to fit a square grid and fully cover the plane.

          10 ...             2
         /  \  \
       11  3  9 20           1
      /  /  \  \  \
    12  4  1--2  8 19    <- y=0
      \  \       |  | 
       13  5--6--7 18       -1
         \          |    
          14-15-16-17       -2
     ^  ^  ^  ^  ^  ^ 
    -2 -1 x=0 1  2  3 ...

The pattern is similar to the SquareSpiral but cuts three corners which makes each cycle is faster. Each cycle is just 5 steps longer than the previous (where it's 8 for a SquareSpiral).


$path = Math::PlanePath::PentSpiral->new ()

Create and return a new PentSpiral spiral object.

($x,$y) = $path->n_to_xy ($n)

Return the x,y coordinates of point number $n on the path.

For $n < 1 the return is an empty list, it being considered the path starts at 1.

$n = $path->xy_to_n ($x,$y)

Return the point number for coordinates $x,$y. $x and $y are each rounded to the nearest integer, which has the effect of treating each point in the path as a square of side 1.


Math::PlanePath, Math::PlanePath::SquareSpiral, Math::PlanePath::DiamondSpiral, Math::PlanePath::HexSpiralSkewed




Math-PlanePath is Copyright 2010 Kevin Ryde

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.