NAME

Math::PlanePath::HexSpiralSkewed -- integer points in a diamond shape

SYNOPSIS

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

DESCRIPTION

This path makes a hexagonal spiral with points skewed so as to fit a square grid and fully cover the plane.

    13--12--11   ...              2
     |         \   \
    14   4---3  10  23            1
     |   |     \   \   \
    15   5   1---2   9  22    <- y=0
      \   \          |   | 
        16   6---7---8  21       -1
          \              |    
            17--18--19--20       -2

      ^   ^  ^   ^   ^   ^ 
     -2  -1 x=0  1   2   3  ...

The sequence is the same as for the plain HexSpiral, but this arrangement fits more points on a square grid. It's similar to the SquareSpiral but cuts two corners so each loop is 6 steps longer than the previous whereas for the SquareSpiral it's 8. See the DiamondSpiral for cutting all 4 corners.

FUNCTIONS

$path = Math::PlanePath::HexSpiral->new (key=>value, ...)

Create and return a new HexSpiral 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.

SEE ALSO

Math::PlanePath, Math::PlanePath::HexSpiral

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

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/>.