++ed by:
BHANN EGOR

2 PAUSE users

Kevin Ryde
and 1 contributors

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 the plain HexSpiral, but this arrangement fits more points on a square grid. The skew pushes the top horizontal to the left, as illustrated by the following portion from the two. The bottom horizontal is similarly skewed but to the right.

    HexSpiralSkewed               HexSpiral

    13--12--11                   13--12--11       
     |         \                /          \      
    14          10            14            10    
     |             \         /                \  
    15               9     15                  9

Corners

HexSpiralSkeweed is similar to the SquareSpiral but cuts off the top right and bottom left two corners so that each loop is 6 steps longer than the previous whereas for the SquareSpiral it's 8. See "Corners" in Math::PlanePath::SquareSpiral for other corner cutting.

FUNCTIONS

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

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, Math::PlanePath::HeptSpiralSkewed, Math::PlanePath::PentSpiralSkewed, Math::PlanePath::DiamondSpiral

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/>.