++ed by:
BHANN EGOR

2 PAUSE users

Kevin Ryde
and 1 contributors

NAME

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

SYNOPSIS

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

DESCRIPTION

This path makes a hexagonal spiral, with points spread out horizontally to fit on a square grid.

             28 -- 27 -- 26 -- 25                  3
            /                    \
          29    13 -- 12 -- 11    24               2
         /     /              \     \
       30    14     4 --- 3    10    23            1
      /     /     /         \     \    \
    31    15     5     1 --- 2     9    22    <- y=0
      \     \     \              /     /
       32    16     6 --- 7 --- 8    21           -1
         \     \                    /
          33    17 -- 18 -- 19 -- 20              -2
            \
             34 -- 35 ...                         -3

     ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
    -6 -5 -4 -3 -2 -1 x=0 1  2  3  4  5  6

Each horizontal gap is 2, so for instance n=1 is at x=0,y=0 then n=2 is at x=2,y=0. The diagonals are just 1 across, so n=3 is at x=1,y=1. Each alternate row is offset from the one above or below. The resulting "triangles" between the points are flatter than they ought to be. Drawn on a square grid the angle up is 45 degrees making an isosceles right triangle instead of 60 for an equilateral triangle.

FUNCTIONS

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

Create and return a new HexSpiral path 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 $n in the path as a square of side 1.

Only every second square in the plane has an N. If $x,$y is a position without an N then the return is undef.

SEE ALSO

Math::PlanePath, Math::PlanePath::HexSpiralSkewed, Math::PlanePath::TriangleSpiral

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/>.