Math::PlanePath::PentSpiral -- integer points in a pentagonal shape
use Math::PlanePath::PentSpiral; my $path = Math::PlanePath::PentSpiral->new; my ($x, $y) = $path->n_to_xy (123);
This path makes a pentagonal (five-sided) spiral with points spread out to fit on a square grid.
22 3 23 10 21 2 24 11 3 9 20 1 25 12 4 1 2 8 19 <- y=0 26 13 5 6 7 18 ... -1 27 14 15 16 17 33 -2 28 29 30 31 32 -2 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ -6 -5 -4 -3 -2 -1 x=0 1 2 3 4 5 6 7
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 lower diagonals are 1 across and 1 down, so n=17 is at x=4,y=-2 and n=18 is x=5,y=-1. But the upper angles go 2 across and 1 up, so n=20 is x=4,y=1 then n=21 is x=2,y=2.
The effect is to make the sides equal length, except for a kink at the lower right corner. Only every second square in the plane is used. In the top half (y>=0) those squares line up, in the lower half (y<0) they're offset on alternate rows.
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::PentSpiral->new ()
Create and return a new pentagon spiral object.
($x,$y) = $path->n_to_xy ($n)
Return the X,Y coordinates of point number
$non the path.
$n < 1the 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
$yare each rounded to the nearest integer, which has the effect of treating each point in the path as a square of side 1.
Copyright 2010, 2011 Kevin Ryde
This file is part of Math-PlanePath.
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.
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