NAME
Math::PlanePath::PeanoRounded -- 3x3 self-similar quadrant traversal, with rounded corners
SYNOPSIS
use Math::PlanePath::PeanoRounded;
my $path = Math::PlanePath::PeanoRounded->new;
my ($x, $y) = $path->n_to_xy (123);
# or another radix digits ...
my $path5 = Math::PlanePath::PeanoRounded->new (radix => 5);DESCRIPTION
This is a version of the PeanoCurve with rounded-off corners,
11 | 76-75 72-71 68-67
| / \ / \ / \
10 | 77 74-73 70-69 66
| | |
9 | 78 81-82 61-62 65
| \ / \ / \ /
8 | 79-80 83 60 63-64
| | |
7 | 88-87 84 59 56-55
| / \ / \ / \
6 | ...-89 86-85 58-57 54
| |
5 | 13-14 17-18 21-22 49-50 53
| / \ / \ / \ / \ /
4 | 12 15-16 19-20 23 48 51-52
| | | |
3 | 11 8--7 28-27 24 47 44-43
| \ / \ / \ / \ / \
2 | 10--9 6 29 26-25 46-45 42
| | | |
1 | 1--2 5 30 33-34 37-38 41
| / \ / \ / \ / \ /
Y=0 | 0 3--4 31-32 35-36 39-40
+------------------------------------------------------
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Radix
The radix parameter can do the calculation in a base other than 3, using the same kind of direction reversals. For example radix 5 gives 5x5 groups,
9 | 41-42 45-46 49-...
| / \ / \ /
8 | 40 43-44 47-48
| | radix=5
7 | 39 36-35 32-31
| \ / \ / \
6 | 38-37 34-33 30
| |
5 | 21-22 25-26 29
| / \ / \ /
4 | 20 23-24 27-28
| |
3 | 19 16-15 12-11
| \ / \ / \
2 | 18-17 14-13 10
| |
1 | 1--2 5--6 9
| / \ / \ /
Y=0 | 0 3--4 7--8
|
+---------------------------------
X=0 1 2 3 4 5 6 7 8 9If the radix is even then the ends of each group don't join up. For example in radix 4 N=31 isn't next to N=32.
7 | 30-29 26-25 32
| / \ / \ \
6 | 31 28-27 24 33--...
| |
5 | 17-18 21-22 |
| / \ / \ |
4 | 16 19-20 23
| |
3 | | 14-13 10--9
| | / \ / \
2 | 15 12-11 8
| |
1 | 1--2 5--6 |
| / \ / \ |
Y=0 | 0 3--4 7
+-----------------------------------------
X=0 1 2 4 5 6 7 8 9 10FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::PeanoRounded->new ()$path = Math::PlanePath::PeanoRounded->new (radix => $r)-
Create and return a new path object.
The optional
radixparameter gives the base for digit splitting. The default is ternary,radix => 3. ($x,$y) = $path->n_to_xy ($n)-
Return the X,Y coordinates of point number
$non the path. Points begin at 0 and if$n < 0then the return is an empty list.Fractional positions give an X,Y position along a straight line between the integer positions.
SEE ALSO
Math::PlanePath, Math::PlanePath::PeanoCurve, Math::PlanePath::DragonRounded
Guiseppe Peano, "Sur une courbe, qui remplit toute une aire plane", Mathematische Annalen, volume 36, number 1, 1890, p157-160
http://www.springerlink.com/content/w232301n53960133/
DOI 10.1007/BF01199438HOME PAGE
http://user42.tuxfamily.org/math-planepath/index.html
LICENSE
Copyright 2011, 2012 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.
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/>.