NAME

Math::PlanePath::TerdragonRounded -- triangular dragon curve, with rounded corners

SYNOPSIS

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

 # or another radix digits ...
 my $path5 = Math::PlanePath::TerdragonRounded->new (radix => 5);

DESCRIPTION

This is a version of the terdragon curve with rounded-off corners,

    ...         44----43                                   14
      \        /        \
       46----45     .    42                                13
                        /
           .    40----41                                   12
               /
             39     .    24----23          20----19        11
               \        /        \        /        \
           .    38    25     .    22----21     .    18     10
               /        \                          /
       36----37     .    26----27     .    16----17         9
      /                          \        /
    35     .    32----31     .    28    15     .            8
      \        /        \        /        \
       34----33          30----29     .    14               7
                                          /
                             .    12----13     .            6
                                 /
                               11     .     8-----7         5
                                 \        /        \
                                  10-----9     .     6      4
                                                   /
                                      .     4-----5         3
                                          /
                                         3                  2
                                          \
                                      .     2               1
                                          /
                             .     0-----1     .       <- Y=0

     ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
    -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8

The plain TerdragonCurve is tripled in size and two points on each edge are visited by the TerdragonRounded here.

Arms

Multiple copies of the curve can be selected, each advancing successively. Like the main terdragon the rounded curve is 1/6 of the plane and 6 arms rotated by 60, 120, 180, 240 and 300 degrees mesh together perfectly.

arms => 6 begins as follows. N=0,6,12,18,etc is the first arm (the curve shown above), then N=1,7,13,19 the second copy rotated 60 degrees, N=2,8,14,20 the third rotated 120, etc.

    arms=>6              43----37          72--...
                        /        \        /
               ...    49          31    66          48----42
               /        \        /        \        /        \
             73          55    25          60----54          36
               \        /        \                          /
                67----61          19----13          24----30
                                          \        /
       38----32          14-----8           7    18          71---...
      /        \        /        \        /        \        /
    44          26----20           2     1          12    65
      \                                            /        \
       50----56           9     3     .     0-----6          59----53
               \        /                                            \
    ...         62    15           4     5          23----29          47
      \        /        \        /        \        /        \        /
       74----68          21    10          11----17          35----41
                        /        \
                33----27          16----22          64----70
               /                          \        /        \
             39          57----63          28    58          76
               \        /        \        /        \        /
                45----51          69    34          52    ...
                                 /        \        /
                          ...--75          40----46

     ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
    -11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8  9 10 11

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

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

$path = Math::PlanePath::TerdragonRounded->new (arms => $count)

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

Fractional positions give an X,Y position along a straight line between the integer positions.

FORMULAS

X,Y Visited

When arms=6 all "hex centred" points of the plane are visited, being those points with

    X+3Y mod 6 == 2 or 4        "hex_centred"

SEE ALSO

Math::PlanePath, Math::PlanePath::TerdragonCurve, Math::PlanePath::TerdragonMidpoint, Math::PlanePath::DragonRounded

Jorg Arndt http://www.jjj.de/fxt/#fxtbook section 1.31.4 "Terdragon and Hexdragon", where this rounded terdragon is called hexdragon.

HOME PAGE

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

LICENSE

Copyright 2012, 2013 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/>.