Provided by: libmath-planepath-perl_129-1_all bug

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 3-long edge are
       visited by the "TerdragonRounded" here.

   Arms
       Multiple copies of the curve can be selected, each advancing successively.  The curve is
       1/6 of the plane (like the plain terdragon) 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.

   Level Methods
       "($n_lo, $n_hi) = $path->level_to_n_range($level)"
           Return "(0, 2 * 3**$level - 1)", or for multiple arms return "(0, 2 * $arms *
           3**$level - 1)".

           These level ranges are like "TerdragonMidpoint" but with 2 points on each line segment
           terdragon line segment instead of 1.

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, 2014, 2015, 2016, 2017, 2018, 2019, 2020 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/>.