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 8The 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 11FUNCTIONS
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
$non the path. Points begin at 0 and if$n < 0then the return is an empty list.Fractional positions give an X,Y position along a straight line between the integer positions.
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
TerdragonMidpointbut 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/>.