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Math::PlanePath::TerdragonRounded -- triangular dragon curve, with rounded corners
Contents
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
Formulas
X,YVisited
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"
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.
LevelMethods
"($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.
Home Page
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/>.
perl v5.32.0 2021-01-23 Math::PlanePath::TerdragonRounded(3pm)
Name
Math::PlanePath::TerdragonRounded -- triangular dragon curve, with rounded corners
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.
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);
PNG Icons