| Math::PlanePath::TerdragonRounded(3pm) | User Contributed Perl Documentation | Math::PlanePath::TerdragonRounded(3pm) |
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¶
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/>.
| 2021-01-23 | perl v5.32.0 |