--- name: "Math::PlanePath::TerdragonRounded" section: "3pm" platform: "linux" package: "libmath-planepath-perl" version: "129-1" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/Math::PlanePath::TerdragonRounded" --- # 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 \.