1Math::PlanePath::TerdraUgsoenrRoCuonndterdi(b3u)ted PerlMaDtohc:u:mPelnatnaetPiaotnh::TerdragonRounded(3)
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NAME

6       Math::PlanePath::TerdragonRounded -- triangular dragon curve, with
7       rounded corners
8

SYNOPSIS

10        use Math::PlanePath::TerdragonRounded;
11        my $path = Math::PlanePath::TerdragonRounded->new;
12        my ($x, $y) = $path->n_to_xy (123);
13
14        # or another radix digits ...
15        my $path5 = Math::PlanePath::TerdragonRounded->new (radix => 5);
16

DESCRIPTION

18       This is a version of the terdragon curve with rounded-off corners,
19
20           ...         44----43                                   14
21             \        /        \
22              46----45     .    42                                13
23                               /
24                  .    40----41                                   12
25                      /
26                    39     .    24----23          20----19        11
27                      \        /        \        /        \
28                  .    38    25     .    22----21     .    18     10
29                      /        \                          /
30              36----37     .    26----27     .    16----17         9
31             /                          \        /
32           35     .    32----31     .    28    15     .            8
33             \        /        \        /        \
34              34----33          30----29     .    14               7
35                                                 /
36                                    .    12----13     .            6
37                                        /
38                                      11     .     8-----7         5
39                                        \        /        \
40                                         10-----9     .     6      4
41                                                          /
42                                             .     4-----5         3
43                                                 /
44                                                3                  2
45                                                 \
46                                             .     2               1
47                                                 /
48                                    .     0-----1     .       <- Y=0
49
50            ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
51           -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8
52
53       The plain "TerdragonCurve" is tripled in size and two points on each
54       3-long edge are visited by the "TerdragonRounded" here.
55
56   Arms
57       Multiple copies of the curve can be selected, each advancing
58       successively.  The curve is 1/6 of the plane (like the plain terdragon)
59       and 6 arms rotated by 60, 120, 180, 240 and 300 degrees mesh together
60       perfectly.
61
62       "arms => 6" begins as follows.  N=0,6,12,18,etc is the first arm (the
63       curve shown above), then N=1,7,13,19 the second copy rotated 60
64       degrees, N=2,8,14,20 the third rotated 120, etc.
65
66           arms=>6              43----37          72--...
67                               /        \        /
68                      ...    49          31    66          48----42
69                      /        \        /        \        /        \
70                    73          55    25          60----54          36
71                      \        /        \                          /
72                       67----61          19----13          24----30
73                                                 \        /
74              38----32          14-----8           7    18          71---...
75             /        \        /        \        /        \        /
76           44          26----20           2     1          12    65
77             \                                            /        \
78              50----56           9-----3     .     0-----6          59----53
79                      \        /                                            \
80           ...         62    15           4     5          23----29          47
81             \        /        \        /        \        /        \        /
82              74----68          21    10          11----17          35----41
83                               /        \
84                       33----27          16----22          64----70
85                      /                          \        /        \
86                    39          57----63          28    58          76
87                      \        /        \        /        \        /
88                       45----51          69    34          52    ...
89                                        /        \        /
90                                 ...--75          40----46
91
92            ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
93           -11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8  9 10 11
94

FUNCTIONS

96       See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path
97       classes.
98
99       "$path = Math::PlanePath::TerdragonRounded->new ()"
100       "$path = Math::PlanePath::TerdragonRounded->new (arms => $count)"
101           Create and return a new path object.
102
103       "($x,$y) = $path->n_to_xy ($n)"
104           Return the X,Y coordinates of point number $n on the path.  Points
105           begin at 0 and if "$n < 0" then the return is an empty list.
106
107           Fractional positions give an X,Y position along a straight line
108           between the integer positions.
109
110   Level Methods
111       "($n_lo, $n_hi) = $path->level_to_n_range($level)"
112           Return "(0, 2 * 3**$level - 1)", or for multiple arms return "(0, 2
113           * $arms * 3**$level - 1)".
114
115           These level ranges are like "TerdragonMidpoint" but with 2 points
116           on each line segment terdragon line segment instead of 1.
117

FORMULAS

119   X,Y Visited
120       When arms=6 all "hex centred" points of the plane are visited, being
121       those points with
122
123           X+3Y mod 6 == 2 or 4        "hex_centred"
124

SEE ALSO

126       Math::PlanePath, Math::PlanePath::TerdragonCurve,
127       Math::PlanePath::TerdragonMidpoint, Math::PlanePath::DragonRounded
128
129       Jorg Arndt "http://www.jjj.de/fxt/#fxtbook" section 1.31.4 "Terdragon
130       and Hexdragon", where this rounded terdragon is called hexdragon.
131

HOME PAGE

133       <http://user42.tuxfamily.org/math-planepath/index.html>
134

LICENSE

136       Copyright 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin
137       Ryde
138
139       This file is part of Math-PlanePath.
140
141       Math-PlanePath is free software; you can redistribute it and/or modify
142       it under the terms of the GNU General Public License as published by
143       the Free Software Foundation; either version 3, or (at your option) any
144       later version.
145
146       Math-PlanePath is distributed in the hope that it will be useful, but
147       WITHOUT ANY WARRANTY; without even the implied warranty of
148       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
149       General Public License for more details.
150
151       You should have received a copy of the GNU General Public License along
152       with Math-PlanePath.  If not, see <http://www.gnu.org/licenses/>.
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156perl v5.36.0                      2023-01-2M0ath::PlanePath::TerdragonRounded(3)
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