1Math::PlanePath::StaircUasseerAlCtoenrtnraitbiuntge(d3M)Paetrhl::DPolcaunmeePnattaht:i:oSntaircaseAlternating(3)
2
6 Math::PlanePath::StaircaseAlternating -- stair-step diagonals up and
7 down
8
10 use Math::PlanePath::StaircaseAlternating;
11 my $path = Math::PlanePath::StaircaseAlternating->new;
12 my ($x, $y) = $path->n_to_xy (123);
13
15 This path makes a staircase pattern up from Y axis down to the X and
16 then back up again.
17 10 46
19 |
20 9 47--48
21 |
22 8 45 49--50
23 | |
24 7 44--43 51--52
25 | |
26 6 16 42--41 53--54
27 | | |
28 5 17--18 40--39 55--...
29 | |
30 4 15 19--20 38--37
31 | | |
32 3 14--13 21--22 36--35
33 | | |
34 2 2 12--11 23--24 34--33
35 | | | |
36 1 3-- 4 10-- 9 25--26 32--31
37 | | | |
38 Y=0 -> 1 5-- 6 8-- 7 27--28 30--29
39 ^
41 X=0 1 2 3 4 5 6 7 8
42 Square Ends
44 Option "end_type => "square"" changes the path as follows, omitting one
45 point at each end so as to square up the joins.
46 9 42--43
48 | |
49 8 41 44--45
50 | |
51 7 40--39 46--47
52 | |
53 6 . 38--37 48--49
54 | |
55 5 14--15 36--35 50--...
56 | | |
57 4 13 16--17 34--33
58 | | |
59 3 12--11 18--19 32--31
60 | | |
61 2 . 10-- 9 20--21 30--29
62 | | |
63 1 2-- 3 8-- 7 22--23 28--27
64 | | | | |
65 Y=0 -> 1 4-- 5-- 6 . 24--25--26
66 ^
68 X=0 1 2 3 4 5 6 7 8
69 The effect is to shorten each diagonal by a constant 1 each time. The
71 lengths of each diagonal still grow by +4 each time (or by +16 up and
72 back).
73 N Start
75 The default is to number points starting N=1 as shown above. An
76 optional "n_start" can give a different start, in the same pattern.
77 For example to start at 0,
78 n_start => 0 n_start => 0, end_type=>"square"
80 46 47 41 42
82 44 48 49 40 43 44
83 43 42 50 51 39 38 45 46
84 15 41 40 52 53 37 36 47 48
85 16 17 39 38 ... 13 14 35 34 ...
86 14 18 19 37 36 12 15 16 33 32
87 13 12 20 21 35 34 11 10 17 18 31 30
88 1 11 10 22 23 33 32 9 8 19 20 29 28
89 2 3 9 8 24 25 31 30 1 2 7 6 21 22 27 26
90 0 4 5 7 6 26 27 29 28 0 3 4 5 23 24 25
91
93 See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
94 classes.
95 "$path = Math::PlanePath::StaircaseAlternating->new ()"
97 "$path = Math::PlanePath::StaircaseAlternating->new (end_type => $str,
98 n_start => $n)"
99 Create and return a new path object. The "end_type" choices are
100 "jump" (the default)
102 "square"
103 "($x,$y) = $path->n_to_xy ($n)"
105 Return the X,Y coordinates of point number $n on the path.
106
108 Entries in Sloane's Online Encyclopedia of Integer Sequences related to
109 this path include
110 <http://oeis.org/A084849> (etc)
112 end_type=jump, n_start=1 (the defaults)
114 A084849 N on diagonal X=Y
115 end_type=jump, n_start=0
116 A014105 N on diagonal X=Y, second hexagonal numbers
117 end_type=jump, n_start=2
118 A096376 N on diagonal X=Y
119 end_type=square, n_start=1
121 A058331 N on diagonal X=Y, 2*squares+1
122 end_type=square, n_start=0
123 A001105 N on diagonal X=Y, 2*squares
124
126 Math::PlanePath, Math::PlanePath::Staircase,
127 Math::PlanePath::DiagonalsAlternating
128
130 <http://user42.tuxfamily.org/math-planepath/index.html>
131
133 Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 Kevin Ryde
134 Math-PlanePath is free software; you can redistribute it and/or modify
136 it under the terms of the GNU General Public License as published by
137 the Free Software Foundation; either version 3, or (at your option) any
138 later version.
139 Math-PlanePath is distributed in the hope that it will be useful, but
141 WITHOUT ANY WARRANTY; without even the implied warranty of
142 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
143 General Public License for more details.
144 You should have received a copy of the GNU General Public License along
146 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
147perl v5.32.0 2020-M0a7t-h2:8:PlanePath::StaircaseAlternating(3)