| Math::PlanePath::StaircaseAlternating(3pm) | User Contributed Perl Documentation | Math::PlanePath::StaircaseAlternating(3pm) |
NAME¶
Math::PlanePath::StaircaseAlternating -- stair-step diagonals up and down
SYNOPSIS¶
use Math::PlanePath::StaircaseAlternating; my $path = Math::PlanePath::StaircaseAlternating->new; my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION¶
This path makes a staircase pattern up from Y axis down to the X and then back up again.
10 46
|
9 47--48
|
8 45 49--50
| |
7 44--43 51--52
| |
6 16 42--41 53--54
| | |
5 17--18 40--39 55--...
| |
4 15 19--20 38--37
| | |
3 14--13 21--22 36--35
| | |
2 2 12--11 23--24 34--33
| | | |
1 3-- 4 10-- 9 25--26 32--31
| | | |
Y=0 -> 1 5-- 6 8-- 7 27--28 30--29
^
X=0 1 2 3 4 5 6 7 8
Square Ends¶
Option "end_type => "square"" changes the path as follows, omitting one point at each end so as to square up the joins.
9 42--43
| |
8 41 44--45
| |
7 40--39 46--47
| |
6 . 38--37 48--49
| |
5 14--15 36--35 50--...
| | |
4 13 16--17 34--33
| | |
3 12--11 18--19 32--31
| | |
2 . 10-- 9 20--21 30--29
| | |
1 2-- 3 8-- 7 22--23 28--27
| | | | |
Y=0 -> 1 4-- 5-- 6 . 24--25--26
^
X=0 1 2 3 4 5 6 7 8
The effect is to shorten each diagonal by a constant 1 each time. The lengths of each diagonal still grow by +4 each time (or by +16 up and back).
N Start¶
The default is to number points starting N=1 as shown above. An optional "n_start" can give a different start, in the same pattern. For example to start at 0,
n_start => 0 n_start => 0, end_type=>"square"
46 47 41 42
44 48 49 40 43 44
43 42 50 51 39 38 45 46
15 41 40 52 53 37 36 47 48
16 17 39 38 ... 13 14 35 34 ...
14 18 19 37 36 12 15 16 33 32
13 12 20 21 35 34 11 10 17 18 31 30
1 11 10 22 23 33 32 9 8 19 20 29 28
2 3 9 8 24 25 31 30 1 2 7 6 21 22 27 26
0 4 5 7 6 26 27 29 28 0 3 4 5 23 24 25
FUNCTIONS¶
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
- "$path = Math::PlanePath::StaircaseAlternating->new ()"
- "$path = Math::PlanePath::StaircaseAlternating->new (end_type => $str, n_start => $n)"
- Create and return a new path object. The
"end_type" choices are
"jump" (the default) "square" - "($x,$y) = $path->n_to_xy ($n)"
- Return the X,Y coordinates of point number $n on the path.
OEIS¶
Entries in Sloane's Online Encyclopedia of Integer Sequences related to this path include
end_type=jump, n_start=1 (the defaults)
A084849 N on diagonal X=Y
end_type=jump, n_start=0
A014105 N on diagonal X=Y, second hexagonal numbers
end_type=jump, n_start=2
A096376 N on diagonal X=Y
end_type=square, n_start=1
A058331 N on diagonal X=Y, 2*squares+1
end_type=square, n_start=0
A001105 N on diagonal X=Y, 2*squares
SEE ALSO¶
Math::PlanePath, Math::PlanePath::Staircase, Math::PlanePath::DiagonalsAlternating
HOME PAGE¶
LICENSE¶
Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde
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 |