Provided by: libmath-planepath-perl_129-1_all bug

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

           <http://oeis.org/A084849> (etc)

           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

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

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/>.