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Math-PlanePath-77
River stage one • 3 direct dependents • 4 total dependents
2 ++
/ Math::PlanePath::DiagonalsAlternating

NAME

Math::PlanePath::DiagonalsAlternating -- points in diagonal stripes of alternating directions

SYNOPSIS

 use Math::PlanePath::DiagonalsAlternating;
 my $path = Math::PlanePath::DiagonalsAlternating->new;
 my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This path follows successive diagonals going from the Y axis down to the X axis and then back again,

      7  |  29 
      6  |  28  30
      5  |  16  27  31
      4  |  15  17  26  ...
      3  |   7  14  18  25 
      2  |   6   8  13  19  24 
      1  |   2   5   9  12  20  23
    Y=0  |   1   3   4  10  11  21  22
         +----------------------------
           X=0   1   2   3   4   5   6

The triangular numbers 1,3,6,10,etc, k*(k+1)/2, fall alternately on the X axis and Y axis. So 1,6,15,28,etc on the Y axis, and 3,10,21,36,etc on the X axis. Those on the Y axis are the hexagonal numbers j*(2j-1) and those on the X axis are the hexagonals of the second kind j*(2j+1).

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.

$path = Math::PlanePath::DiagonalsAlternating->new ()

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.

For $n < 1 the return is an empty list, it being considered the path begins at 1.

FORMULAS

Rectangle to N Range

Within each row increasing X is increasing N, and in each column increasing Y is increasing N. So in a rectangle the lower left corner is the minimum N and the upper right is the maximum N.

SEE ALSO

Math::PlanePath, Math::PlanePath::Diagonals, Math::PlanePath::DiagonalsOctant

HOME PAGE

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

LICENSE

Copyright 2010, 2011, 2012 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 <http://www.gnu.org/licenses/>.