NAME

       Math::PlanePath::Columns -- points in fixed-height columns

SYNOPSIS

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

DESCRIPTION

       This path is columns of a given fixed height.  For example height 5 would be

                |
             4  |   5  10  15  20        <---  height==5
             3  |   4   9  14  19
             2  |   3   8  13  18
             1  |   2   7  12  17  ...
           Y=0  |   1   6  11  16  21
                 ----------------------
                  X=0   1   2   3   4  ...

   N Start
       The default is to number points starting N=1 as shown above.  An optional "n_start" can
       give a different start, with the same shape.  For example to start at 0,

           n_start => 0, height => 5

             4  |   4   9  14  19
             3  |   3   8  13  18
             2  |   2   7  12  17
             1  |   1   6  11  16  ...
           Y=0  |   0   5  10  15  20
                 ----------------------
                  X=0   1   2   3   4  ...

       The only effect is to push the N values around by a constant amount.  It might help match
       coordinates with something else zero-based.

FUNCTIONS

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

       "$path = Math::PlanePath::Columns->new (height => $h)"
       "$path = Math::PlanePath::Columns->new (height => $h, n_start => $n)"
           Create and return a new path object.  A "height" parameter must be supplied.

       "($x,$y) = $path->n_to_xy ($n)"
           Return the X,Y coordinates of point number $n in the path.

       "$n = $path->xy_to_n ($x,$y)"
           Return the point number for coordinates "$x,$y".

           $x and $y are rounded to the nearest integers, which has the effect of treating each
           point in the path as a square of side 1, so a rectangle $x >= -0.5 and -0.5 <= y <
           height+0.5 is covered.

       "($n_lo, $n_hi) = $path->rect_to_n_range ($x1,$y1, $x2,$y2)"
           The returned range is exact, meaning $n_lo and $n_hi are the smallest and biggest in
           the rectangle.

SEE ALSO

       Math::PlanePath, Math::PlanePath::Rows, Math::PlanePath::CoprimeColumns

HOME PAGE

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

LICENSE

       Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 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/>.