NAME
Math::PlanePath::Columns  points in fixedheight 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 zerobased.
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/mathplanepath/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde
This file is part of MathPlanePath.
MathPlanePath 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.
MathPlanePath 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 MathPlanePath. If not, see <http://www.gnu.org/licenses/>.