 Math::PlanePath::Columns(3) 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.

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