++ed by:
Kevin Ryde
and 1 contributors

# 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.

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