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# NAME

Math::PlanePath::Rows -- points in fixed-width rows

# SYNOPSIS

`````` use Math::PlanePath::Rows;
my \$path = Math::PlanePath::Rows->new (width => 20);
my (\$x, \$y) = \$path->n_to_xy (123);``````

# DESCRIPTION

This path is rows of a given fixed width. For example width=7 is

``````    width => 7

3  |  22  23  24 ...
2  |  15  16  17  18  19  20  21
1  |   8   9  10  11  12  13  14
Y=0  |   1   2   3   4   5   6   7
-------------------------------
X=0   1   2   3   4   5   6``````

## 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, width => 7

3  |  21  22  23  24 ...
2  |  14  15  16  17  18  19  20
1  |   7   8   9  10  11  12  13
Y=0  |   0   1   2   3   4   5   6
-------------------------------
X=0   1   2   3   4   5   6``````

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::Rows->new (width => \$w)`
`\$path = Math::PlanePath::Rows->new (width => \$w, n_start => \$n)`

Create and return a new path object. A `width` 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 column -0.5 <= x < width+0.5 and y>=-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.

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