++ed by:
Kevin Ryde
and 1 contributors

# NAME

Math::PlanePath::HexSpiral -- integer points in a diamond shape

# SYNOPSIS

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

# DESCRIPTION

This path makes a hexagonal spiral, with points spread out horizontally to fit on a square grid.

``````             28 -- 27 -- 26 -- 25                  3
/                    \
29    13 -- 12 -- 11    24               2
/     /              \     \
30    14     4 --- 3    10    23            1
/     /     /         \     \    \
31    15     5     1 --- 2     9    22    <- y=0
\     \     \              /     /
32    16     6 --- 7 --- 8    21           -1
\     \                    /
33    17 -- 18 -- 19 -- 20              -2
\
34 -- 35 ...                         -3

^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
-6 -5 -4 -3 -2 -1 x=0 1  2  3  4  5  6``````

Each horizontal gap is 2, so for instance n=1 is at x=0,y=0 then n=2 is at x=2,y=0. The diagonals are just 1 across, so n=3 is at x=1,y=1. Each alternate row is offset from the one above or below. The resulting "triangles" between the points are flatter than they ought to be. Drawn on a square grid the angle up is 45 degrees making an isosceles right triangle instead of 60 for an equilateral triangle.

# FUNCTIONS

`\$path = Math::PlanePath::HexSpiral->new ()`

Create and return a new HexSpiral path object.

`(\$x,\$y) = \$path->n_to_xy (\$n)`

Return the x,y coordinates of point number `\$n` on the path.

For `\$n < 1` the return is an empty list, it being considered the path starts at 1.

`\$n = \$path->xy_to_n (\$x,\$y)`

Return the point number for coordinates `\$x,\$y`. `\$x` and `\$y` are each rounded to the nearest integer, which has the effect of treating each `\$n` in the path as a square of side 1.

Only every second square in the plane has an N. If `\$x,\$y` is a position without an N then the return is `undef`.