Generic hex field definition

Direction ranges from 0 to 5 by sides of the hexagon, we use North, South, West, East definitions for simplicity

Get q coordinate for Hex as Float value

q IntCubeHex ( 2, 3, -5 ) == 2.0

Get q coordinate for Hex as Int value, its generally not recommended to use on FloatCubeHex

intQ IntCubeHex ( 2, 3, -5 ) == 2

Get r coordinate for Hex as Float value

r IntCubeHex ( 2, 3, -5 ) == 3.0

Get r coordinate for Hex as Int value, its generally not recommended to use on FloatCubeHex

intR IntCubeHex ( 2, 3, -5 ) == 3

Get s coordinate for Hex as Float value

s IntCubeHex ( 2, 3, -5 ) == -5.0

Get s coordinate for Hex as Int value, its generally not recommended to use on FloatCubeHex

intS IntCubeHex ( 2, 3, -5 ) == 3

Build Hex object from Int coordinates

intFactory ( 2, 3 )
    |> eq (IntCubeHex ( 2, 3, -5 ))

Build Hex object from Float coordinates

floatFactory ( 2.5, 3.5 )
    |> eq (FloatCubeHex ( 2.5, 3.5, -6.0 ))

Convert Hex to IntCubeHex coordinate systems

FloatCubeHex ( 2.5, 3.5, -6.0 )
    |> toIntHex
    |> eq (IntCubeHex ( 2, 4, -6 ))

Convert Hex to FloatCubeHex coordinate systems

IntCubeHex ( 2, 3, -5 )
    |> toFloatHex
    |> eq (FloatCubeHex ( 2.0, 3.0, -5.0 ))

Compare two Hex definitions, support both axial and cubic coordinates.

Not a strict comparation, FloatCubeHex is converted to IntCubeHex.

IntCubeHex ( 2, 3, -5 )
    |> eq (IntCubeHex ( 2, 3, -5 ))


AxialHex ( 2, 3 )
    |> eq (AxialHex ( 2, 3 ))

Compare two Hex definitions, if they are not equal, inversion of eq

IntCubeHex ( 2, 3, -5 )
    |> noteq (IntCubeHex ( 1, 1, -2 ))


AxialHex ( 2, 3 )
    |> noteq (AxialHex ( 2, 1 ))

Since cube coordinates come from 3d cartesian coordinates, I automatically get things like addition, subtraction, multiplication, and division. For example, you can have Hex(2, 0, -2) that represents two steps northeast, and add that to location Hex(3, -5, 2) the obvious way: Hex(2 + 3, 0 + -5, -2 + -2). With other coordinate systems like offset coordinates, you can’t do that and get what you want. These operations are just what you’d implement with 3d cartesian vectors, but I am using q, r, s names in this class instead of x, y, z

IntCubeHex ( 2, 3, -5 )
    |> add (IntCubeHex ( 1, 2, -3 ))
    |> eq (IntCubeHex ( 3, 5, -8 ))

Subtraction of Hexes, more info in sum description

IntCubeHex ( 1, 2, -3 )
    |> sub (IntCubeHex ( 2, 3, -5 ))
    |> eq (IntCubeHex ( 1, 1, -2 ))

Multiplication of Hexes, more info in sum description

IntCubeHex ( 2, 3, -5 )
    |> mult 5
    |> eq (IntCubeHex ( 10, 15, -25 ))

Length of Hex.

length (IntCubeHex ( 2, 3, -5 )) == 5


length (FloatCubeHex ( 2.2, 3.3, -5.5 )) == 5

The distance between two hexes is the length of the line between them.

distance (IntCubeHex ( 2, 3, -5 )) (FloatCubeHex ( 3.2, 4.3, -7.5 )) == 2

Direction relative to Hex polygon lines, we used shortcuts for the mix of North, East, South, West directions

With distance, we defined two functions: length works on one argument and distance works with two. The same is true with neighbors. The direction function is with one argument and the neighbor function is with two.

neighbor (IntCubeHex ( 2, 3, -5 )) NW
    |> eq (IntCubeHex ( 2, 4, -6 ))