Class HexMath

Hexagon math helper class. Coordinate conversions and hexagon geometry calculations. Supports axial, cube and offset coordinates. Supports flat top and pointy top hexagons. Supports odd and even layouts.

Inheritance
object
HexMath
Inherited Members
Namespace: Fwt.Core
Assembly: fwt.core.dll
Syntax
[BurstCompile]
public static class HexMath

Fields

Directions_Axial

All directions for axial coordinates

Declaration
public static readonly FixedArray8<int2> Directions_Axial
Field Value
Type Description
FixedArray8<int2>

Directions_Cube

All directions for cube coordinates

Declaration
public static readonly FixedArray8<int3> Directions_Cube
Field Value
Type Description
FixedArray8<int3>

Directions_Offset_Even_Flat

All directions for even layout flat top hexagons

Declaration
public static readonly FixedArray16<int2> Directions_Offset_Even_Flat
Field Value
Type Description
FixedArray16<int2>

Directions_Offset_Even_Point

All directions for even layout pointy top hexagons

Declaration
public static readonly FixedArray16<int2> Directions_Offset_Even_Point
Field Value
Type Description
FixedArray16<int2>

Directions_Offset_Odd_Flat

All directions for odd layout flat top hexagons

Declaration
public static readonly FixedArray16<int2> Directions_Offset_Odd_Flat
Field Value
Type Description
FixedArray16<int2>

Directions_Offset_Odd_Point

All directions for odd layout pointy top hexagons

Declaration
public static readonly FixedArray16<int2> Directions_Offset_Odd_Point
Field Value
Type Description
FixedArray16<int2>

Sqrt3

Square root of 3 (used for calculations with hexagons)

Declaration
public static readonly float Sqrt3
Field Value
Type Description
float

Methods

AxialToCube(in int2)

Converts axial coordinates to cube coordinates

Declaration
public static int3 AxialToCube(in int2 axialCoord)
Parameters
Type Name Description
int2 axialCoord

Axial coordinate to be converted
Returns
Type Description
int3

Converted cube coordinate

AxialToPixel(in int2, in float, in HexRotations)

Converts axial coordinates to pixel coordinates (point in world)

Declaration
public static float2 AxialToPixel(in int2 axial, in float sideSize, in HexRotations hexRotation)
Parameters
Type Name Description
int2 axial

axial coordinate
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
Returns
Type Description
float2

pixel coordinate (point in world)

AxialToPixel(in int2, in float, in bool)

Converts axial coordinates to pixel coordinates (point in world)

Declaration
public static float2 AxialToPixel(in int2 axial, in float sideSize, in bool isFlatTop)
Parameters
Type Name Description
int2 axial

axial coordinate
float sideSize

side length (radius) of hexagon
bool isFlatTop

true = flat top, false = point top
Returns
Type Description
float2

pixel coordinate (point in world)

CellCoordAdd_Cube(int3, int3)

Adds offset to the cell coordinates (cube coordinates)

Declaration
public static int3 CellCoordAdd_Cube(int3 origin, int3 offset)
Parameters
Type Name Description
int3 origin

origin cube coordinates
int3 offset

target cube coordinates
Returns
Type Description
int3

cube coordinate

CubeToAxial(in int3)

Converts cube coordinates to axial coordinates

Declaration
public static int2 CubeToAxial(in int3 cubeCoord)
Parameters
Type Name Description
int3 cubeCoord

Cube coordinate to be converted
Returns
Type Description
int2

Converted axial coordinates

CubeToOffset(in int3, in HexRotations, in HexLayouts)

Converts cube coordinates to offset coordinates

Declaration
public static int2 CubeToOffset(in int3 cubeCoord, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int3 cubeCoord

cube coordinate
HexRotations hexRotation

rotation of hexagon (point/flat top)
HexLayouts hexLayout

layout of hexagons (odd/even)
Returns
Type Description
int2

offset coordinate

CubeToOffset(in int3, in bool, in bool)

Converts cube coordinates to offset coordinates

Declaration
public static int2 CubeToOffset(in int3 cubeCoord, in bool isFlatTop, in bool isOddLayout)
Parameters
Type Name Description
int3 cubeCoord

Cube coordinate
bool isFlatTop

if true - flat top, false - point top
bool isOddLayout

true - odd layout, flase - even layout
Returns
Type Description
int2

offset coordinate

CubeToPixel(in int3, in float, in HexRotations)

Converts cube coordinates to pixel coordinates (point in world)

Declaration
public static float2 CubeToPixel(in int3 cube, in float sideSize, in HexRotations hexRotation)
Parameters
Type Name Description
int3 cube

cube coordinate
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
Returns
Type Description
float2

pixel coordinate (point in world)

DistanceBetweenCells_Axial(in int2, in int2)

Calculates distance between two cells in axial coordinates

Declaration
public static int DistanceBetweenCells_Axial(in int2 from_axial, in int2 to_axial)
Parameters
Type Name Description
int2 from_axial

origin axial coordinate
int2 to_axial

target axial coordinate
Returns
Type Description
int

Axial coordinate

DistanceBetweenCells_Cube(in int3, in int3)

Calculates distance between two cells in cube coordinates

Declaration
public static int DistanceBetweenCells_Cube(in int3 from_cube, in int3 to_cube)
Parameters
Type Name Description
int3 from_cube

origin cube coordinate
int3 to_cube

target cube coordinate
Returns
Type Description
int

cube coordinate

DistanceBetweenCells_Offset(in int2, in int2, in HexRotations, in HexLayouts)

Calculates distance between two cells in offset coordinates

Declaration
public static int DistanceBetweenCells_Offset(in int2 from_offset, in int2 to_offset, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 from_offset

origin offset coordinate
int2 to_offset

target offset coordinate
HexRotations hexRotation

hexagon rotation (flat/point top)
HexLayouts hexLayout

laout rotation (odd/even)
Returns
Type Description
int

offset coordinate

DistanceBetweenCells_Offset_F(in int2, in int2, in HexRotations, in HexLayouts)

Calculates distance between two cells in offset coordinates

Declaration
public static float DistanceBetweenCells_Offset_F(in int2 from_offset, in int2 to_offset, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 from_offset

origin offset coordinate
int2 to_offset

target offset coordinate
HexRotations hexRotation

hexagon rotation (point/flat top)
HexLayouts hexLayout

laoyout rotation (odd/even)
Returns
Type Description
float

offset coordinate

GetAdjacentCell_Axial(in int2, in int)

Returns adjacent cell for given cell and neighbour index

Declaration
public static int2 GetAdjacentCell_Axial(in int2 cell, in int neighbourIndex)
Parameters
Type Name Description
int2 cell

axial coordinate of the cell to find neighbour for
int neighbourIndex

index of neighbour (6 neighbors)
Returns
Type Description
int2

axial coordinate of the neighbour

GetAdjacentCell_Cube(in int3, in int)

Returns adjacent cell for given cell and neighbour index

Declaration
public static int3 GetAdjacentCell_Cube(in int3 cell, in int neighbourIndex)
Parameters
Type Name Description
int3 cell

cube coordinate of the cell to find neighbour for
int neighbourIndex

index of neighbour (6 neighbors)
Returns
Type Description
int3

cube coordinate of the neighbour

GetAdjacentCell_Offset(in int2, in int, in HexRotations, in HexLayouts)

Returns adjacent cell for given cell and neighbour index

Declaration
public static int2 GetAdjacentCell_Offset(in int2 cell, in int neighbourIndex, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 cell

offset coordinate of the cell to get neighbour for
int neighbourIndex

index of neighbour (6 neighbors)
HexRotations hexRotation

hexagon rotation (point/flat top)
HexLayouts hexLayout

layout of hexagons (odd/even)
Returns
Type Description
int2

offset coordinate of adjacent cell

GetAdjacentCell_Offset(in int2, in int, in bool, in bool)

Returns adjacent cell for given cell and neighbour index

Declaration
public static int2 GetAdjacentCell_Offset(in int2 cell, in int neighbourIndex, in bool isOddLayout, in bool isFlatTop)
Parameters
Type Name Description
int2 cell

offset coordinate of the cell to get neighbour for
int neighbourIndex

index of neighbour (6 neighbors)
bool isOddLayout

true = odd layout, false = even layout
bool isFlatTop

true = flat top, false = point top
Returns
Type Description
int2

offset coordinate of adjacent cell

GetCellsRange_Axial(in int2, int, Allocator)

Creates a results list with given allocator, Calculates range and fills results list with them

Declaration
public static NativeList<int2> GetCellsRange_Axial(in int2 center, int rangeSize, Allocator allocator)
Parameters
Type Name Description
int2 center
int rangeSize
Allocator allocator
Returns
Type Description
NativeList<int2>

axial coordinate

GetCellsRange_Axial(in int2, int, NativeList<int2>)

Calculates range and fills given list with coordinates. Returns filled list

Declaration
public static NativeList<int2> GetCellsRange_Axial(in int2 center, int rangeSize, NativeList<int2> results)
Parameters
Type Name Description
int2 center
int rangeSize
NativeList<int2> results
Returns
Type Description
NativeList<int2>

axial coordinate

GetCellsRange_Cube(in int3, int, Allocator)

Creates a results list with given allocator, Calculates range and fills results list with them

Declaration
public static NativeList<int3> GetCellsRange_Cube(in int3 center, int rangeSize, Allocator allocator)
Parameters
Type Name Description
int3 center
int rangeSize
Allocator allocator
Returns
Type Description
NativeList<int3>

cube coordinate

GetCellsRange_Cube(in int3, int, NativeList<int3>)

Calculates range and fills given list with coordinates. Returns filled list

Declaration
public static NativeList<int3> GetCellsRange_Cube(in int3 center, int rangeSize, NativeList<int3> results)
Parameters
Type Name Description
int3 center
int rangeSize
NativeList<int3> results
Returns
Type Description
NativeList<int3>

cube coordinate

GetCellsRange_Offset(in int2, int, in HexRotations, in HexLayouts, Allocator)

Creates a results list with given allocator, Calculates range and fills results list with them

Declaration
public static NativeList<int2> GetCellsRange_Offset(in int2 center, int rangeSize, in HexRotations hexRotation, in HexLayouts hexLayout, Allocator allocator)
Parameters
Type Name Description
int2 center
int rangeSize
HexRotations hexRotation
HexLayouts hexLayout
Allocator allocator
Returns
Type Description
NativeList<int2>

offset coordinate

GetCellsRange_Offset(in int2, int, in HexRotations, in HexLayouts, NativeList<int2>)

Calculates range and fills given list with coordinates. Returns filled list

Declaration
public static NativeList<int2> GetCellsRange_Offset(in int2 center, int rangeSize, in HexRotations hexRotation, in HexLayouts hexLayout, NativeList<int2> results)
Parameters
Type Name Description
int2 center
int rangeSize
HexRotations hexRotation
HexLayouts hexLayout
NativeList<int2> results
Returns
Type Description
NativeList<int2>

offset coordinate

GetDirection_Axial(in int)

Returns direction for given cell and neighbour index

Declaration
public static int2 GetDirection_Axial(in int directionIndex)
Parameters
Type Name Description
int directionIndex

index of neihbour to find direction towards (6 neigbours)
Returns
Type Description
int2

direction towards the adjacent cell

GetDirection_Cube(in int)

Returns direction for given cell and neighbour index

Declaration
public static int3 GetDirection_Cube(in int directionIndex)
Parameters
Type Name Description
int directionIndex

index of neighbour to find direction towards (6 neigbours)
Returns
Type Description
int3

cube coordinate

GetDirection_Offset(in int2, in int, in HexRotations, in HexLayouts)

Returns direction for given cell and neighbour index

Declaration
public static int2 GetDirection_Offset(in int2 cell, in int neighbourIndex, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 cell

offset coordinate of the cell to get neighbour for
int neighbourIndex

index of neighbour (6 neighbors)
HexRotations hexRotation

hexagon rotation (point/flat top)
HexLayouts hexLayout

layout of hexagon (odd/even)
Returns
Type Description
int2

direction towards the adjacent cell

GetDirection_Offset(in int2, in int, in bool, in bool)

Returns direction for given cell and neighbour index

Declaration
public static int2 GetDirection_Offset(in int2 cell, in int neighbourIndex, in bool isOddLayout, in bool isFlatTop)
Parameters
Type Name Description
int2 cell

cell to find a direction from
int neighbourIndex

index of neighbour to find a direction towards (6 neigbours)
bool isOddLayout

true = odd layout, false = even layout
bool isFlatTop

true = flat top, false = point top
Returns
Type Description
int2

direction towards the adjacent cell

GetHexGridSize(in float, in int2, in HexRotations)

Returns size of the rectangle for hexagon grid with given sideLength and hexCount

Declaration
public static float2 GetHexGridSize(in float sideLength, in int2 hexCount, in HexRotations hexRotation)
Parameters
Type Name Description
float sideLength

Side length (radius) of the hexagon
int2 hexCount

Size of the grid of hexagons
HexRotations hexRotation

hexagon rotation (point/flat top)
Returns
Type Description
float2

size of the hexagons grid

GetHexGridSize(in float, in int2, in bool)

Returns size of the rectangle for hexagon grid with given sideLength and hexCount

Declaration
public static float2 GetHexGridSize(in float sideLength, in int2 hexCount, in bool isFlatTop)
Parameters
Type Name Description
float sideLength

Side length (radius) of the hexagon
int2 hexCount

Size of the grid of hexagons
bool isFlatTop

if true - flat top, false - point top
Returns
Type Description
float2

size of the hexagons grid

GetHexagonSize(in float, in HexRotations)

Returns size of the rectangle for hexagon with provided sideLength

Declaration
public static float2 GetHexagonSize(in float sideLength, in HexRotations hexRotation)
Parameters
Type Name Description
float sideLength

Side length (radius) of the hexagon
HexRotations hexRotation

Rotation of the hexagon (point/flat top)
Returns
Type Description
float2

Size of the hexagon

GetHexagonSize(in float, in bool)

Returns size of the rectangle for hexagon with gived sideLength

Declaration
public static float2 GetHexagonSize(in float sideLenght, in bool isFlatTop)
Parameters
Type Name Description
float sideLenght
bool isFlatTop
Returns
Type Description
float2

size of the hexagon

HexCornerPosition(in float2, in float, in int, in HexRotations)

returns position of hexagon's corner of given index for flat top and pointy top hexagon orientation

Declaration
public static float2 HexCornerPosition(in float2 center, in float sideSize, in int cornerIndex, in HexRotations hexRotation)
Parameters
Type Name Description
float2 center

center of the hexagon
float sideSize

size of the side of the hexagon
int cornerIndex

every next corner adds 60 degrees from starting point
HexRotations hexRotation

rotation of the hexagon (point/flat top)
Returns
Type Description
float2

corner position

HexCornerPosition(in float2, in float, in int, in bool)

returns position of hexagon's corner of given index for flat top and pointy top hexagon orientation

Declaration
public static float2 HexCornerPosition(in float2 center, in float sideSize, in int cornerIndex, in bool isFlatTop)
Parameters
Type Name Description
float2 center

center of the hexagon
float sideSize

size of the side of the hexagon
int cornerIndex

every next corner adds 60 degrees from starting point
bool isFlatTop

true - hexagon with flat top; false - hexagon with pointy top
Returns
Type Description
float2

corner position

HexCornerPosition(in float2, in float, in float)

Gives position for hexagon corner (point on circle around center) with given angle in radians

Declaration
public static float2 HexCornerPosition(in float2 center, in float size, in float angle_rad)
Parameters
Type Name Description
float2 center

center of the circle
float size

radius of the circle
float angle_rad

angle of the point in radians
Returns
Type Description
float2

corner position

OffsetToAxial(in int2, in HexRotations, in HexLayouts)

Converts offset coordinates to axial coordinates

Declaration
public static int2 OffsetToAxial(in int2 offset, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 offset

offset coordinate
HexRotations hexRotation

hexagon rotation (point/flat top)
HexLayouts hexLayout
Returns
Type Description
int2

offset coordinate

OffsetToAxial(in int2, in bool, in bool)

Converts offset coordinates to axial coordinates

Declaration
public static int2 OffsetToAxial(in int2 offset, in bool isFlatTop, in bool isOddLayout)
Parameters
Type Name Description
int2 offset
bool isFlatTop
bool isOddLayout
Returns
Type Description
int2

offset coordinate

OffsetToCube(in int2, in HexRotations, in HexLayouts)

Converts offset coordinates to cube coordinates

Declaration
public static int3 OffsetToCube(in int2 offsetCoord, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 offsetCoord

offset coordinate
HexRotations hexRotation

rotation of hexagons (point/flat top)
HexLayouts hexLayout

layout of hexagons (odd/even)
Returns
Type Description
int3

cube coordinate

OffsetToCube(in int2, in bool, in bool)

Converts offset coordinates to cube coordinates

Declaration
public static int3 OffsetToCube(in int2 offsetCoord, in bool isFlatTop, in bool isOddLayout)
Parameters
Type Name Description
int2 offsetCoord

offset coordinate
bool isFlatTop

true = flat top, false = point top
bool isOddLayout

true = odd layout, false = even layout
Returns
Type Description
int3

cube coordinate

OffsetToPixel(in int2, in float, in HexRotations, in HexLayouts)

Converts offset coordinates to pixel coordinates (point in world)

Declaration
public static float2 OffsetToPixel(in int2 offset, in float sideSize, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
int2 offset

offset coordinate
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
HexLayouts hexLayout

layout of hexagon (odd/even)
Returns
Type Description
float2

pixel coordinate (point in world)

PixelToAxial(in float2, in float, in HexRotations)

Converts pixel coordinates to axial coordinates

Declaration
public static int2 PixelToAxial(in float2 pixel, in float sideSize, in HexRotations hexRotation)
Parameters
Type Name Description
float2 pixel

pixel coordinate (point in the world)
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
Returns
Type Description
int2

axial coordinate

PixelToAxial(in float2, in float, in bool)

Converts pixel coordinates to axial coordinates

Declaration
public static int2 PixelToAxial(in float2 pixel, in float sideSize, in bool isFlatTop)
Parameters
Type Name Description
float2 pixel

pixel coordinate (point in the world)
float sideSize

side length (radius) of hexagon
bool isFlatTop

true = flat top, false = point top
Returns
Type Description
int2

axial coordinate

PixelToCube(in float2, in float, in HexRotations)

Converts pixel coordinates to cube coordinates

Declaration
public static int3 PixelToCube(in float2 pixel, in float sideSize, in HexRotations hexRotation)
Parameters
Type Name Description
float2 pixel

pixel coordinate (point in the world)
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
Returns
Type Description
int3

cube coordinate

PixelToOffset(in float2, in float, in HexRotations, in HexLayouts)

Converts pixel coordinates to offset coordinates

Declaration
public static int2 PixelToOffset(in float2 pixel, in float sideSize, in HexRotations hexRotation, in HexLayouts hexLayout)
Parameters
Type Name Description
float2 pixel

pixel coordinate (point in the world)
float sideSize

side length (radius) of hexagon
HexRotations hexRotation

rotation of hexagon (point/flat top)
HexLayouts hexLayout

layout of hexagons (odd/even)
Returns
Type Description
int2

offset coordinate