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HexGrid library provides easy and intuitive way of working with hexagonal grids.


Swift 5.3 Swift Package Manager Compatible MIT License Documentation

Development in progress!

API might change without further notice until first major release 1.x.x.

HexGrid library provides easy and intuitive way of working with hexagonal grids. Under the hood it handles all the math so you can focus on more important stuff.

  • Support any gird shape, including irregular one or grid with holes.

The library is meant for generic backend use. Therefore it doesn't not offer any UI or rendering stuff. However, it provides calculations needed for grid rendering.


  • ☑ Create or generate a grid with hexagonal cells.
  • ☑ Various coordinate systems (cube, axial, offset).
  • ☑ Rotation, Manhattan distance, linear interpolation.
  • ☑ Get Neighbors or diagonal neighbors.
  • ☑ Get Line (get all hexes making a line from A to B).
  • ☑ Get Ring (get all hexes making a ring from an origin coordinates in specified radius).
  • ☑ Get Filled Ring (get all hexes making a filled ring from an origin coordinates in specified radius).
  • ☑ Find reachable hexes within n steps (Breath First Search).
  • ☑ Find the shortest path from A to B (optimized A* search algorithm).
  • ☑ FieldOfView algorithm (ShadowCasting designed for hexagonal grids).
  • ☑ Hexagon rendering related stuff (e.g. polygon corners).
  • ☑ Code inline documentation (quick help).
  • ☑ Solid unit tests coverage.
  • ☑ Automated documentation generator (SwiftDoc + GitHub Actions -> hosted on repo GitHub Pages).

What's coming next?

  • ☐ Review and update readme.md.
  • ☐ Demo with visualization.

Getting Started

Integrating HexGrid to your project

Add HexGrid as a dependency to your Package.swift file.

import PackageDescription

let package = Package(
name: "MyApp",
dependencies: [
// Add HexGrid package here
.package(url: "https://github.com/fananek/hex-grid.git", from: "0.4.4")
targets: [
        .target(name: "App", dependencies: [
            .product(name: "HexGrid", package: "hex-grid"),

Import HexGrid package to your code.

import HexGrid
// your code goes here


Creating a grid

Grid can be initialized either with set of cells or HexGrid can generate some of standard shapes for you.

Standard shape grids


// create grid of hexagonal shape
var grid = HexGrid(shape: GridShape.hexagon(10))
// or rectangular shape
var grid = HexGrid(shape: GridShape.rectangle(8, 12))
// or triangular shape
var grid = HexGrid(shape: GridShape.triangle(6))

Custom grids


// create new HexGrid

let gridCells: Set<Cell> = try [
Cell(CubeCoordinates(x:  2,  y: -2,  z:  0)),
Cell(CubeCoordinates(x:  0,  y: -1,  z:  1)),
Cell(CubeCoordinates(x: -1,  y:  1,  z:  0)),
Cell(CubeCoordinates(x:  0,  y:  2,  z: -2))
var grid = HexGrid(cells: gridCells)

HexGrid <-> JSON

HexGrid conforms to swift Codable protocol so it can be easily encoded to or decoded from JSON.


// encode (grid to JSON)
let grid = HexGrid(shape: GridShape.hexagon(5) )
let encoder = JSONEncoder()
let data = try encoder.encode(grid)
// decode (JSON to grid)
let decoder = JSONDecoder()
let grid = try decoder.decode(HexGrid.self, from: data)

Grid operations examples

Almost all functions has two variants. One works with Cell and the other one works with CubeCoordinates. Use those which better fulfill your needs.

Get Cell at coordinates

let cell = grid.cellAt(try CubeCoordinates(x: 1, y: 0, z: -1))

Validate coordinates

Check whether some coordinates are valid (means it exist on a grid).

// returns Bool
isValidCoordinates(try CubeCoordinates(x: 2, y: 4, z: -6))

Get blocked or non blocked Cells

let blockedCells = grid.blockedCells()
// or
let nonBlockedCells = grid.nonBlockedCells()

Get single neighbor

// get neighbor for a specific Cell
let neighbor = try grid.neighbor(
            for: someCell,
            at: Direction.Pointy.northEast.rawValue)

// get just neighbor coordinates
let neighborCoordinates = try grid.neighborCoordinates(
            for: someCoordinates,
            at: Direction.Pointy.northEast.rawValue)

Get all neighbors

// get all neighbors for a specific Cell
let neighbors = try grid.neighbors(for: someCell)

// get only coordinates of all neighbors
let neighborsCoords = try grid.neighbors(for: someCoordinates)

Get line from A to B

// returns nil in case line doesn't exist
let line = try grid.line(from: originCell, to: targetCell)

Get ring

// returns all cells making a ring from origin cell in radius
let ring = try grid.ring(from: originCell, in: 2)

Get filled ring

// returns all cells making a filled ring from origin cell in radius
let ring = try grid.filledRing(from: originCell, in: 2)

Find reachable cells

// find all reachable cells (max. 4 steps away from origin)
let reachableCells = try grid.findReachable(from: origin, in: 4)

Find shortest path

// returns nil in case path doesn't exist at all
let path = try grid.findPath(from: originCell, to: targetCell)

Calculate field of view (FOV)

Cell has an attribute called isOpaque. Its value can be true or false. Based on this information it's possible to calculate so called field of view. It means all cells visible from specific position on grid, considering all opque obstacles.

// set cell as opaque
obstacleCell.isOpaque = true 

In order to get field of view, simply call following function.

// find all hexes visible in radius 4 from origin cell
let visibleHexes = try grid.fieldOfView(from: originCell, in: 4)

By default cell is considered visible as soon as its center is visible from the origin cell. If you want to include partially visible cells as well, use optional paramter includePartiallyVisible.

// find all hexes even partially visible in radius 4 from origin cell
let visibleHexesIncludingPartials = try grid.fieldOfView(from: originCell, in: 4, includePartiallyVisible: true)

Drawing related functions

If you want to render a grid, you will need screen coordinates of polygon corners for a Cell.

let corners = grid.polygonCorners(for: someCell)

Converting cell coordinates to pixel coordinates and vice versa might be handy as well.

// return Ponit struct with x: and y: values
let screenCoords = grid.pixelCoordinates(for: cell)

// return cell for specified screen coordinates (or nil if such cell doesn't exists)
let cell = try grid.cellAt(point)

Implementation fundamentals

For detailed information see complete documentation

Data structures you should know


Represents the grid itself as well as it's an entry point of the HexGrid library.

HexGrid is defined by set of Cells and few other properties. All together makes a grid setup. In other words it put grid cells into a meaningful context. Therefore most of available operations are being called directly on a grid instance because it make sense only with such context (grid setup).


  • cells: Set<Cell> - grid cells
  • orientation: Orientation - see Orientation enumeration
  • offsetLayout: OffsetLayout - see OffsetLayout enumeration
  • hexSize: HexSize - width and height of a hexagon
  • origin: Point - 'display coordinates' (x, y) of a grid origin
  • pixelWidth: Double - pixel width of a grid
  • pixelHeight: Double - pixel width of a grid
  • attributes: [String: Attribute] - dictionary of custom attributes (most primitive types are supported as well as nesting)


Cell is a building block of a grid.


  • coordinates: CubeCoordinates - cell placement on a grid coordinate system
  • attributes: [String: Attribute] - dictionary of custom attributes (most primitive types are supported as well as nesting)
  • isBlocked: Bool - used by algorithms (reachableCells, pathfinding etc.)
  • isOpaque: Bool - used by fieldOfView algorithm
  • cost: Float - used by pathfinding algorithm. For the sake of simplicity let's put graph theory aside. You can imagine cost as an amount of energy needed to pass a cell. Pathfinding algorithm then search for path requiring the less effort.


The most common coordinates used within HexGrid library is cube coordinate system. This type of coordinates has three axis x, y and z. The only condition is that sum of its all values has to be equal zero.

// valid cube coordinates
CubeCoordinates(x: 1, y: 0, z: -1) -> sum = 0

// invalid cube coordinates
CubeCoordinates(x: 1, y: 1, z: -1) -> sum = 1 -> throws error

For more details check Amit Patel's explanation.




  • pointyOnTop - ⬢
  • flatOnTop - ⬣

OffsetLayout is used primarily for rectangular shaped grids. It has two options but their meaning can differ based on grid orientation.


  • odd
  • even

There are four offset types depending on orientation of hexagons. The “row” types are used with with pointy top hexagons and the “column” types are used with flat top.

  • Pointy on top orientation
    • odd-row (slide alternate rows right)
    • even-row (slide alternate rows left)
  • Flat on top orientation
    • odd-column (slide alternate columns up)
    • even-column (slide alternate columns down)


  • rectangle(Int, Int) - rectangle width and height
  • hexagon(Int) - radius of hexagon
  • triangle(Int) - size of triangle side


  • left
  • right

Direction enumeration is consistent and human recognizable direction naming. Using direction enumeration is not only much more convenient but it also help to avoid errors. It's better to say just "Hey, I'm on cell X and want to go north." than think "What the hack was that index of north direction?", isn't it?


  • Direction.Flat
    • north
    • northEast
    • southEast
    • south
    • southWest
    • northWest
  • Direction.Pointy
    • northEast
    • east
    • southEast
    • southWest
    • west
    • northWest

There is actually separate set of directions for each grid orientation. It's because of two reasons. First, some directions are valid only for one or another orientation. Second, direction raw values are shifted based on orientation.


See also the list of contributors who participated in this project.


All code contained in the HexGrid package is under the MIT license agreement.


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