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fastmath.grid

Grid calculation functions.

Convert 2d coordinates into various grid coordinates and back.

Terms used:

  • cell type - grid cell shape: square, triangular, hexagonal, rhomboidal
  • coords - 2d euclidean coordinates (x,y)
  • cell - cell coordinates (q,r)
  • anchor - cell position in 2d euclidean space
  • corners - shape vertices
  • size - size of the cell.

Grids

Each grid is defined by cell type and size. Optionally you can provide translating vector.

Each cell has it’s own coordinates, mostly axial based (only square has offset).

For hexagonal cell size is a radius from midpoint to corner. For the rest it is the size of the side.

Cell types are:

  • :square
  • :shifted-square
  • :triangle
  • :rhombus
  • :flat-hex - flat topped
  • :pointy-hex - pointy topped

Notes

  • Hexagonal grids are based on https://www.redblobgames.com/grids/hexagons/
  • Only hexagonal cells have anchor at the center. For the rest the anchor is at the top left vertex.
    • Anchors for triangular grids are shared between two cells: even and odd q coordinate. Even q is pointy topped, odd q is flat topped which is marked in the third coordinate of anchor.

Categories

    Other vars: cell->anchor cell->mid cell-names coords->anchor coords->cell coords->mid corners flat-hex-corners grid grid-type pointy-hex-corners

    cell->anchor

    (cell->anchor g cell)(cell->anchor g q r)

    Converts cell coordinates (q,r) to anchor coordinates (x,y).

    Examples

    Usage

    (cell->anchor (grid :triangle 20 10 10) [5 5])
;;=> [100.0 96.60254037844386 1.0]

    More examples (grid g same as above). For triangle grid pair of cells share the same anchor, third coordinate indicates if it’s up (0) or down (1) triangle.

    (cell->anchor g [0 0])
;;=> [10.0 10.0 0.0]
(cell->anchor g [1 0])
;;=> [10.0 10.0 1.0]
(cell->anchor g [2 0])
;;=> [30.0 10.0 0.0]
(cell->anchor g [3 0])
;;=> [30.0 10.0 1.0]
(cell->anchor (grid :shifted-square 20 10 10) [5 5])
;;=> [160.0 110.0]
    view source

    cell->mid

    (cell->mid g cell)(cell->mid g x y)

    Converts cell coordinates (q,r) to mid point (x,y).

    Examples

    Usage

    (cell->mid (grid :triangle 20 10 10) [4 5])
;;=> [100.0 108.14954576223637]

    More examples (grid g same as above).

    (cell->mid g [0 0])
;;=> [10.0 21.547005383792513]
(cell->mid g [1 0])
;;=> [20.0 15.773502691896256]
(cell->mid g [2 0])
;;=> [30.0 21.547005383792513]
(cell->mid g [3 0])
;;=> [40.0 15.773502691896256]
(cell->mid (grid :shifted-square 20 10 10) [5 5])
;;=> [170.0 120.0]
    view source

    cell-names

    Examples

    List of all grid types.

    cell-names
;;=> [:square :shifted-square :triangle :rhombus :flat-hex :pointy-hex]
    view source

    coords->anchor

    (coords->anchor g coords)(coords->anchor g x y)

    Converts 2d coordinates (x,y) to cell anchor (x,y).

    Examples

    Usage

    (coords->anchor (grid :rhombus) [105 105])
;;=> [100.0 103.92304845413263]
(coords->anchor (grid :rhombus) [100 100])
;;=> [95.0 95.26279441628824]
(coords->anchor (grid :rhombus) [99 99])
;;=> [95.0 95.26279441628824]
    view source

    coords->cell

    (coords->cell g coords)(coords->cell g x y)

    Converts 2d space coordinates (x,y) to cell coordinates (q,r).

    Examples

    Usage

    (coords->cell (grid :pointy-hex 20 10 10) [50 50])
;;=> [1.0 3.0]

    More examples (grid g same as above)

    (coords->cell g [0 0])
;;=> [0.0 -1.0]
(coords->cell g [100 100])
;;=> [2.0 6.0]
(coords->cell g [-150 -150])
;;=> [-4.0 -11.0]
    view source

    coords->mid

    (coords->mid g coords)(coords->mid g x y)

    Converts 2d space coordinates (x,y) into cell midpoint (x,y).

    Examples

    Usage

    (coords->mid (grid :pointy-hex 20 10 10) [50 50])
;;=> [53.301270189221924 55.0]

    More examples (grid g same as above)

    (coords->mid g [0 0])
;;=> [1.3397459621556145 -5.0]
(coords->mid g [100 100])
;;=> [96.60254037844385 100.0]
(coords->mid g [-150 -150])
;;=> [-154.54482671904333 -155.0]
    view source

    corners

    (corners g coords)(corners g coords scale)(corners g x y scale)

    Returns list of cell vertices for given 2d space coordinates.

    Examples

    Usage

    (corners (grid :flat-hex 20) [100 100])
;;=> ([115.0 95.26279441628824]
;;=>  [110.0 103.92304845413263]
;;=>  [100.0 103.92304845413264]
;;=>  [95.0 95.26279441628824]
;;=>  [100.0 86.60254037844386]
;;=>  [110.0 86.60254037844386])
(corners (grid :triangle 10 10 10) [100 100])
;;=> [[100.0 96.60254037844386] [105.0 105.26279441628824]
;;=>  [95.0 105.26279441628824]]
    view source

    flat-hex-corners

    Function which returns vertices for flat topped hexagon for given size and coordinates.

    Examples

    Generate vertices for flat topped hexagon for given position and size

    (flat-hex-corners 100 [15 15])
;;=> ([115.0 15.0]
;;=>  [65.0 101.60254037844386]
;;=>  [-34.999999999999986 101.60254037844388]
;;=>  [-85.0 15.000000000000012]
;;=>  [-35.000000000000064 -71.60254037844382]
;;=>  [65.0 -71.60254037844386])
(flat-hex-corners 1 [0 0])
;;=> ([1.0 0.0]
;;=>  [0.5 0.8660254037844386]
;;=>  [-0.49999999999999983 0.8660254037844388]
;;=>  [-1.0 1.224646799076922E-16]
;;=>  [-0.5000000000000007 -0.8660254037844383]
;;=>  [0.5 -0.8660254037844386])
(flat-hex-corners 100 0 0)
;;=> ([100.0 0.0]
;;=>  [50.0 86.60254037844386]
;;=>  [-49.999999999999986 86.60254037844388]
;;=>  [-100.0 1.224646799076922E-14]
;;=>  [-50.000000000000064 -86.60254037844382]
;;=>  [50.0 -86.60254037844386])
    view source

    grid

    (grid type size sx sy)(grid type size)(grid type)(grid)

    Create grid for given type, size and optional translating vector.

    Examples

    Usage

    (grid :pointy-hex 20)
;;=> pointy-hex, size=10.0
(grid :triangular 10 5.0 5.0)
;;=> triangular, size=10.0
(name (grid :square))
;;=> square
(str (grid :rhombus))
;;=> rhombus, size=10.0
(grid)
;;=> square, size=10.0

    Pointy hex (red dot: mid point, cyan circle: anchor)

    Flat hex (red dot: mid point, cyan circle: anchor)

    Rhombus (red dot: mid point, cyan circle: anchor)

    Triangle (red dot: mid point, cyan circle: anchor)

    Square (red dot: mid point, cyan circle: anchor)

    Shifted square (red dot: mid point, cyan circle: anchor)

    view source

    grid-type

    (grid-type g)

    Returns type of the cell.

    Examples

    Usage

    (grid-type (grid :flat-hex 10))
;;=> :flat-hex
    view source

    pointy-hex-corners

    Function which returns vertices for pointy topped hexagon for given size and coordinates.

    Examples

    Generate vertices for pointy topped hexagon for given position and size

    (pointy-hex-corners 100 [15 15])
;;=> ([101.60254037844388 64.99999999999999]
;;=>  [15.000000000000005 115.0]
;;=>  [-71.60254037844386 65.00000000000001]
;;=>  [-71.60254037844386 -35.000000000000014]
;;=>  [14.999999999999982 -85.0]
;;=>  [101.60254037844382 -35.000000000000064])
(pointy-hex-corners 1 [0 0])
;;=> ([0.8660254037844387 0.4999999999999999]
;;=>  [6.12323399538461E-17 1.0]
;;=>  [-0.8660254037844386 0.5000000000000001]
;;=>  [-0.8660254037844386 -0.5000000000000001]
;;=>  [-1.83697019874463E-16 -1.0]
;;=>  [0.8660254037844382 -0.5000000000000007])
(pointy-hex-corners 100 0 0)
;;=> ([86.60254037844388 49.999999999999986]
;;=>  [6.12323399538461E-15 100.0]
;;=>  [-86.60254037844386 50.000000000000014]
;;=>  [-86.60254037844386 -50.000000000000014]
;;=>  [-1.83697019874463E-14 -100.0]
;;=>  [86.60254037844382 -50.000000000000064])
    view source