hexyz is tower defense game, and a lua library for dealing with hexagonal grids
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----- [[ AXIAL/CUBE COORDINATE HEXAGON LIBRARY FOR AMULET/LUA]] ----------------
--[[ author@churchianity.ca
-- INTRODUCTION
this is a hexagonal grid library for amulet/lua.
it uses axial coordinates or cube/hex coordinates when necessary.
by amulet convention, hexes are either vec2(s, t) or vec3(s, t, z)
but nearly always the former.
-- RESOURCES USED TO DEVELOP THIS LIBRARY, AND FOR WHICH I AM GRATEFUL
https://catlikecoding.com/unity/tutorials/hex-map/
https://redblobgames.com/grid/hexagons
http://amulet.xyz/doc
]]
----- [[ GENERALLY USEFUL FUNCTIONS ]] -----------------------------------------
-- rounds numbers. would've been cool to have math.round in lua.
local function round(n)
return n % 1 >= 0.5 and math.ceil(n) or math.floor(n)
end
----- [[ HEX CONSTANTS & UTILITY FUNCTIONS ]] ----------------------------------
-- all possible vector directions from a given hex by edge
local HEX_DIRECTIONS = {vec2( 1 , 0),
vec2( 1 , -1),
vec2( 0 , -1),
vec2(-1 , 0),
vec2(-1 , 1),
vec2( 0 , 1)}
-- return hex vector direction via integer index |direction|.
function hex_direction(direction)
return HEX_DIRECTIONS[(6 + (direction % 6)) % 6 + 1]
end
-- return hexagon adjacent to |hex| in integer index |direction|.
function hex_neighbour(hex, direction)
return hex + HEX_DIRECTIONS[(6 + (direction % 6)) % 6 + 1]
end
-- TODO
function hex_rotate_left(hex)
end
function hex_rotate_right(hex)
end
-- rounds hexes. without this, pixel_to_hex returns fractional coordinates.
function hex_round(s, t)
local rs = round(s)
local rt = round(t)
local rz = round(-s - t)
local sdelta = math.abs(rs - s)
local tdelta = math.abs(rt - t)
local zdelta = math.abs(rz - (-s - t))
if sdelta > tdelta and sdelta > zdelta then
rs = -rt - rz
elseif tdelta > zdelta then
rt = -rs - rz
else
rz = -rs - rt
end
return vec2(rs, rt)
end
----- [[ LAYOUT, ORIENTATION & COORDINATE CONVERSION ]] -----------------------
-- forward & inverse matrices used for the flat orientation.
local FLAT = {M = mat2(3.0/2.0, 0.0, 3.0^0.5/2.0, 3.0^0.5 ),
W = mat2(2.0/3.0, 0.0, -1.0/3.0 , 3.0^0.5/3.0),
start_angle = 0.0}
-- forward & inverse matrices used for the pointy orientation.
local POINTY = {M = mat2(3.0^0.5, 3.0^0.5/2.0, 0.0, 3.0/2.0),
W = mat2(3.0^0.5/3.0, -1.0/3.0, 0.0, 2.0/3.0),
start_angle = 0.5}
-- TODO encapsulate hex_to_pixel and pixel_to_hex in layout table.
-- stores layout information that does not pertain to map shape
function hex_layout(origin, size, orientation)
return {origin = origin or vec2(0),
size = size or vec2(12),
orientation = orientation or FLAT}
end
-- hex to screen
function hex_to_pixel(hex, layout)
local M = layout.orientation.M
local x = (M[1][1] * hex.s + M[1][2] * hex.t) * layout.size.x
local y = (M[2][1] * hex.s + M[2][2] * hex.t) * layout.size.y
return vec2(x + layout.origin.x, y + layout.origin.y)
end
-- screen to hex
function pixel_to_hex(pix, layout)
local W = layout.orientation.W
local pix = (pix - layout.origin) / layout.size
local s = W[1][1] * pix.x + W[1][2] * pix.y
local t = W[2][1] * pix.x + W[2][2] * pix.y
return hex_round(s, t)
end
-- TODO test
function hex_corner_offset(layout, corner)
local angle = 2.0 * math.pi * layout.orientation.start_angle + corner / 6
return vec2(layout.size.x * math.cos(angle), layout.size.y * math.sin(angle))
end
-- TODO make do stuff
function hex_corners(layout, hex)
local corners = {}
end
----- [[ MAP STORAGE & RETRIEVAL ]] --------------------------------------------
--[[
]]
-- TODO make all functions work regardless of layout.
-- returns ordered ring-shaped map of |radius| from |center|.
function hex_ring_map(center, radius)
local map = {}
local walk = center + HEX_DIRECTIONS[6] * radius
for i = 1, 6 do
for j = 1, radius do
table.insert(map, walk)
walk = hex_neighbour(walk, i)
end
end
return map
end
-- returns ordered hexagonal map of |radius| rings from |center|.
function hex_spiral_map(center, radius)
local map = {center}
for i = 1, radius do
table.append(map, hex_ring_map(center, i))
end
return map
end
-- returns unordered parallelogram-shaped map of |width| and |height|.
function hex_parallelogram_map(width, height)
local map = {}
local mt = {__index={width=width, height=height}}
setmetatable(map, mt)
for s = 0, width do
for t = 0, height do
map[vec2(s, t)] = true
end
end
return map
end
-- returns unordered triangular map of |size|.
function hex_triangular_map(size)
local map = {}
local mt = {__index={size=size}}
setmetatable(map, mt)
for s = 0, size do
for t = size - s, size do
map[vec2(s, t)] = true
end
end
return map
end
-- returns unordered hexagonal map of |radius|.
function hex_hexagonal_map(radius)
local map = {}
local mt = {__index={radius=radius}}
setmetatable(map, mt)
for s = -radius, radius do
local t1 = math.max(-radius, -s - radius)
local t2 = math.min(radius, -s + radius)
for t = t1, t2 do
map[vec2(s, t)] = true
end
end
return map
end
-- returns unordered rectangular map of |width| and |height|.
function hex_rectangular_map(width, height)
local map = {}
local mt = {__index={width=width, height=height}}
setmetatable(map, mt)
for s = 0, width do
for t = 0, height do
map[vec2(s, t - math.floor(s/2))] = true
end
end
return map
end