everything is so much cleaner now.

hex.lua

@@ -1,81 +1,64 @@
---[[ AXIAL/CUBE COORDINATE SYSTEM FOR AMULET/LUA]]
---[[
-
-    all hexes in functions are assumed to be amulet vectors. 
-    in amulet, vector arithmetic works already with [ + - * / ]
-    things like equality and distance are implemented here.
-
-    some algorithms use axial coordinates for hexes: vec2(s, t)
-    others use cube coordinates: vec3(s, t, z) where s + t + z = 0
-    this is for simplicity - many algorithms don't care about the
-    third coordinate, and if they do, the missing coordinate can 
-    be calculated from the other two.
-
-        -- note on orientation:
-    because of the way amulet draws hexagons, it's much easier to assume
-    the user wants to use the flat map. rotation after the fact to
-    achieve other orienations is probably possible, but might have some
-    aliasing issues. TODO work on this.
-
-    some of the primary resources used to develop this library:
-    - https://redblobgames.com/grid/hexagons    - simply amazing. 
-    - http://amulet.xyz/doc                     - amulet documentation
-    - TODO that place that had the inner circle/outer circle ratio?? 
+----- [[ AXIAL/CUBE COORDINATE SYSTEM FOR AMULET/LUA]] -------------------------
+--[[                                                     author@churchianity.ca
+        -- INTRODUCTION
+    this is a library for making grids of hexagons using lua.
+    it has made use of exclusively standard lua 5.2 functionality,
+    making it as portable as possible. it doesn't even use a point 
+    class, (or classes/metatables at all) simply returning tables 
+    of integers, which can later be unpacked into your amulet 
+    vectors, or whatever else you want to use. 
+
+    this can result in some nasty looking lines with lots of table 
+    unpacks, but if your graphics library likes traditional lua
+    types, you will be better off. 
+
+    it supports triangular, hexagonal, rectangular, and 
+    parallelogram map shapes. 
+    
+    it supports non-regular hexagons, though it's trickier to get
+    working in amulet. TODO work on this.
+
+        -- NOTE ON ORIENTATION + AMULET
+    because of the way amulet draws hexagons (amulet essentially
+    draws a 6-sided circle from a centerpoint, instead of of a 
+    series of lines connecting points), the flat orientation is 
+    default and recommended. other orientations are possible 
+    with am.rotate, but can cause aliasing issues. TODO work on this.
+
+        -- RESOURCES USED TO DEVELOP THIS LIBRARY
+    https://redblobgames.com/grid/hexagons    - simply amazing. amit is a god. 
+    http://amulet.xyz/doc                     - amulet documentation
+    TODO that place that had the inner circle/outer circle ratio?? 
 
   ]]
 
+----- [[ GENERALLY USEFUL FUNCTIONS ]] -----------------------------------------
 
--- GENERALLY USEFUL FUNCTIONS --------------------------------------------------
-
+-- just incase you don't already have a rounding function.  
 function round(n)
     return n % 1 >= 0.5 and math.ceil(n) or math.floor(n)
 end
 
+---- [[ HEX CONSTANTS ]] -------------------------------------------------------
 
--- HEX CONSTANTS ---------------------------------------------------------------
-
-    -- all possible vector directions from a given hex by edge
-HEX_DIRECTIONS = {vec2( 1 ,  0), 
-                  vec2( 1 , -1), 
-                  vec2( 0 , -1),
-                  vec2(-1 ,  0), 
-                  vec2(-1 ,  1), 
-                  vec2( 0 ,  1)}
+-- all possible vector directions from a given hex by edge
+HEX_DIRECTIONS = {{ 1 ,  0}, 
+                  { 1 , -1}, 
+                  { 0 , -1},
+                  {-1 ,  0}, 
+                  {-1 ,  1}, 
+                  { 0 ,  1}}
 
 -- HEX UTILITY FUNCTIONS -------------------------------------------------------
 
-function hex_equals(a, b)
-    return a.s == a.t and b.s == b.t
-end
-
-function hex_nequals(a, b)
-    return not hex_equals(a, b)
-end
-
-function hex_length(hex)
-    return ((math.abs(hex.s) + math.abs(hex.t) + math.abs(-hex.s - hex.t)) / 2)
-end
-
-function hex_distance(a, b)
-    return hex_length(a - b)
-end
-
-function hex_direction(direction)
-    return HEX_DIRECTIONS[direction]
-end
-
-function hex_neighbour(hex, direction)
-    return hex + HEX_DIRECTIONS[direction] 
-end
-
-function hex_round(hex)
-    rs = round(hex.s)
-    rt = round(hex.t)
-    rz = round(-hex.s + -hex.t)
+function hex_round(s, t)
+    rs = round(s)
+    rt = round(t)
+    rz = round(-s - t)
 
-    sdelta = math.abs(rs - hex.s)
-    tdelta = math.abs(rt - hex.t)
-    zdelta = math.abs(rz + hex.s + hex.t)
+    sdelta = math.abs(rs - s)
+    tdelta = math.abs(rt - t)
+    zdelta = math.abs(rz + s + t)
 
     if sdelta > tdelta and sdelta > zdelta then
         rs = -rt - rz
@@ -85,33 +68,106 @@ function hex_round(hex)
         rz = -rs - rt
     end
 
-    return vec2(rs, rt)
+    return {rs, rt}
+end
+
+----- [[ LAYOUT, ORIENTATION & COORDINATE CONVERSION  ]] -----------------------
+
+-- forward & inverse matrices used for the flat orientation.
+FLAT_ORIENTATION = {3.0/2.0,  0.0,  3.0^0.5/2.0,  3.0^0.5, 
+                    2.0/3.0,  0.0,  -1.0/3.0   ,  3.0^0.5/3.0}
+
+-- forward & inverse matrices used for the pointy orientation. 
+POINTY_ORIENTATION = {3.0^0.5,  3.0^0.5/2.0,  0.0,  3.0/2.0,  
+                      3.0^0.5/3.0,  -1.0/3.0,  0.0,  2.0/3.0}
+
+-- layout. 
+function layout(size, orientation, origin, width, height, radius)
+    return {size        = size or {11, 11},
+            orientation = orientation or FLAT_ORIENTATION,
+            origin      = origin or {0, 0},
+            width       = width or 45,
+            height      = height or 31,
+            radius      = radius or width or 6} 
+end    
+
+-- hex to screen
+function hex_to_pixel(s, t, layout)
+    M = layout.orientation
+    
+    x = (M[1] * s + M[2] * t) * layout.size[1]
+    y = (M[3] * s + M[4] * t) * layout.size[2]
+
+    return {x + layout.origin[1], y + layout.origin[2]}
 end
 
--- COORDINATE CONVERSION FUNCTIONS ---------------------------------------------
+-- screen to hex
+function pixel_to_hex(x, y, layout)
+    M = layout.orientation
 
-    -- forward & inverse matrices used for coordinate conversion
-local M = mat2(3.0/2.0,     0.0,    3.0^0.5/2.0,    3.0^0.5    )
-local W = mat2(2.0/3.0,     0.0,    -1.0/3.0   ,    3.0^0.5/3.0)
+    px = {(x - layout.origin[1]) / layout.size[1], 
+          (y - layout.origin[2]) / layout.size[2]}
 
-    -- hex to screen
-function hex_to_pixel(hex)
+    s = M[5] * px[1] + M[6] * px[2]
+    t = M[7] * px[1] + M[8] * px[2]
 
-    x = (M[1][1] * hex.s + M[1][2] * hex.t) * map.size
-    y = (M[2][1] * hex.s + M[2][2] * hex.t) * map.size
+    return hex_round(s, t) 
+end
+
+----- [[ MAP STORAGE & RETRIEVAL ]] --------------------------------------------
+--[[ all functions return a table of tables; a map of points
+     storage functions take a range of hex coordinates, and return pixel ones.
+     retrieval functions do the opposite.
+     everything except map shape is determined by layout.
+     pick a pair of functions based on the shape of map you want to use. 
+     it is not advised to use a single layout instance with multiple shapes. ]]
+
+-- returns parallelogram-shaped map. width and height are used.
+function ogram_map_store(layout)
+    map = {}
+    for s = 0, layout.width do
+        for t = 0, layout.height do
+            table.insert(map, hex_to_pixel(s, t, layout)) 
+        end
+    end
+    return map
+end
 
-    return vec2(x + map.origin.x, y + map.origin.y)
+-- returns triangular map. radius is used as the triangle side length.
+function tri_map_store(layout)
+    map = {}
+    for s = 0, layout.radius do
+        for t = layout.radius - s, layout.radius do
+            table.insert(map, hex_to_pixel(s, t, layout))
+        end
+    end
+    return map
 end
 
-    -- screen to hex
-function pixel_to_hex(pix)
-    pix = vec2(pix.x - map.origin.x) / map.size, 
-              (pix.y - map.origin.y) / map.size
+-- returns hexagonal map. length of map is radius * 2 + 1 
+function hex_map_store(layout) 
+    map = {}
+    for s = -layout.radius, layout.radius do
+        t1 = math.max(-layout.radius, -s - layout.radius)
+        t2 = math.min(layout.radius, -s + layout.radius)
 
-    s = W[1][1] * pix.x + W[1][2] * pix.y
-    t = W[2][1] * pix.x + W[2][2] * pix.y
+        for t = t1, t2 do
+            table.insert(map, hex_to_pixel(s, t, layout))
+        end
+    end
+    return map
+end
+
+-- returns rectangular map. width and height are used.
+function rect_map_store(layout)
+    map = {}
+    for s = 0, layout.width do
+        soffset = math.floor(s / 2)
 
-    return hex_round(vec2(s, t)) 
+        for t = -soffset, layout.height - soffset do
+            table.insert(map, hex_to_pixel(s, t, layout))
+        end
+    end
+    return map
 end
 
--- MAP FUNCTIONS ---------------------------------------------------------------

main.lua

@@ -1,32 +1,68 @@
---[[ WARZONE 2 - HEXAGONAL GRID RESOURCE BASED TOWER DEFENSE GAME]]
---[[
+----- [[ WARZONE 2 - HEXAGONAL GRID RESOURCE BASED TOWER DEFENSE GAME]] -------
+--[[                                                    author@churchianity.ca
 
   ]]
 
 require "hex"
 
--- ENTRY POINT -----------------------------------------------------------------
-win = am.window {
+----- [[ DUMMY FUNCTIONS ]] ------------------------------------------------------
+
+function draw_axes()
+    xaxis = am.line(vec2(-win.width / 2, 0) , vec2(win.width / 2, 0))
+    yaxis = am.line(vec2(0, -win.height / 2), vec2(0, win.height / 2))
+
+    title_scene:append(xaxis)
+    title_scene:append(yaxis)
+end
+
+function rcolor()
+    return vec4(math.random(20, 80) / 100)
+end
+
+function show_hex_coords()
+    win.scene:action(function()
+        x, y = unpack(pixel_to_hex(win:mouse_position().x, win:mouse_position().y, layout))
+        test_scene = (
+        am.translate(vec2(unpack(hex_to_pixel(x, y, layout))))
+        ^ am.text(string.format("%d, %d", x, y)))
+    end)
+end
+
+local win = am.window {
     title = "Warzone 2: Electric Boogaloo",
     
     -- BASE RESOLUTION = 3/4 * WXGA Standard 16:10 Aspect Ratio
-    width = 1280 * 3 / 4,
-    height = 800 * 3 / 4,
+    width = 1280 * 3 / 4, -- 960
+    height = 800 * 3 / 4} -- 600
+
+local layout = layout({11, 11}, 
+                      FLAT_ORIENTATION,
+                      vec2(win.left, win.bottom),
+                      45, 31)
 
-    clear_color = vec4(0, 0, 0, 0)
-}
+----- [[ MAP RENDERING ]] ------------------------------------------------
 
--- GROUPS
-local grid = am.group()
+function render_map(layout)
+    coords = rect_map_store(layout)
+    map = am.group()
 
---[[
-xaxis = am.line(vec2(-win.width / 2, 0) , vec2(win.width / 2, 0))
-yaxis = am.line(vec2(0, -win.height / 2), vec2(0, win.height / 2))
+    for _,v in pairs(coords) do
+        map:append(am.circle(vec2(unpack(v)), layout.size[1], rcolor(), 6))
+    end
+    return map
+end
 
-grid:append(xaxis)
-grid:append(yaxis)
---]]
+----- [[ MAIN ]] -----------------------------------------------------------
 
-win.scene = grid
+local game_scene        = render_map(layout)
+local test_scene        = am.group()
 
+win.scene = am.group{test_scene, game_scene}
 
+test_scene:action(function() 
+    x, y = unpack(pixel_to_hex(win:mouse_position().x, win:mouse_position().y, layout))
+    test_scene:replace("text", 
+    am.translate(vec2(unpack(hex_to_pixel(x, y, layout))))
+    ^ am.text(string.format("%d, %d", x, y)))
+    am.delay(1)
+end)