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--[[============================================================================ |
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-- HEX CONSTANTS AND UTILITY FUNCTIONS |
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--============================================================================ |
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-- HEX CONSTANTS AND UTILITY FUNCTIONS |
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]] |
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-- 'size' here is distance from the centerpoint to any vertex in pixel |
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local DEFAULT_HEX_SIZE = 20 |
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-- wherever 'orientation' appears as an argument, use one of these two, or set a default just below |
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ORIENTATION = { |
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-- Forward & Inverse Matrices used for the Flat Orientation |
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FLAT = { |
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M = mat2(3.0/2.0, 0.0, 3.0^0.5/2.0, 3.0^0.5 ), |
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W = mat2(2.0/3.0, 0.0, -1.0/3.0 , 3.0^0.5/3.0), |
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angle = 0.0 |
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}, |
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-- wherever orientation appears as an argument, if it isn't provided, use this |
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local orientation = FLAT |
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-- Forward & Inverse Matrices used for the Pointy Orientation |
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POINTY = { |
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M = mat2(3.0^0.5, 3.0^0.5/2.0, 0.0, 3.0/2.0), |
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W = mat2(3.0^0.5/3.0, -1.0/3.0, 0.0, 2.0/3.0), |
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angle = 0.5 |
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} |
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} |
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function get_default_hex_size() |
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return DEFAULT_HEX_SIZE |
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end |
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-- whenver |orientation| appears as an argument, if it isn't provided, this is used instead. |
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local DEFAULT_ORIENTATION = ORIENTATION.FLAT |
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-- 'size' here is distance from the centerpoint to any vertex in pixel |
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local DEFAULT_HEX_SIZE = 20 |
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-- actual width (longest contained horizontal line) of the hexagon |
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function hex_width(size, orientation) |
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function hex_width(size, orientation) |
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if orientation == FLAT then |
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local orientation = orientation or DEFAULT_ORIENTATION |
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if orientation == ORIENTATION.FLAT then |
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return size * 2 |
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return size * 2 |
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elseif orientation == POINTY then |
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elseif orientation == ORIENTATION.POINTY then |
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return math.sqrt(3) * size |
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return math.sqrt(3) * size |
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end |
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end |
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end |
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end |
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-- actual height (tallest contained vertical line) of the hexagon |
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function hex_height(size, orientation) |
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function hex_height(size, orientation) |
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return hex_width(size, orientation == FLAT and POINTY or FLAT) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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-- hex_width in one orientation == the height in the opposite orientation |
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return hex_width(size, orientation == ORIENTATION.FLAT and ORIENTATION.POINTY or ORIENTATION.FLAT) |
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end |
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end |
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-- returns actual width and height of a hexagon given it's |size| which is the distance |
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-- from the centerpoint to any vertex in pixels |
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-- returns actual width and height of a hexagon given it's |size| which is the distance from the centerpoint to any vertex in pixels |
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function hex_dimensions(size, orientation) |
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function hex_dimensions(size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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return vec2(hex_width(size, orientation), hex_height(size, orientation)) |
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return vec2(hex_width(size, orientation), hex_height(size, orientation)) |
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end |
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end |
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-- distance between two horizontally adjacent hexagon centerpoints |
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function hex_horizontal_spacing(size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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if orientation == ORIENTATION.FLAT then |
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return hex_width(size, orientation) * 3/4 |
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elseif orietnation == ORIENTATION.POINTY then |
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return hex_height(size, orientation) |
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end |
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end |
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-- distance between two vertically adjacent hexagon centerpoints |
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function hex_vertical_spacing(size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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-- hex_horizontal_spacing in one orientation == the vertical spacing in the opposite orientation |
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return hex_horizontal_spacing(size, orientation == ORIENTATION.FLAT and ORIENTATION.POINTY or ORIENTATION.FLAT) |
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end |
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-- returns the distance between adjacent hexagon centers in a grid |
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function hex_spacing(size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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return vec2(hex_horizontal_spacing(size, orientation), hex_vertical_spacing(size, orientation)) |
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end |
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-- All Non-Diagonal Vector Directions from a Given Hex by Edge |
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-- All Non-Diagonal Vector Directions from a Given Hex by Edge |
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HEX_DIRECTIONS = { vec2( 1 , -1), vec2( 1 , 0), vec2(0 , 1), |
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HEX_DIRECTIONS = { vec2( 1 , -1), vec2( 1 , 0), vec2(0 , 1), |
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vec2(-1 , 1), vec2(-1 , 0), vec2(0 , -1) } |
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vec2(-1 , 1), vec2(-1 , 0), vec2(0 , -1) } |
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@ -76,27 +121,10 @@ local function hex_round(x, y, z) |
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return vec2(rx, ry) |
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return vec2(rx, ry) |
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end |
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end |
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--[[==========================================================================-- |
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-- ORIENTATION & LAYOUT |
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]] |
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-- Forward & Inverse Matrices used for the Flat Orientation |
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local FLAT = { |
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M = mat2(3.0/2.0, 0.0, 3.0^0.5/2.0, 3.0^0.5 ), |
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W = mat2(2.0/3.0, 0.0, -1.0/3.0 , 3.0^0.5/3.0), |
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angle = 0.0 |
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} |
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-- Forward & Inverse Matrices used for the Pointy Orientation |
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local POINTY = { |
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M = mat2(3.0^0.5, 3.0^0.5/2.0, 0.0, 3.0/2.0), |
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W = mat2(3.0^0.5/3.0, -1.0/3.0, 0.0, 2.0/3.0), |
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angle = 0.5 |
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} |
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-- Hex to Screen -- Orientation Must be Either POINTY or FLAT |
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-- Hex to Screen -- Orientation Must be Either POINTY or FLAT |
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function hex_to_pixel(hex, size, orientation) |
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function hex_to_pixel(hex, size, orientation) |
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local M = orientation.M |
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local M = orientation and orientation.M or DEFAULT_ORIENTATION.M |
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local x = (M[1][1] * hex[1] + M[1][2] * hex[2]) * (size and size[1] or DEFAULT_HEX_SIZE) |
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local x = (M[1][1] * hex[1] + M[1][2] * hex[2]) * (size and size[1] or DEFAULT_HEX_SIZE) |
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local y = (M[2][1] * hex[1] + M[2][2] * hex[2]) * (size and size[2] or DEFAULT_HEX_SIZE) |
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local y = (M[2][1] * hex[1] + M[2][2] * hex[2]) * (size and size[2] or DEFAULT_HEX_SIZE) |
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@ -106,7 +134,7 @@ end |
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-- Screen to Hex -- Orientation Must be Either POINTY or FLAT |
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-- Screen to Hex -- Orientation Must be Either POINTY or FLAT |
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function pixel_to_hex(pix, size, orientation) |
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function pixel_to_hex(pix, size, orientation) |
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local W = orientation.W |
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local W = orientation and orientation.W or DEFAULT_ORIENTATION.W |
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local pix = pix / (size or vec2(DEFAULT_HEX_SIZE)) |
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local pix = pix / (size or vec2(DEFAULT_HEX_SIZE)) |
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@ -118,12 +146,14 @@ end |
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-- TODO test, learn am.draw |
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-- TODO test, learn am.draw |
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function hex_corner_offset(corner, size, orientation) |
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function hex_corner_offset(corner, size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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local angle = 2.0 * math.pi * orientation.angle + corner / 6 |
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local angle = 2.0 * math.pi * orientation.angle + corner / 6 |
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return vec2(size[1] * math.cos(angle), size[2] * math.sin(angle)) |
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return vec2(size[1] * math.cos(angle), size[2] * math.sin(angle)) |
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end |
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end |
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-- TODO test this thing |
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-- TODO test this thing |
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function hex_corners(hex, size, orientation) |
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function hex_corners(hex, size, orientation) |
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local orientation = orientation or DEFAULT_ORIENTATION |
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local corners = {} |
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local corners = {} |
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local center = hex_to_pixel(hex, size, orientation) |
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local center = hex_to_pixel(hex, size, orientation) |
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for i = 0, 5 do |
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for i = 0, 5 do |
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@ -139,10 +169,9 @@ function hex_to_offset(hex) |
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function offset_to_hex(off) |
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function offset_to_hex(off) |
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return vec2(off[1], off[2] - math.floor((off[1] - 1 * (off[1] % 2))) / 2) end |
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return vec2(off[1], off[2] - math.floor((off[1] - 1 * (off[1] % 2))) / 2) end |
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--[[============================================================================ |
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--============================================================================ |
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-- MAPS & STORAGE |
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-- MAPS & STORAGE |
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]] |
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-- Returns Ordered Ring-Shaped Map of |radius| from |center| |
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-- Returns Ordered Ring-Shaped Map of |radius| from |center| |
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function ring_map(center, radius) |
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function ring_map(center, radius) |
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local map = {} |
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local map = {} |
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@ -158,7 +187,6 @@ function ring_map(center, radius) |
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return setmetatable(map, {__index={center=center, radius=radius}}) |
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return setmetatable(map, {__index={center=center, radius=radius}}) |
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end |
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end |
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-- Returns Ordered Spiral Hexagonal Map of |radius| Rings from |center| |
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-- Returns Ordered Spiral Hexagonal Map of |radius| Rings from |center| |
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function spiral_map(center, radius) |
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function spiral_map(center, radius) |
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local map = {center} |
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local map = {center} |
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@ -195,7 +223,6 @@ function parallelogram_map(width, height, seed) |
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return setmetatable(map, {__index={width=width, height=height, seed=seed}}) |
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return setmetatable(map, {__index={width=width, height=height, seed=seed}}) |
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end |
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end |
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-- Returns Unordered Triangular (Equilateral) Map of |size| with Simplex Noise |
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-- Returns Unordered Triangular (Equilateral) Map of |size| with Simplex Noise |
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function triangular_map(size, seed) |
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function triangular_map(size, seed) |
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local seed = seed or math.random(size * math.cos(size) / 2) |
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local seed = seed or math.random(size * math.cos(size) / 2) |
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@ -222,7 +249,6 @@ function triangular_map(size, seed) |
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return setmetatable(map, {__index={size=size, seed=seed}}) |
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return setmetatable(map, {__index={size=size, seed=seed}}) |
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end |
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end |
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-- Returns Unordered Hexagonal Map of |radius| with Simplex Noise |
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-- Returns Unordered Hexagonal Map of |radius| with Simplex Noise |
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function hexagonal_map(radius, seed) |
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function hexagonal_map(radius, seed) |
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local seed = seed or math.random(radius * 2 * math.pi) |
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local seed = seed or math.random(radius * 2 * math.pi) |
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@ -276,18 +302,9 @@ function rectangular_map(width, height, seed) |
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end |
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end |
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j = j - math.floor(i/2) -- this is what makes it rectangular |
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j = j - math.floor(i/2) -- this is what makes it rectangular |
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-- store two dimensions as a single number |
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map[i][j] = noise |
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map[i][j] = noise |
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end |
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end |
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end |
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end |
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return setmetatable(map, {__index={width=width, height=height, seed=seed}}) |
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return setmetatable(map, {__index={width=width, height=height, seed=seed}}) |
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end |
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end |
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--[[==========================================================================-- |
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----- PATHFINDING ----- |
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============================================================================]]-- |
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-- big ol' TODO |
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