mirror of
https://github.com/mlepage/heightmap.git
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107 lines
2.9 KiB
Lua
107 lines
2.9 KiB
Lua
-- Heightmap module
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-- Copyright (C) 2011 Marc Lepage
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local max, random = math.max, math.random
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module(...)
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-- Find power of two sufficient for size
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local function pot(size)
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local pot = 2
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while true do
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if size <= pot then return pot end
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pot = 2*pot
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end
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end
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-- Create a table with 0 to n zero values
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local function tcreate(n)
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local t = {}
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for i = 0, n do t[i] = 0 end
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return t
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end
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-- Square step
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-- Sets map[x][y] from square of radius d using height function f
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local function square(map, x, y, d, f)
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local sum, num = 0, 0
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if 0 <= x-d then
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if 0 <= y-d then sum, num = sum + map[x-d][y-d], num + 1 end
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if y+d <= map.h then sum, num = sum + map[x-d][y+d], num + 1 end
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end
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if x+d <= map.w then
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if 0 <= y-d then sum, num = sum + map[x+d][y-d], num + 1 end
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if y+d <= map.h then sum, num = sum + map[x+d][y+d], num + 1 end
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end
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map[x][y] = f(map, x, y, d, sum/num)
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end
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-- Diamond step
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-- Sets map[x][y] from diamond of radius d using height function f
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local function diamond(map, x, y, d, f)
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local sum, num = 0, 0
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if 0 <= x-d then sum, num = sum + map[x-d][y], num + 1 end
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if x+d <= map.w then sum, num = sum + map[x+d][y], num + 1 end
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if 0 <= y-d then sum, num = sum + map[x][y-d], num + 1 end
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if y+d <= map.h then sum, num = sum + map[x][y+d], num + 1 end
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map[x][y] = f(map, x, y, d, sum/num)
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end
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-- Diamond square algorithm generates cloud/plasma fractal heightmap
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-- http://en.wikipedia.org/wiki/Diamond-square_algorithm
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-- Size must be power of two
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-- Height function f must look like f(map, x, y, d, h) and return h'
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local function diamondsquare(size, f)
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-- create map
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local map = { w = size, h = size }
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for c = 0, size do map[c] = tcreate(size) end
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-- seed four corners
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local d = size
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map[0][0] = f(map, 0, 0, d, 0)
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map[0][d] = f(map, 0, d, d, 0)
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map[d][0] = f(map, d, 0, d, 0)
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map[d][d] = f(map, d, d, d, 0)
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d = d/2
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-- perform square and diamond steps
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while 1 <= d do
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for x = d, map.w-1, 2*d do
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for y = d, map.h-1, 2*d do
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square(map, x, y, d, f)
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end
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end
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for x = d, map.w-1, 2*d do
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for y = 0, map.h, 2*d do
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diamond(map, x, y, d, f)
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end
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end
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for x = 0, map.w, 2*d do
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for y = d, map.h-1, 2*d do
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diamond(map, x, y, d, f)
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end
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end
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d = d/2
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end
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return map
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end
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-- Default height function
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-- d is depth (from size to 1 by powers of two)
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-- h is mean height at map[x][y] (from square/diamond of radius d)
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-- returns h' which is used to set map[x][y]
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function defaultf(map, x, y, d, h)
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return h + (random()-0.5)*d
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end
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-- Create a heightmap using the specified height function (or default)
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-- map[x][y] where x from 0 to map.w and y from 0 to map.h
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function create(width, height, f)
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f = f and f or defaultf
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-- make heightmap
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local map = diamondsquare(pot(max(width, height)), f)
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-- clip heightmap to desired size
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for x = 0, map.w do for y = height+1, map.h do map[x][y] = nil end end
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for x = width+1, map.w do map[x] = nil end
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map.w, map.h = width, height
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return map
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end
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