//Description: 学习roblox的地形工具
//Create Date: 2021-09-28 09:35:39
//Author: channy
用voxel体素表示地形数据，每个voxel有occupancy和materail两个数据，其中occupancy表示该voxel中地形占有率，material表示材质
使用了Perlin噪声，多层叠加。各种不同的地貌通过调整Perlin噪声的参数可得。
roblox的笔刷使用的不是sdf而是occupancy
roblox的网格化使用surfacenet算法
//roblox-terrain-generation.lua
local rock = 6
local snow = 4
local ice = 7
local grass = 1
local ground = 18
local mud = 10
local slate = 13
local concrete = 14
local lava = 8
local basalt = 20
local air = 0
local sand = 5
local sandstone = 17
local water = 3
local noise = math.noise
local min = math.min
local max = math.max
local sin = math.sin
local cos = math.cos
local floor = math.floor
local ceil = math.ceil
local sqrt = math.sqrt
local randomseed = math.randomseed
local random = math.random
local pi = math.pi
local tau = math.pi*2
-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/
local function BitAND(a,b)--Bitwise and
local p,c=1,0
while a>0 and b>0 do
local ra,rb=a%2,b%2
if ra+rb>1 then c=c+p end
a,b,p=(a-ra)/2,(b-rb)/2,p*2
end
return c
end
perlin = {}
perlin.p = {}
perlin.permutation = { 151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
}
perlin.size = 256
perlin.gx = {}
perlin.gy = {}
perlin.randMax = 256
function perlin:load( )
for i=1,self.size do
self.p[i] = self.permutation[i]
self.p[255+i] = self.p[i]
end
end
function perlin:noise( x, y, z )
local X = BitAND(math.floor(x), 255) + 1
local Y = BitAND(math.floor(y), 255) + 1
local Z = BitAND(math.floor(z), 255) + 1
x = x - math.floor(x)
y = y - math.floor(y)
z = z - math.floor(z)
local u = fade(x)
local v = fade(y)
local w = fade(z)
local A = self.p[X]+Y
local AA = self.p[A]+Z
local AB = self.p[A+1]+Z
local B = self.p[X+1]+Y
local BA = self.p[B]+Z
local BB = self.p[B+1]+Z
return lerp(w, lerp(v, lerp(u, grad(self.p[AA ], x , y , z ),
grad(self.p[BA ], x-1, y , z )),
lerp(u, grad(self.p[AB ], x , y-1, z ),
grad(self.p[BB ], x-1, y-1, z ))),
lerp(v, lerp(u, grad(self.p[AA+1], x , y , z-1),
grad(self.p[BA+1], x-1, y , z-1)),
lerp(u, grad(self.p[AB+1], x , y-1, z-1),
grad(self.p[BB+1], x-1, y-1, z-1))))
end
function fade( t )
return t * t * t * (t * (t * 6 - 15) + 10)
end
function lerp( t, a, b )
return a + t * (b - a)
end
function grad( hash, x, y, z )
local h = BitAND(hash, 15)
local u = h < 8 and x or y
local v = h < 4 and y or ((h == 12 or h == 14) and x or z)
return ((h and 1) == 0 and u or -u) + ((h and 2) == 0 and v or -v)
end
local masterSeed = 618033988
local mapWidth = 30
local mapHeight = 30
local biomeSize = 100
local generateCaves = false
local waterLevel = .48
local surfaceThickness = .018
local biomes = {}
randomseed(6180339)
theseed={}
for i=1,999 do
table.insert(theseed,math.random())
end
perlin:load()
local function getNoise(x,y,z,seed1)
local x = x or 0
local y = y or 0
local z = z or 0
local seed1 = seed1 or 7
local wtf=x+y+z+seed1+masterSeed + (masterSeed-x)*(seed1+z) + (seed1-y)*(masterSeed+z) -- + x*(y+z) + z*(masterSeed+seed1) + seed1*(x+y) --x+y+z+seed1+masterSeed + x*y*masterSeed-y*z+(z+masterSeed)*x --((x+y)*(y-seed1)*seed1)-(x+z)*seed2+x*11+z*23-y*17
return theseed[(floor(wtf%(#theseed)))+1]
end
local function getPerlin(x,y,z,seed,scale,raw)
local seed = seed or 0
local scale = scale or 1
if not raw then
return perlin:noise(x/scale+(seed*17)+masterSeed,y/scale-masterSeed,z/scale-seed*seed)*.5 + .5 -- accounts for bleeding from interpolated line
else
return perlin:noise(x/scale+(seed*17)+masterSeed,y/scale-masterSeed,z/scale-seed*seed)
end
end
local function thresholdFilter(value, bottom, size)
if value <= bottom then
return 0
elseif value >= bottom+size then
return 1
else
return (value-bottom)/size
end
end
local function ridgedFilter(value) --absolute and flip for ridges. and normalize
return value<.5 and value*2 or 2-value*2
end
local function ridgedFlippedFilter(value) --unflipped
return value < .5 and 1-value*2 or value*2-1
end
local function advancedRidgedFilter(value, cutoff)
local cutoff = cutoff or .5
value = value - cutoff
return 1 - (value < 0 and -value or value) * 1/(1-cutoff)
end
local function fractalize(operation,x,y,z, operationCount, scale, offset, gain)
local operationCount = operationCount or 3
local scale = scale or .5
local offset = 0
local gain = gain or 1
local totalValue = 0
local totalScale = 0
for i=1, operationCount do
local thisScale = scale^(i-1)
totalScale = totalScale + thisScale
totalValue = totalValue + (offset + gain * operation(x,y,z,i))*thisScale
end
return totalValue/totalScale
end
local function mountainsOperation(x,y,z,i)
return ridgedFilter(getPerlin(x,y,z,100+i,(1/i)*160))
end
local canyonBandingMaterial = {rock,mud,sand,sand,sandstone,sandstone,sandstone,sandstone,sandstone,sandstone,}
local function findBiomeInfo(choiceBiome,x,y,z,verticalGradientTurbulence)
local choiceBiomeValue = .5
local choiceBiomeSurface = grass
local choiceBiomeFill = rock
if choiceBiome == 'City' then
choiceBiomeValue = .55
choiceBiomeSurface = concrete
choiceBiomeFill = slate
elseif choiceBiome == 'Water' then
choiceBiomeValue = .36+getPerlin(x,y,z,2,50)*.08
choiceBiomeSurface =
(1-verticalGradientTurbulence < .44 and slate)
or sand
elseif choiceBiome == 'Marsh' then
local preLedge = getPerlin(x+getPerlin(x,0,z,5,7,true)*10+getPerlin(x,0,z,6,30,true)*50,0,z+getPerlin(x,0,z,9,7,true)*10+getPerlin(x,0,z,10,30,true)*50,2,70) --could use some turbulence
local grassyLedge = thresholdFilter(preLedge,.65,0)
local largeGradient = getPerlin(x,y,z,4,100)
local smallGradient = getPerlin(x,y,z,3,20)
local smallGradientThreshold = thresholdFilter(smallGradient,.5,0)
choiceBiomeValue = waterLevel-.04
+preLedge*grassyLedge*.025
+largeGradient*.035
+smallGradient*.025
choiceBiomeSurface =
(grassyLedge >= 1 and grass)
or (1-verticalGradientTurbulence < waterLevel-.01 and mud)
or (1-verticalGradientTurbulence < waterLevel+.01 and ground)
or grass
choiceBiomeFill = slate
elseif choiceBiome == 'Plains' then
local rivulet = ridgedFlippedFilter(getPerlin(x+getPerlin(x,y,z,17,40)*25,0,z+getPerlin(x,y,z,19,40)*25,2,200))
local rivuletThreshold = thresholdFilter(rivulet,.01,0)
local rockMap = thresholdFilter(ridgedFlippedFilter(getPerlin(x,0,z,101,7)),.3,.7) --rocks
* thresholdFilter(getPerlin(x,0,z,102,50),.6,.05) --zoning
choiceBiomeValue = .5 --.51
+getPerlin(x,y,z,2,100)*.02 --.05
+rivulet*.05 --.02
+rockMap*.05 --.03
+rivuletThreshold*.005
local verticalGradient = 1-((y-1)/(mapHeight-1))
local surfaceGradient = verticalGradient*.5 + choiceBiomeValue*.5
local thinSurface = surfaceGradient > .5-surfaceThickness*.4 and surfaceGradient < .5+surfaceThickness*.4
choiceBiomeSurface =
(rockMap>0 and rock)
or (not thinSurface and mud)
or (thinSurface and rivuletThreshold <=0 and water)
or (1-verticalGradientTurbulence < waterLevel-.01 and sand)
or grass
choiceBiomeFill =
(rockMap>0 and rock)
or sandstone
elseif choiceBiome == 'Canyons' then
local canyonNoise = ridgedFlippedFilter(getPerlin(x,0,z,2,200))
local canyonNoiseTurbed = ridgedFlippedFilter(getPerlin(x+getPerlin(x,0,z,5,20,true)*20,0,z+getPerlin(x,0,z,9,20,true)*20,2,200))
local sandbank = thresholdFilter(canyonNoiseTurbed,0,.05)
local canyonTop = thresholdFilter(canyonNoiseTurbed,.125,0)
local mesaSlope = thresholdFilter(canyonNoise,.33,.12)
local mesaTop = thresholdFilter(canyonNoiseTurbed,.49,0)
choiceBiomeValue = .42
+getPerlin(x,y,z,2,70)*.05
+canyonNoise*.05
+sandbank*.04 --canyon bottom slope
+thresholdFilter(canyonNoiseTurbed,.05,0)*.08 --canyon cliff
+thresholdFilter(canyonNoiseTurbed,.05,.075)*.04 --canyon cliff top slope
+canyonTop*.01 --canyon cliff top ledge
+thresholdFilter(canyonNoiseTurbed,.0575,.2725)*.01 --plane slope
+mesaSlope*.06 --mesa slope
+thresholdFilter(canyonNoiseTurbed,.45,0)*.14 --mesa cliff
+thresholdFilter(canyonNoiseTurbed,.45,.04)*.025 --mesa cap
+mesaTop*.02 --mesa top ledge
choiceBiomeSurface =
(1-verticalGradientTurbulence < waterLevel+.015 and sand) --this for biome blending in to lakes
or (sandbank>0 and sandbank<1 and sand) --this for canyonbase sandbanks
--or (canyonTop>0 and canyonTop<=1 and mesaSlope<=0 and grass) --this for grassy canyon tops
--or (mesaTop>0 and mesaTop<=1 and grass) --this for grassy mesa tops
or sandstone
choiceBiomeFill = canyonBandingMaterial[ceil((1-getNoise(1,y,2))*10)]
elseif choiceBiome == 'Hills' then
local rivulet = ridgedFlippedFilter(getPerlin(x+getPerlin(x,y,z,17,20)*20,0,z+getPerlin(x,y,z,19,20)*20,2,200))^(1/2)
local largeHills = getPerlin(x,y,z,3,60)
choiceBiomeValue = .48
+largeHills*.05
+(.05
+largeHills*.1
+getPerlin(x,y,z,4,25)*.125)
*rivulet
local surfaceMaterialGradient = (1-verticalGradientTurbulence)*.9 + rivulet*.1
choiceBiomeSurface =
(surfaceMaterialGradient < waterLevel-.015 and mud)
or (surfaceMaterialGradient < waterLevel and ground)
or grass
choiceBiomeFill = slate
elseif choiceBiome == 'Dunes' then
local duneTurbulence = getPerlin(x,0,z,227,20)*24
local layer1 = ridgedFilter(getPerlin(x,0,z,201,40))
local layer2 = ridgedFilter(getPerlin(x/10+duneTurbulence,0,z+duneTurbulence,200,48))
choiceBiomeValue = .4+.1*(layer1 + layer2)
choiceBiomeSurface = sand
choiceBiomeFill = sandstone
elseif choiceBiome == 'Mountains' then
local rivulet = ridgedFlippedFilter(getPerlin(x+getPerlin(x,y,z,17,20)*20,0,z+getPerlin(x,y,z,19,20)*20,2,200))
choiceBiomeValue = -.4 --.3
+fractalize(mountainsOperation,x,y/20,z, 8, .65)*1.2
+rivulet*.2
choiceBiomeSurface =
(verticalGradientTurbulence < .275 and snow)
or (verticalGradientTurbulence < .35 and rock)
or (verticalGradientTurbulence < .4 and ground)
or (1-verticalGradientTurbulence < waterLevel and rock)
or (1-verticalGradientTurbulence < waterLevel+.01 and mud)
or (1-verticalGradientTurbulence < waterLevel+.015 and ground)
or grass
elseif choiceBiome == 'Lavaflow' then
local crackX = x+getPerlin(x,y*.25,z,21,8,true)*5
local crackY = y+getPerlin(x,y*.25,z,22,8,true)*5
local crackZ = z+getPerlin(x,y*.25,z,23,8,true)*5
local crack1 = ridgedFilter(getPerlin(crackX+getPerlin(x,y,z,22,30,true)*30,crackY,crackZ+getPerlin(x,y,z,24,30,true)*30,2,120))
local crack2 = ridgedFilter(getPerlin(crackX,crackY,crackZ,3,40))*(crack1*.25+.75)
local crack3 = ridgedFilter(getPerlin(crackX,crackY,crackZ,4,20))*(crack2*.25+.75)
local generalHills = thresholdFilter(getPerlin(x,y,z,9,40),.25,.5)*getPerlin(x,y,z,10,60)
local cracks = max(0,1-thresholdFilter(crack1,.975,0)-thresholdFilter(crack2,.925,0)-thresholdFilter(crack3,.9,0))
local spireVec = CFrame.Angles(.7,.7,0)*Vector3.new(crackX,crackY,crackZ)
local spires = thresholdFilter(getPerlin(spireVec.x/40,spireVec.y/300,spireVec.z/30,123,1),.6,.4)
choiceBiomeValue = waterLevel+.02
+cracks*(.5+generalHills*.5)*.02
+generalHills*.05
+spires*.3
+((1-verticalGradientTurbulence > waterLevel+.01 or spires>0) and .04 or 0) --This lets it lip over water
choiceBiomeFill = (spires>0 and rock) or (cracks<1 and lava) or basalt
choiceBiomeSurface = (choiceBiomeFill == lava and 1-verticalGradientTurbulence < waterLevel and basalt) or choiceBiomeFill
elseif choiceBiome == 'Arctic' then
local preBoundary = getPerlin(x+getPerlin(x,0,z,5,8,true)*5,y/8,z+getPerlin(x,0,z,9,8,true)*5,2,20)
--local cliffs = thresholdFilter(preBoundary,.5,0)
local boundary = ridgedFilter(preBoundary)
local roughChunks = getPerlin(x,y/4,z,436,2)
local boundaryMask = thresholdFilter(boundary,.8,.1) --,.7,.25)
local boundaryTypeMask = getPerlin(x,0,z,6,74)-.5
local boundaryComp = 0
if boundaryTypeMask < 0 then --divergent
boundaryComp = (boundary > (1+boundaryTypeMask*.5) and -.17 or 0)
--* boundaryTypeMask*-2
else --convergent
boundaryComp = boundaryMask*.1*roughChunks
* boundaryTypeMask
end
choiceBiomeValue = .55
+boundary*.05*boundaryTypeMask --.1 --soft slope up or down to boundary
+boundaryComp --convergent/divergent effects
+getPerlin(x,0,z,123,25)*.025 --*cliffs --gentle rolling slopes
choiceBiomeSurface = (1-verticalGradientTurbulence < waterLevel-.1 and ice) or (boundaryMask>.6 and boundaryTypeMask>.1 and roughChunks>.5 and ice) or snow
choiceBiomeFill = ice
end
return choiceBiomeValue, choiceBiomeSurface, choiceBiomeFill
end
function findBiomeTransitionValue(biome,weight,value,averageValue)
if biome == 'Arctic' then
return (weight>.2 and 1 or 0)*value
elseif biome == 'Canyons' then
return (weight>.7 and 1 or 0)*value
elseif biome == 'Mountains' then
local weight = weight^3 --This improves the ease of mountains transitioning to other biomes
return averageValue*(1-weight)+value*weight
else
return averageValue*(1-weight)+value*weight
end
end
local allBiomes = {
['Mountains'] = true,
['Canyons'] = false,
['Dunes'] = false,
['Arctic'] = false,
['Lavaflow'] = false,
['Hills'] = true,
['Plains'] = true,
['Marsh'] = false,
['Water'] = false,
}
function generate()
local mapWidth = mapWidth
local biomeSize = biomeSize
local biomeBlendPercent = .25 --(biomeSize==50 or biomeSize == 100) and .5 or .25
local biomeBlendPercentInverse = 1-biomeBlendPercent
local biomeBlendDistortion = biomeBlendPercent
local smoothScale = .5/mapHeight
biomes = {}
for i,v in pairs(allBiomes) do
if v then
table.insert(biomes,i)
end
end
if #biomes<=0 then
--table.insert(biomes,'Hills')
--table.insert(biomes, 'Mountains')
table.insert(biomes, 'Dunes')
end
--local oMap = {}
--local mMap = {}
for x = 1, mapWidth do
local oMapX = {}
--oMap[x] = oMapX
local mMapX = {}
--mMap[x] = mMapX
for z = 1, mapWidth do
local biomeNoCave = false
local cellToBiomeX = x/biomeSize + getPerlin(x,0,z,233,biomeSize*.3)*.25 + getPerlin(x,0,z,235,biomeSize*.05)*.075
local cellToBiomeZ = z/biomeSize + getPerlin(x,0,z,234,biomeSize*.3)*.25 + getPerlin(x,0,z,236,biomeSize*.05)*.075
local closestPoint = {0,0,0}
local closestDistance = 1000000
local biomePoints = {}
for vx=-1,1 do
for vz=-1,1 do
local gridPointX = floor(cellToBiomeX+vx+.5)
local gridPointZ = floor(cellToBiomeZ+vz+.5)
--local pointX, pointZ = getBiomePoint(gridPointX,gridPointZ)
local pointX = gridPointX+(getNoise(gridPointX,gridPointZ,53)-.5)*.75 --de-uniforming grid for vornonoi
local pointZ = gridPointZ+(getNoise(gridPointX,gridPointZ,73)-.5)*.75
local dist = sqrt((pointX-cellToBiomeX)^2 + (pointZ-cellToBiomeZ)^2)
if dist < closestDistance then
closestPoint = {pointX,0,pointZ}
closestDistance = dist
end
table.insert(biomePoints,{
x = pointX,
z = pointZ,
dist = dist,
biomeNoise = getNoise(gridPointX,gridPointZ),
weight = 0
})
end
end
local weightTotal = 0
local weightPoints = {}
for _,point in pairs(biomePoints) do
local weight = point.dist == closestDistance and 1 or ((closestDistance / point.dist)-biomeBlendPercentInverse)/biomeBlendPercent
if weight > 0 then
local weight = weight^2.1 --this smooths the biome transition from linear to cubic InOut
weightTotal = weightTotal + weight
local biome = biomes[ceil(#biomes*(1-point.biomeNoise))] --inverting the noise so that it is limited as (0,1]. One less addition operation when finding a random list index
weightPoints[biome] = {
weight = weightPoints[biome] and weightPoints[biome].weight + weight or weight
}
end
end
for biome,info in pairs(weightPoints) do
info.weight = info.weight / weightTotal
if biome == 'Arctic' then --biomes that don't have caves that breach the surface
biomeNoCave = true
end
end
for y = 1, mapHeight do
local oMapY = oMapX[y] or {}
oMapX[y] = oMapY
local mMapY = mMapX[y] or {}
mMapX[y] = mMapY
--[[local oMapY = {}
oMapX[y] = oMapY
local mMapY = {}
mMapX[z] = mMapY]]
local verticalGradient = 1-((y-1)/(mapHeight-1))
local caves = 0
local verticalGradientTurbulence = verticalGradient*.9 + .1*getPerlin(x,y,z,107,15)
local choiceValue = 0
local choiceSurface = lava
local choiceFill = rock
if verticalGradient > .65 or verticalGradient < .1 then
--under surface of every biome; don't get biome data; waste of time.
choiceValue = .5
elseif #biomes == 1 then
choiceValue, choiceSurface, choiceFill = findBiomeInfo(biomes[1],x,y,z,verticalGradientTurbulence)
else
local averageValue = 0
--local findChoiceMaterial = -getNoise(x,y,z,19)
for biome,info in pairs(weightPoints) do
local biomeValue, biomeSurface, biomeFill = findBiomeInfo(biome,x,y,z,verticalGradientTurbulence)
info.biomeValue = biomeValue
info.biomeSurface = biomeSurface
info.biomeFill = biomeFill
local value = biomeValue * info.weight
averageValue = averageValue + value
--[[if findChoiceMaterial < 0 and findChoiceMaterial + weight >= 0 then
choiceMaterial = biomeMaterial
end
findChoiceMaterial = findChoiceMaterial + weight]]
end
for biome,info in pairs(weightPoints) do
local value = findBiomeTransitionValue(biome,info.weight,info.biomeValue,averageValue)
if value > choiceValue then
choiceValue = value
choiceSurface = info.biomeSurface
choiceFill = info.biomeFill
end
end
end
local preCaveComp = verticalGradient*.5 + choiceValue*.5
local surface = preCaveComp > .5-surfaceThickness and preCaveComp < .5+surfaceThickness
if generateCaves --user wants caves
and (not biomeNoCave or verticalGradient > .65) --biome allows caves or deep enough
and not (surface and (1-verticalGradient) < waterLevel+.005) --caves only breach surface above waterlevel
and not (surface and (1-verticalGradient) > waterLevel+.58) then --caves don't go too high so that they don't cut up mountain tops
local ridged2 = ridgedFilter(getPerlin(x,y,z,4,30))
local caves2 = thresholdFilter(ridged2,.84,.01)
local ridged3 = ridgedFilter(getPerlin(x,y,z,5,30))
local caves3 = thresholdFilter(ridged3,.84,.01)
local ridged4 = ridgedFilter(getPerlin(x,y,z,6,30))
local caves4 = thresholdFilter(ridged4,.84,.01)
local caveOpenings = (surface and 1 or 0) * thresholdFilter(getPerlin(x,0,z,143,62),.35,0) --.45
caves = caves2 * caves3 * caves4 - caveOpenings
caves = caves < 0 and 0 or caves > 1 and 1 or caves
end
local comp = preCaveComp - caves
local smoothedResult = thresholdFilter(comp,.5,smoothScale)
---below water level -above surface -no terrain
if 1-verticalGradient < waterLevel and preCaveComp <= .5 and smoothedResult <= 0 then
smoothedResult = 1
choiceSurface = water
choiceFill = water
surface = true
end
oMapY[z] = (y == 1 and 1) or smoothedResult
mMapY[z] = (y == 1 and lava) or (smoothedResult <= 0 and air) or (surface and choiceSurface) or choiceFill
--sdf and material
print(x, y, z, oMapY[z], mMapY[z]);
end
end
end
--print('Generation Complete')
end
generate()