Added gradient calculations and moved resolution to a static #define.
This commit is contained in:
Bruce Hill
parent
7d72317846
commit
48f9da8196
74
main.lua
74
main.lua
@ -11,12 +11,12 @@ local function rng()
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local r = love.math.newRandomGenerator(1)
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return function() return r:random() end
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end
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local n1 = Noise.make1d(8,rng(),decay)
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local n2 = Noise.make2d(9,rng(),decay)
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local n3 = Noise.make3d(11,rng(),decay)
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local s1 = Noise.make1dShader(9,rng(),decay)
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local s2 = Noise.make2dShader(13,rng(),decay)
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local s3 = Noise.make3dShader(17,rng(),decay)
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local n1,g1 = Noise.make1d(8,rng(),decay)
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local n2,g2 = Noise.make2d(9,rng(),decay)
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local n3,g3 = Noise.make3d(11,rng(),decay)
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local s1,s1g = Noise.make1dShader(9,rng(),decay)
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local s2,s2g = Noise.make2dShader(13,rng(),decay)
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local s3,s3g = Noise.make3dShader(17,rng(),decay)
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local cw,ch = W/2,H/3
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local canv = lg.newCanvas(cw,ch)
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@ -52,17 +52,38 @@ function love.draw()
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local p1 = {}
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for x=0,W-H/3,DRAW_RES do
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table.insert(p1,x)
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table.insert(p1,(1-n1(x/SCALE+xOffset))*H/3)
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table.insert(p1,n1(x/SCALE+xOffset)*H/3)
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end
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lg.line(p1)
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do -- Draw tangent line
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local mx = love.mouse.getX()
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local y, dydx = n1(mx/SCALE + xOffset), g1(mx/SCALE + xOffset)
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y = y * H/3
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dydx = dydx * H/3 / SCALE
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local h = 50/math.sqrt(1+dydx^2)
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lg.setColor(255,255,0)
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lg.line(mx-h, y - h*dydx, mx + h, y + h*dydx)
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lg.setColor(255,255,255)
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end
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local p2 = {}
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local t = love.timer.getTime()-t0
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for x=0,W-H/3,DRAW_RES do
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table.insert(p2,x)
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table.insert(p2,(1+1-n2(x/SCALE+xOffset,t))*H/3)
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table.insert(p2,(1+n2(x/SCALE+xOffset,t))*H/3)
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end
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lg.line(p2)
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do -- Draw tangent line
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local mx = love.mouse.getX()
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local y = n2(mx/SCALE + xOffset, t)
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local dydx, dydz = g2(mx/SCALE + xOffset, t)
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y = (1+y) * H/3
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dydx = dydx * H/3 / SCALE
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local h = 50/math.sqrt(1+dydx^2)
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lg.setColor(255,255,0)
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lg.line(mx-h, y - h*dydx, mx + h, y + h*dydx)
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lg.setColor(255,255,255)
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end
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for y=0,H/6*1.2,2*DRAW_RES do
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local p3 = {}
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@ -87,19 +108,36 @@ function love.draw()
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lg.line(p3)
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end
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end
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do -- Draw tangent line
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local mx = love.mouse.getX()
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local my = love.mouse.getY()/2 - 1/3*H
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if my < 1/6*H then my = 1/6*H end
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mx = mx + .5*my
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local y = 2/3*H+H/6*(1-n3(mx/SCALE + xOffset, my/SCALE + yOffset, t))+my
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local dydx, dydz, _ = g3(mx/SCALE + xOffset, my/SCALE + yOffset, t)
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dydx = dydx * H/3 / SCALE
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local h = 50/math.sqrt(1+dydx^2)
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lg.setColor(255,255,0)
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lg.line(mx-h, y - h*dydx, mx + h, y + h*dydx)
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lg.setColor(255,255,255)
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end
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lg.setShader(s1)
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s1:send("range_min", xOffset)
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s1:send("range_max", xOffset+2*cw/SCALE)
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local shader
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shader = love.keyboard.isDown('g') and s1g or s1
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lg.setShader(shader)
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shader:send("range_min", xOffset)
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shader:send("range_max", xOffset+2*cw/SCALE)
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lg.draw(canv,W-cw,0)
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lg.setShader(s2)
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s2:send("range_min", {xOffset,yOffset})
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s2:send("range_max", {xOffset+2*cw/SCALE,yOffset+2*ch/SCALE})
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shader = love.keyboard.isDown('g') and s2g or s2
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lg.setShader(shader)
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shader:send("range_min", {xOffset,yOffset})
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shader:send("range_max", {xOffset+2*cw/SCALE,yOffset+2*ch/SCALE})
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lg.draw(canv,W-cw,ch)
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lg.setShader(s3)
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s3:send("range_min", {xOffset,yOffset})
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s3:send("range_max", {xOffset+2*cw/SCALE,yOffset+2*ch/SCALE})
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s3:send('z', t)
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shader = love.keyboard.isDown('g') and s3g or s3
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lg.setShader(shader)
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shader:send("range_min", {xOffset,yOffset})
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shader:send("range_max", {xOffset+2*cw/SCALE,yOffset+2*ch/SCALE})
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shader:send('z', t)
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lg.draw(canv,W-cw,2*ch)
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lg.setShader(nil)
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333
noise.lua
333
noise.lua
@ -1,11 +1,15 @@
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local noise = {}
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local exp,sin,cos,floor,log,acos,sqrt = math.exp,math.sin,math.cos,math.floor,math.log,math.acos,math.sqrt
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local exp,sin,cos,floor,log,acos,sqrt,abs = math.exp,math.sin,math.cos,math.floor,math.log,math.acos,math.sqrt,math.abs
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local GR, PI, TAU, SQRT5, LOG_GR = (sqrt(5)+1)/2, math.pi, 2*math.pi, sqrt(5), log((sqrt(5)+1)/2)
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local function cdf(x,sigma)
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local function cdf(x)
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return .5 + .5*(x<0 and -1 or 1)*sqrt(1.-exp(-4./TAU * x*x))
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end
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local function cdf_prime(x, dx)
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return (0.31831 * exp(-2/PI * x*x) * abs(x)*dx)/sqrt(1-exp(-2/PI*x*x))
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end
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local function _defaultArgs(resolution,random,decayFn)
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if not resolution then resolution = 4 end
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if not random then random = math.random end
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@ -19,6 +23,7 @@ local function _amplitudesAndOffsets(decayFn,numAmplitudes, numOffsets, random)
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for i=1,numAmplitudes do
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local a = decayFn((i-1+random())/numAmplitudes)
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amplitudes[i] = a
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assert(a > 0.0001)
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sigma = sigma + a^2
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end
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sigma = math.sqrt(sigma/2)
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@ -29,45 +34,83 @@ local function _amplitudesAndOffsets(decayFn,numAmplitudes, numOffsets, random)
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return amplitudes,sigma,offsets
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end
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local function sign(x)
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if x == 0 then return 0
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elseif x < 0 then return -1 else return 1 end
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end
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noise.make1d = function(resolution,random,decayFn)
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resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
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local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,resolution,random)
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return function(x)
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local noise = 0
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local function noise(x)
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local n = 0
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for i,a in ipairs(amplitudes) do
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noise = noise + a*cos(x/a + offsets[i])
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n = n + a*cos(x/a + offsets[i])
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end
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return cdf(noise/sigma);
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n = n/sigma
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return cdf(n)
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end
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local function gradient(x)
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local n, dndx = 0, 0
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for i,a in ipairs(amplitudes) do
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n = n + a*cos(x/a + offsets[i])
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dndx = dndx - sin(x/a + offsets[i])
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end
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dndx = dndx/sigma
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n = n/sigma
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return cdf_prime(n,dndx)
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end
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return noise, gradient
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end
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noise.make2d = function(resolution,random,decayFn)
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resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
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local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,2*resolution,random)
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sigma = sigma/sqrt(2)
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return function(x,y)
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local noise = 0
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local function noise(x,y)
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local n = 0
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for i,a in ipairs(amplitudes) do
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local angle = ((i*GR) % 1)*TAU
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local u = x*cos(angle) - y*sin(angle)
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local v = x*cos(angle+TAU/4) - y*sin(angle+TAU/4)
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noise = noise + a/2*(cos(u/a + offsets[2*i]) + cos(v/a + offsets[2*i-1]))
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local sina, cosa = sin(angle), cos(angle)
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local u = x*cosa - y*sina
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local v = -x*sina - y*cosa
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local k, w = offsets[2*i], offsets[2*i-1]
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n = n + a*(cos(u/a + k) + cos(v/a + w))
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end
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return cdf(noise/sigma);
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n = n/(2*sigma)
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return cdf(n)
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end
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local function gradient(x,y)
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local n, dx, dy = 0,0,0
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for i,a in ipairs(amplitudes) do
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local angle = ((i*GR) % 1)*TAU
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local sina, cosa = sin(angle), cos(angle)
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local u = x*cosa - y*sina
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local v = -x*sina - y*cosa
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local k, w = offsets[2*i], offsets[2*i-1]
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n = n + a*(cos(u/a + k) + cos(v/a + w))
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dx = dx + (sina*sin(v/a + w) - cosa*sin(u/a + k))
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dy = dy + (sina*sin(u/a + k) + cosa*sin(v/a + w))
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end
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n = n/(2*sigma)
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dx = dx/(2*sigma)
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dy = dy/(2*sigma)
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return cdf_prime(n,dx), cdf_prime(n,dy)
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end
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return noise, gradient
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end
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noise.make3d = function(resolution,random,decayFn)
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resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
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local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,3*resolution,random)
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sigma = sigma/sqrt(3)
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return function(x,y,z)
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local function noise(x,y,z)
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-- Find the biggest fibonacci number F_n such that F_n < resolution
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local n = floor(log((resolution-1)*SQRT5 + .5)/LOG_GR)
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local dec = floor(.5 + (GR^n)/SQRT5) -- F_n, using closed form Fibonacci
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local inc = floor(.5 + dec/GR) -- F_(n-1)
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local noise,i,j = 0,0,0
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local n,i,j = 0,0,0
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for i=0,resolution-1 do
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if j >= dec then
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j = j - dec
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@ -82,24 +125,71 @@ noise.make3d = function(resolution,random,decayFn)
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local theta = acos(-1+2*((j*GR) % 1))
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-- Make an orthonormal basis, where n1 is from polar phi/theta,
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-- n2 is roated 90 degrees along phi, and n3 is the cross product of the two
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local n1 = {sin(phi)*cos(theta), sin(phi)*sin(theta), cos(phi)}
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local n2 = {sin(phi+TAU/4.)*cos(theta), sin(phi+TAU/4.)*sin(theta), cos(phi+TAU/4.)}
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local n1x,n1y,n1z = sin(phi)*cos(theta), sin(phi)*sin(theta), cos(phi)
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local n2x,n2y,n2z = sin(phi+TAU/4.)*cos(theta), sin(phi+TAU/4.)*sin(theta), cos(phi+TAU/4.)
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-- Cross product
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local n3 = {n1[2]*n2[3] - n1[3]*n2[2],
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n1[3]*n2[1] - n1[1]*n2[3],
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n1[1]*n2[2] - n1[2]*n2[1]}
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local n3x,n3y,n3z = n1y*n2z - n1z*n2y,
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n1z*n2x - n1x*n2z,
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n1x*n2y - n1y*n2x
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-- Convert pos from x/y/z coordinates to n1/n2/n3 coordinates
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local u = n1[1]*x + n1[2]*y + n1[3]*z
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local v = n2[1]*x + n2[2]*y + n2[3]*z
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local w = n3[1]*x + n3[2]*y + n3[3]*z
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local u = n1x*x + n1y*y + n1z*z
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local v = n2x*x + n2y*y + n2z*z
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local w = n3x*x + n3y*y + n3z*z
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-- Pull the amplitude from the shuffled array index ("j"), not "i",
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-- otherwise neighboring unit vectors will have similar amplitudes!
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local a = amplitudes[j+1]
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-- Noise is the average of cosine of distance along each axis, shifted by offsets and scaled by amplitude.
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noise = noise + a*(cos(u/a + offsets[3*i+1]) + cos(v/a + offsets[3*i+2]) + cos(w/a + offsets[3*i+3]))/3
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n = n + a*(cos(u/a + offsets[3*i+1]) + cos(v/a + offsets[3*i+2]) + cos(w/a + offsets[3*i+3]))
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end
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return cdf(noise/sigma)
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return cdf(n/(3*sigma))
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end
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local function gradient(x,y,z)
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-- Find the biggest fibonacci number F_n such that F_n < resolution
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local n = floor(log((resolution-1)*SQRT5 + .5)/LOG_GR)
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local dec = floor(.5 + (GR^n)/SQRT5) -- F_n, using closed form Fibonacci
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local inc = floor(.5 + dec/GR) -- F_(n-1)
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local n,i,j = 0,0,0
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local dndx,dndy,dndz = 0,0,0
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for i=0,resolution-1 do
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if j >= dec then
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j = j - dec
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else
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j = j + inc
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if j >= resolution then
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j = j - dec
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end
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end
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-- Convert golden ratio sequence into polar coordinate unit vector
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local phi = ((i*GR) % 1)*TAU
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local theta = acos(-1+2*((j*GR) % 1))
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-- Make an orthonormal basis, where n1 is from polar phi/theta,
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-- n2 is roated 90 degrees along phi, and n3 is the cross product of the two
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local n1x,n1y,n1z = sin(phi)*cos(theta), sin(phi)*sin(theta), cos(phi)
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local n2x,n2y,n2z = sin(phi+TAU/4.)*cos(theta), sin(phi+TAU/4.)*sin(theta), cos(phi+TAU/4.)
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-- Cross product
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local n3x,n3y,n3z = n1y*n2z - n1z*n2y,
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n1z*n2x - n1x*n2z,
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n1x*n2y - n1y*n2x
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-- Convert pos from x/y/z coordinates to n1/n2/n3 coordinates
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local u = n1x*x + n1y*y + n1z*z
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local v = n2x*x + n2y*y + n2z*z
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local w = n3x*x + n3y*y + n3z*z
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-- Pull the amplitude from the shuffled array index ("j"), not "i",
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-- otherwise neighboring unit vectors will have similar amplitudes!
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local a = amplitudes[j+1]
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-- Noise is the average of cosine of distance along each axis, shifted by offsets and scaled by amplitude.
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n = n + a*(cos(u/a + offsets[3*i+1]) + cos(v/a + offsets[3*i+2]) + cos(w/a + offsets[3*i+3]))
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local kx,ky,kz = -sin(u/a+offsets[3*i+1]),-sin(v/a+offsets[3*i+2]),-sin(w/a + offsets[3*i+3])
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dndx = dndx + (n1x*kx + n2x*ky + n3x*kz)
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dndy = dndy + (n1y*kx + n2y*ky + n3y*kz)
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dndz = dndz + (n1z*kx + n2z*ky + n3z*kz)
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end
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n = n / (3*sigma)
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return cdf_prime(n, dndx/(3*sigma)), cdf_prime(n, dndy/(3*sigma)), cdf_prime(n, dndz/(3*sigma))
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end
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return noise, gradient
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end
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local shader1d = [[
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@ -114,78 +204,127 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
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{
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float x = mix(range_min,range_max,texture_coords.x);
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float noise = 0.;
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#ifdef GRADIENT
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float dndx = 0.;
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#endif
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for (int i=0; i < resolution; i++) {
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float a = amplitudes[i];
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noise += a*cos(x/a + offsets[i]);
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#ifdef GRADIENT
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dndx -= sin(x/a + offsets[i]);
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#endif
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}
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noise = noise/sigma;
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noise /= sigma;
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#ifdef GRADIENT
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dndx /= sigma;
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dndx = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndx)/sqrt(1.0-exp(-4./TAU * noise*noise));
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// TODO: normalize properly
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dndx = .5 + .5*dndx;
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return vec4(dndx,dndx,dndx, 1.);
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#else
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noise = .5 + .5*sign(noise)*sqrt(1.-exp(-4./TAU * noise*noise));
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return vec4(noise,noise,noise,1.);
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return vec4(noise,noise,noise, 1.);
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#endif
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}
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]]
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noise.make1dShader = function(resolution,random,decayFn)
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if resolution > 64 then
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error("Resolution cannot exceed 64")
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end
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local shader = lg.newShader(shader1d)
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resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
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if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
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error("Resolution must be a positive integer.")
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end
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local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader1d
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local noiseShader = lg.newShader(shaderCode)
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local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
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local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,resolution,random)
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shader:send("sigma",sigma)
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shader:send("resolution",resolution)
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shader:send("offsets",unpack(offsets))
|
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shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", 0)
|
||||
shader:send("range_max", 0)
|
||||
return shader
|
||||
do -- Dumb hack to work around a bug in Love 0.10.2 not sending the last value
|
||||
table.insert(amplitudes, 1.)
|
||||
table.insert(offsets, 1.)
|
||||
end
|
||||
for _,shader in ipairs{noiseShader, gradShader} do
|
||||
shader:send("sigma",sigma)
|
||||
shader:send("resolution",resolution)
|
||||
shader:send("offsets",unpack(offsets))
|
||||
shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", 0)
|
||||
shader:send("range_max", 0)
|
||||
end
|
||||
return noiseShader,gradShader
|
||||
end
|
||||
|
||||
local shader2d = [[
|
||||
#define TAU 6.283185307179586476925286766559005768394338798750211641949
|
||||
#define PHI 1.618033988749894848204586834365638117720309179805762862135
|
||||
#define MAX_RESOLUTION 64
|
||||
extern int resolution;
|
||||
extern float sigma;
|
||||
extern float amplitudes[MAX_RESOLUTION];
|
||||
extern vec2 offsets[MAX_RESOLUTION];
|
||||
extern float amplitudes[RESOLUTION];
|
||||
extern vec2 offsets[RESOLUTION];
|
||||
extern vec2 range_min, range_max;
|
||||
|
||||
vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
|
||||
{
|
||||
vec2 pos = mix(range_min,range_max,texture_coords);
|
||||
float noise = 0.;
|
||||
for (int i=0; i < resolution; i++) {
|
||||
#ifdef GRADIENT
|
||||
float dndx = 0., dndy = 0.;
|
||||
#endif
|
||||
for (int i=0; i < RESOLUTION; i++) {
|
||||
float angle = mod(float(i)*PHI, 1.)*TAU;
|
||||
float u = pos.x*cos(angle) - pos.y*sin(angle);
|
||||
float v = pos.x*cos(angle+TAU/4.) - pos.y*sin(angle+TAU/4.);
|
||||
float cosa = cos(angle), sina = sin(angle);
|
||||
float u = pos.x*cosa - pos.y*sina;
|
||||
float v = -pos.x*sina - pos.y*cosa;
|
||||
float a = amplitudes[i];
|
||||
noise += a*mix(cos(u/a + offsets[i].x), cos(v/a + offsets[i].y), .5);
|
||||
float k = offsets[i].x, w = offsets[i].y;
|
||||
noise += a*(cos(u/a + k) + cos(v/a + w));
|
||||
#ifdef GRADIENT
|
||||
dndx += -cosa*sin(u/a + k) + sina*sin(v/a + w);
|
||||
dndy += sina*sin(u/a + k) + cosa*sin(v/a + w);
|
||||
#endif
|
||||
}
|
||||
noise = noise/sigma;
|
||||
noise /= 2.*sigma;
|
||||
|
||||
#ifdef GRADIENT
|
||||
dndx /= 2.*sigma;
|
||||
dndx = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndx)/sqrt(1.0-exp(-4./TAU * noise*noise));
|
||||
dndx = .5 + .5*dndx;
|
||||
|
||||
dndy /= 2.*sigma;
|
||||
dndy = (0.31831 * exp(-4./TAU * noise*noise) * abs(noise)*dndy)/sqrt(1.0-exp(-4./TAU * noise*noise));
|
||||
dndy = .5 + .5*dndy;
|
||||
|
||||
return vec4(dndx,dndy,0.,1.);
|
||||
#else
|
||||
noise = .5 + .5*sign(noise)*sqrt(1.-exp(-4./TAU * noise*noise));
|
||||
return vec4(noise,noise,noise,1.);
|
||||
#endif
|
||||
}
|
||||
]]
|
||||
|
||||
noise.make2dShader = function(resolution,random,decayFn)
|
||||
if resolution > 64 then
|
||||
error("Resolution cannot exceed 64")
|
||||
end
|
||||
local shader = lg.newShader(shader2d)
|
||||
resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
|
||||
if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
|
||||
error("Resolution must be a positive integer.")
|
||||
end
|
||||
local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader2d
|
||||
local noiseShader = lg.newShader(shaderCode)
|
||||
local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
|
||||
local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,2*resolution,random)
|
||||
sigma = sigma/sqrt(2)
|
||||
local offsets2 = {}
|
||||
for i=1,#offsets-1,2 do
|
||||
table.insert(offsets2, {offsets[i],offsets[i+1]})
|
||||
end
|
||||
shader:send("sigma",sigma)
|
||||
shader:send("resolution",resolution)
|
||||
shader:send("offsets",unpack(offsets2))
|
||||
shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", {0,0})
|
||||
shader:send("range_max", {1,1})
|
||||
return shader
|
||||
do -- Dumb hack to work around a bug in Love 0.10.2 not sending the last value
|
||||
table.insert(amplitudes, 1.)
|
||||
table.insert(offsets2, {1,1})
|
||||
end
|
||||
for _,shader in ipairs{noiseShader, gradShader} do
|
||||
shader:send("sigma",sigma)
|
||||
shader:send("offsets",unpack(offsets2))
|
||||
shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", {0,0})
|
||||
shader:send("range_max", {1,1})
|
||||
end
|
||||
return noiseShader,gradShader
|
||||
end
|
||||
|
||||
local shader3d = [[
|
||||
@ -193,11 +332,9 @@ local shader3d = [[
|
||||
#define PHI 1.618033988749894848204586834365638117720309179805762862135
|
||||
#define LOG_PHI 0.481211825059603447497758913424368423135184334385660519660
|
||||
#define SQRT5 2.236067977499789696409173668731276235440618359611525724270
|
||||
#define MAX_RESOLUTION 64
|
||||
extern int resolution;
|
||||
extern float sigma, z;
|
||||
extern float amplitudes[MAX_RESOLUTION];
|
||||
extern vec3 offsets[MAX_RESOLUTION];
|
||||
extern float amplitudes[RESOLUTION];
|
||||
extern vec3 offsets[RESOLUTION];
|
||||
extern vec2 range_min, range_max;
|
||||
|
||||
// https://www.graphics.rwth-aachen.de/media/papers/jgt.pdf
|
||||
@ -205,17 +342,20 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
|
||||
{
|
||||
vec3 pos = vec3(mix(range_min,range_max,texture_coords), z);
|
||||
// Find the biggest fibonacci number F_n such that F_n < RESOLUTION
|
||||
int n = int(log((float(resolution)-1.)*SQRT5 + .5)/LOG_PHI);
|
||||
int dec = int(.5 + pow(PHI,n)/SQRT5); // F_n, using closed form Fibonacci
|
||||
int inc = int(.5 + dec/PHI); // F_(n-1)
|
||||
int fib_n = int(log((float(RESOLUTION)-1.)*SQRT5 + .5)/LOG_PHI);
|
||||
int dec = int(.5 + pow(PHI,fib_n)/SQRT5); // F_n, using closed form Fibonacci
|
||||
int inc = int(.5 + dec/PHI); // F_(fib_n-1)
|
||||
|
||||
float noise = 0.;
|
||||
for (int i=0, j=0; i<resolution; ++i) {
|
||||
float n = 0.;
|
||||
#ifdef GRADIENT
|
||||
float dndx = 0., dndy = 0., dndz = 0.;
|
||||
#endif
|
||||
for (int i=0, j=0; i<RESOLUTION; ++i) {
|
||||
if (j >= dec) {
|
||||
j -= dec;
|
||||
} else {
|
||||
j += inc;
|
||||
if (j >= resolution)
|
||||
if (j >= RESOLUTION)
|
||||
j -= dec;
|
||||
}
|
||||
// Convert golden ratio sequence into polar coordinate unit vector
|
||||
@ -235,33 +375,62 @@ vec4 effect(vec4 color, Image texture, vec2 texture_coords, vec2 pixel_coords)
|
||||
float a = amplitudes[j];
|
||||
//float a = pow(mod(float(i+1)*(PHI-1.), 1.), .3);
|
||||
// Noise is the average of cosine of distance along each axis, shifted by offsets and scaled by amplitude.
|
||||
noise += a*(cos(u/a + offsets[i].x) + cos(v/a + offsets[i].y) + cos(w/a + offsets[i].z))/3.;
|
||||
n += a*(cos(u/a + offsets[i].x) + cos(v/a + offsets[i].y) + cos(w/a + offsets[i].z));
|
||||
#ifdef GRADIENT
|
||||
vec3 k = vec3(-sin(u/a+offsets[i].x),-sin(v/a+offsets[i].y),-sin(w/a + offsets[i].z));
|
||||
dndx += (n1.x*k.x + n2.x*k.y + n3.x*k.z)/3.;
|
||||
dndy += (n1.y*k.x + n2.y*k.y + n3.y*k.z)/3.;
|
||||
dndz += (n1.z*k.x + n2.z*k.y + n3.z*k.z)/3.;
|
||||
#endif
|
||||
}
|
||||
noise = noise/sigma;
|
||||
noise = .5 + .5*sign(noise)*sqrt(1.-exp(-4./TAU * noise*noise));
|
||||
return vec4(noise,noise,noise,1.);
|
||||
n /= 3.*sigma;
|
||||
#ifdef GRADIENT
|
||||
dndx /= sigma;
|
||||
dndx = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndx)/sqrt(1.0-exp(-4./TAU * n*n));
|
||||
dndx = .5 + .5*dndx;
|
||||
|
||||
dndy /= sigma;
|
||||
dndy = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndy)/sqrt(1.0-exp(-4./TAU * n*n));
|
||||
dndy = .5 + .5*dndy;
|
||||
|
||||
dndz /= sigma;
|
||||
dndz = (0.31831 * exp(-4./TAU * n*n) * abs(n)*dndz)/sqrt(1.0-exp(-4./TAU * n*n));
|
||||
dndz = .5 + .5*dndz;
|
||||
|
||||
return vec4(dndx,dndy,dndz, 1.);
|
||||
#else
|
||||
n = .5 + .5*sign(n)*sqrt(1.-exp(-4./TAU * n*n));
|
||||
return vec4(n,n,n,1.);
|
||||
#endif
|
||||
}
|
||||
]]
|
||||
|
||||
noise.make3dShader = function(resolution,random,decayFn)
|
||||
if resolution > 64 then
|
||||
error("Resolution cannot exceed 64")
|
||||
end
|
||||
local shader = lg.newShader(shader3d)
|
||||
resolution,random,decayFn = _defaultArgs(resolution,random,decayFn)
|
||||
if type(resolution) ~= 'number' or (resolution % 1 > 0) or (resolution <= 0) then
|
||||
error("Resolution must be a positive integer.")
|
||||
end
|
||||
local shaderCode = "#define RESOLUTION "..tostring(resolution).."\n"..shader3d
|
||||
local noiseShader = lg.newShader(shaderCode)
|
||||
local gradShader = lg.newShader("#define GRADIENT\n"..shaderCode)
|
||||
local amplitudes,sigma,offsets = _amplitudesAndOffsets(decayFn,resolution,3*resolution,random)
|
||||
sigma = sigma/sqrt(3)
|
||||
local offsets2 = {}
|
||||
for i=1,#offsets-1,3 do
|
||||
table.insert(offsets2, {offsets[i],offsets[i+1],offsets[i+2]})
|
||||
end
|
||||
shader:send("sigma",sigma)
|
||||
shader:send("resolution",resolution)
|
||||
shader:send("offsets",unpack(offsets2))
|
||||
shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", {0,0})
|
||||
shader:send("range_max", {1,1})
|
||||
return shader
|
||||
do -- Dumb hack to work around a bug in Love 0.10.2 not sending the last value
|
||||
table.insert(amplitudes, 1.)
|
||||
table.insert(offsets, {1,1,1})
|
||||
end
|
||||
for _,shader in ipairs{noiseShader, gradShader} do
|
||||
shader:send("sigma",sigma)
|
||||
shader:send("offsets",unpack(offsets2))
|
||||
shader:send("amplitudes",unpack(amplitudes))
|
||||
shader:send("range_min", {0,0})
|
||||
shader:send("range_max", {1,1})
|
||||
end
|
||||
return noiseShader, gradShader
|
||||
end
|
||||
|
||||
return noise
|
||||
|
||||
Loading…
Reference in New Issue
Block a user