From a78d58c67dc996b1fa0c368d9df813384e48a49f Mon Sep 17 00:00:00 2001 From: tangent Date: Sat, 15 Aug 2026 02:21:56 -0600 Subject: [PATCH] Fix bad unicode in source. --- simplex.lua | 1084 +++++++++++++++++++++++++-------------------------- 1 file changed, 542 insertions(+), 542 deletions(-) diff --git a/simplex.lua b/simplex.lua index c5f78b6..f2e52a7 100644 --- a/simplex.lua +++ b/simplex.lua @@ -1,543 +1,543 @@ ------------------------------------------------ ----Simplex Noise --- Original Java Source: http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf --- (most) Original comments included ------------------------------------------------ - -local math = math -local table = table -local tonumber = tonumber -local ipairs = ipairs -local error = error -local bit = require("bit") - -local simplex = {} - -simplex.DIR_X = 0 -simplex.DIR_Y = 1 -simplex.DIR_Z = 2 -simplex.DIR_W = 3 -simplex.internalCache = false - - -local Gradients3D = {{1,1,0},{-1,1,0},{1,-1,0},{-1,-1,0}, -{1,0,1},{-1,0,1},{1,0,-1},{-1,0,-1}, -{0,1,1},{0,-1,1},{0,1,-1},{0,-1,-1}}; -local Gradients4D = {{0,1,1,1}, {0,1,1,-1}, {0,1,-1,1}, {0,1,-1,-1}, -{0,-1,1,1}, {0,-1,1,-1}, {0,-1,-1,1}, {0,-1,-1,-1}, -{1,0,1,1}, {1,0,1,-1}, {1,0,-1,1}, {1,0,-1,-1}, -{-1,0,1,1}, {-1,0,1,-1}, {-1,0,-1,1}, {-1,0,-1,-1}, -{1,1,0,1}, {1,1,0,-1}, {1,-1,0,1}, {1,-1,0,-1}, -{-1,1,0,1}, {-1,1,0,-1}, {-1,-1,0,1}, {-1,-1,0,-1}, -{1,1,1,0}, {1,1,-1,0}, {1,-1,1,0}, {1,-1,-1,0}, -{-1,1,1,0}, {-1,1,-1,0}, {-1,-1,1,0}, {-1,-1,-1,0}}; -local p = {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}; - --- To remove the need for index wrapping, double the permutation table length - -for i=1,#p do - p[i-1] = p[i] - p[i] = nil -end - -for i=1,#Gradients3D do - Gradients3D[i-1] = Gradients3D[i] - Gradients3D[i] = nil -end - -for i=1,#Gradients4D do - Gradients4D[i-1] = Gradients4D[i] - Gradients4D[i] = nil -end - -local perm = {} - -for i=0,255 do - perm[i] = p[i] - perm[i+256] = p[i] -end - --- A lookup table to traverse the sim around a given point in 4D. --- Details can be found where this table is used, in the 4D noise method. - -local sim = { -{0,1,2,3},{0,1,3,2},{0,0,0,0},{0,2,3,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,2,3,0}, -{0,2,1,3},{0,0,0,0},{0,3,1,2},{0,3,2,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,3,2,0}, -{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, -{1,2,0,3},{0,0,0,0},{1,3,0,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,3,0,1},{2,3,1,0}, -{1,0,2,3},{1,0,3,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,0,3,1},{0,0,0,0},{2,1,3,0}, -{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, -{2,0,1,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,0,1,2},{3,0,2,1},{0,0,0,0},{3,1,2,0}, -{2,1,0,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,1,0,2},{0,0,0,0},{3,2,0,1},{3,2,1,0}}; - -local function Dot2D(tbl, x, y) - return tbl[1]*x + tbl[2]*y; -end - -local function Dot3D(tbl, x, y, z) - return tbl[1]*x + tbl[2]*y + tbl[3]*z -end - -local function Dot4D( tbl, x,y,z,w) - return tbl[1]*x + tbl[2]*y + tbl[3]*z + tbl[3]*w; -end - -local Prev2D = {} - - --- 2D simplex noise - -function simplex.Noise2D(xin, yin) - if simplex.internalCache and Prev2D[xin] and Prev2D[xin][yin] then return Prev2D[xin][yin] end - - local n0, n1, n2; -- Noise contributions from the three corners - -- Skew the input space to determine which simplex cell we're in - local F2 = 0.5*(math.sqrt(3.0)-1.0); - local s = (xin+yin)*F2; -- Hairy factor for 2D - local i = math.floor(xin+s); - local j = math.floor(yin+s); - local G2 = (3.0-math.sqrt(3.0))/6.0; - - local t = (i+j)*G2; - local X0 = i-t; -- Unskew the cell origin back to (x,y) space - local Y0 = j-t; - local x0 = xin-X0; -- The x,y distances from the cell origin - local y0 = yin-Y0; - - -- For the 2D case, the simplex shape is an equilateral triangle. - -- Determine which simplex we are in. - local i1, j1; -- Offsets for second (middle) corner of simplex in (i,j) coords - if(x0>y0) then - i1=1 - j1=0 -- lower triangle, XY order: (0,0)->(1,0)->(1,1) - else - i1=0 - j1=1 -- upper triangle, YX order: (0,0)->(0,1)->(1,1) - end - - -- A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and - -- a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where - -- c = (3-sqrt(3))/6 - - local x1 = x0 - i1 + G2; -- Offsets for middle corner in (x,y) unskewed coords - local y1 = y0 - j1 + G2; - local x2 = x0 - 1.0 + 2.0 * G2; -- Offsets for last corner in (x,y) unskewed coords - local y2 = y0 - 1.0 + 2.0 * G2; - - -- Work out the hashed gradient indices of the three simplex corners - local ii = bit.band(i , 255) - local jj = bit.band(j , 255) - local gi0 = perm[ii+perm[jj]] % 12; - local gi1 = perm[ii+i1+perm[jj+j1]] % 12; - local gi2 = perm[ii+1+perm[jj+1]] % 12; - - -- Calculate the contribution from the three corners - local t0 = 0.5 - x0*x0-y0*y0; - if t0<0 then - n0 = 0.0; - else - t0 = t0 * t0 - n0 = t0 * t0 * Dot2D(Gradients3D[gi0], x0, y0); -- (x,y) of Gradients3D used for 2D gradient - end - - local t1 = 0.5 - x1*x1-y1*y1; - if (t1<0) then - n1 = 0.0; - else - t1 = t1*t1 - n1 = t1 * t1 * Dot2D(Gradients3D[gi1], x1, y1); - end - - local t2 = 0.5 - x2*x2-y2*y2; - if (t2<0) then - n2 = 0.0; - else - t2 = t2*t2 - n2 = t2 * t2 * Dot2D(Gradients3D[gi2], x2, y2); - end - - - -- Add contributions from each corner to get the final noise value. - -- The result is scaled to return values in the localerval [-1,1]. - - local retval = 70.0 * (n0 + n1 + n2) - - if simplex.internalCache then - if not Prev2D[xin] then Prev2D[xin] = {} end - Prev2D[xin][yin] = retval - end - - return retval; -end - -local Prev3D = {} - --- 3D simplex noise -function simplex.Noise3D(xin, yin, zin) - - if simplex.internalCache and Prev3D[xin] and Prev3D[xin][yin] and Prev3D[xin][yin][zin] then return Prev3D[xin][yin][zin] end - - local n0, n1, n2, n3; -- Noise contributions from the four corners - - -- Skew the input space to determine which simplex cell we're in - local F3 = 1.0/3.0; - local s = (xin+yin+zin)*F3; -- Very nice and simple skew factor for 3D - local i = math.floor(xin+s); - local j = math.floor(yin+s); - local k = math.floor(zin+s); - - local G3 = 1.0/6.0; -- Very nice and simple unskew factor, too - local t = (i+j+k)*G3; - - local X0 = i-t; -- Unskew the cell origin back to (x,y,z) space - local Y0 = j-t; - local Z0 = k-t; - - local x0 = xin-X0; -- The x,y,z distances from the cell origin - local y0 = yin-Y0; - local z0 = zin-Z0; - - -- For the 3D case, the simplex shape is a slightly irregular tetrahedron. - -- Determine which simplex we are in. - local i1, j1, k1; -- Offsets for second corner of simplex in (i,j,k) coords - local i2, j2, k2; -- Offsets for third corner of simplex in (i,j,k) coords - - if (x0>=y0) then - if (y0>=z0) then - i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; -- X Y Z order - elseif (x0>=z0) then - i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; -- X Z Y order - else - i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; -- Z X Y order - end - else -- x0 y0) and 32 or 1; - local c2 = (x0 > z0) and 16 or 1; - local c3 = (y0 > z0) and 8 or 1; - local c4 = (x0 > w0) and 4 or 1; - local c5 = (y0 > w0) and 2 or 1; - local c6 = (z0 > w0) and 1 or 1; - local c = c1 + c2 + c3 + c4 + c5 + c6; - local i1, j1, k1, l1; -- The localeger offsets for the second simplex corner - local i2, j2, k2, l2; -- The localeger offsets for the third simplex corner - local i3, j3, k3, l3; -- The localeger offsets for the fourth simplex corner - - -- sim[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. - -- Many values of c will never occur, since e.g. x>y>z>w makes x=3 and 1 or 0; - j1 = sim[c][2]>=3 and 1 or 0; - k1 = sim[c][3]>=3 and 1 or 0; - l1 = sim[c][4]>=3 and 1 or 0; - -- The number 2 in the "sim" array is at the second largest coordinate. - i2 = sim[c][1]>=2 and 1 or 0; - j2 = sim[c][2]>=2 and 1 or 0; - k2 = sim[c][3]>=2 and 1 or 0; - l2 = sim[c][4]>=2 and 1 or 0; - -- The number 1 in the "sim" array is at the second smallest coordinate. - i3 = sim[c][1]>=1 and 1 or 0; - j3 = sim[c][2]>=1 and 1 or 0; - k3 = sim[c][3]>=1 and 1 or 0; - l3 = sim[c][4]>=1 and 1 or 0; - -- The fifth corner has all coordinate offsets = 1, so no need to look that up. - local x1 = x0 - i1 + G4; -- Offsets for second corner in (x,y,z,w) coords - local y1 = y0 - j1 + G4; - local z1 = z0 - k1 + G4; - local w1 = w0 - l1 + G4; - local x2 = x0 - i2 + 2.0*G4; -- Offsets for third corner in (x,y,z,w) coords - local y2 = y0 - j2 + 2.0*G4; - local z2 = z0 - k2 + 2.0*G4; - local w2 = w0 - l2 + 2.0*G4; - local x3 = x0 - i3 + 3.0*G4; -- Offsets for fourth corner in (x,y,z,w) coords - local y3 = y0 - j3 + 3.0*G4; - local z3 = z0 - k3 + 3.0*G4; - local w3 = w0 - l3 + 3.0*G4; - local x4 = x0 - 1.0 + 4.0*G4; -- Offsets for last corner in (x,y,z,w) coords - local y4 = y0 - 1.0 + 4.0*G4; - local z4 = z0 - 1.0 + 4.0*G4; - local w4 = w0 - 1.0 + 4.0*G4; - - -- Work out the hashed gradient indices of the five simplex corners - local ii = bit.band(i , 255) - local jj = bit.band(j , 255) - local kk = bit.band(k , 255) - local ll = bit.band(l , 255) - local gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32; - local gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32; - local gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32; - local gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32; - local gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32; - - - -- Calculate the contribution from the five corners - local t0 = 0.5 - x0*x0 - y0*y0 - z0*z0 - w0*w0; - if (t0<0) then - n0 = 0.0; - else - t0 = t0*t0; - n0 = t0 * t0 * Dot4D(Gradients4D[gi0], x0, y0, z0, w0); - end - - local t1 = 0.5 - x1*x1 - y1*y1 - z1*z1 - w1*w1; - if (t1<0) then - n1 = 0.0; - else - t1 = t1*t1; - n1 = t1 * t1 * Dot4D(Gradients4D[gi1], x1, y1, z1, w1); - end - - local t2 = 0.5 - x2*x2 - y2*y2 - z2*z2 - w2*w2; - if (t2<0) then - n2 = 0.0; - else - t2 = t2*t2; - n2 = t2 * t2 * Dot4D(Gradients4D[gi2], x2, y2, z2, w2); - end - - local t3 = 0.5 - x3*x3 - y3*y3 - z3*z3 - w3*w3; - if (t3<0) then - n3 = 0.0; - else - t3 = t3*t3; - n3 = t3 * t3 * Dot4D(Gradients4D[gi3], x3, y3, z3, w3); - end - - local t4 = 0.5 - x4*x4 - y4*y4 - z4*z4 - w4*w4; - if (t4<0) then - n4 = 0.0; - else - t4 = t4*t4; - n4 = t4 * t4 * Dot4D(Gradients4D[gi4], x4, y4, z4, w4); - end - - -- Sum up and scale the result to cover the range [-1,1] - - local retval = 27.0 * (n0 + n1 + n2 + n3 + n4) - - if simplex.internalCache then - if not Prev4D[x] then Prev4D[x] = {} end - if not Prev4D[x][y] then Prev4D[x][y] = {} end - if not Prev4D[x][y][z] then Prev4D[x][y][z] = {} end - Prev4D[x][y][z][w] = retval - end - - return retval; - - -end - -local e = 2.71828182845904523536 - -local PrevBlur2D = {} - -function simplex.GBlur2D(x,y,stdDev) - if simplex.internalCache and PrevBlur2D[x] and PrevBlur2D[x][y] and PrevBlur2D[x][y][stdDev] then return PrevBlur2D[x][y][stdDev] end - local pwr = ((x^2+y^2)/(2*(stdDev^2)))*-1 - local ret = (1/(2*math.pi*(stdDev^2)))*(e^pwr) - - if simplex.internalCache then - if not PrevBlur2D[x] then PrevBlur2D[x] = {} end - if not PrevBlur2D[x][y] then PrevBlur2D[x][y] = {} end - PrevBlur2D[x][y][stdDev] = ret - end - return ret -end - -local PrevBlur1D = {} - -function simplex.GBlur1D(x,stdDev) - if simplex.internalCache and PrevBlur1D[x] and PrevBlur1D[x][stdDev] then return PrevBlur1D[x][stdDev] end - local pwr = (x^2/(2*stdDev^2))*-1 - local ret = (1/(math.sqrt(2*math.pi)*stdDev))*(e^pwr) - - if simplex.internalCache then - if not PrevBlur1D[x] then PrevBlur1D[x] = {} end - PrevBlur1D[x][stdDev] = ret - end - return ret -end - -function simplex.FractalSum(func, iter, ...) - local ret = func(...) - for i=1,iter do - local power = 2^iter - local s = power/i - - local scaled = {} - for elem in ipairs({...}) do - table.insert(scaled, elem*s) - end - ret = ret + (i/power)*(func(unpack(scaled))) - end - return ret -end - -function simplex.FractalSumAbs(func, iter, ...) - local ret = math.abs(func(...)) - for i=1,iter do - local power = 2^iter - local s = power/i - - local scaled = {} - for elem in ipairs({...}) do - table.insert(scaled, elem*s) - end - ret = ret + (i/power)*(math.abs(func(unpack(scaled)))) - end - return ret -end - -function simplex.Turbulence(func, direction, iter, ...) - local ret = math.abs(func(...)) - for i=1,iter do - local power = 2^iter - local s = power/i - - local scaled = {} - for elem in ipairs({...}) do - table.insert(scaled, elem*s) - end - ret = ret + (i/power)*(math.abs(func(unpack(scaled)))) - end - local args = {...} - local dir_component = args[direction+1] - return math.sin(dir_component+ret) -end - +----------------------------------------------- +---Simplex Noise +-- Original Java Source: http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf +-- (most) Original comments included +----------------------------------------------- + +local math = math +local table = table +local tonumber = tonumber +local ipairs = ipairs +local error = error +local bit = require("bit") + +local simplex = {} + +simplex.DIR_X = 0 +simplex.DIR_Y = 1 +simplex.DIR_Z = 2 +simplex.DIR_W = 3 +simplex.internalCache = false + + +local Gradients3D = {{1,1,0},{-1,1,0},{1,-1,0},{-1,-1,0}, +{1,0,1},{-1,0,1},{1,0,-1},{-1,0,-1}, +{0,1,1},{0,-1,1},{0,1,-1},{0,-1,-1}}; +local Gradients4D = {{0,1,1,1}, {0,1,1,-1}, {0,1,-1,1}, {0,1,-1,-1}, +{0,-1,1,1}, {0,-1,1,-1}, {0,-1,-1,1}, {0,-1,-1,-1}, +{1,0,1,1}, {1,0,1,-1}, {1,0,-1,1}, {1,0,-1,-1}, +{-1,0,1,1}, {-1,0,1,-1}, {-1,0,-1,1}, {-1,0,-1,-1}, +{1,1,0,1}, {1,1,0,-1}, {1,-1,0,1}, {1,-1,0,-1}, +{-1,1,0,1}, {-1,1,0,-1}, {-1,-1,0,1}, {-1,-1,0,-1}, +{1,1,1,0}, {1,1,-1,0}, {1,-1,1,0}, {1,-1,-1,0}, +{-1,1,1,0}, {-1,1,-1,0}, {-1,-1,1,0}, {-1,-1,-1,0}}; +local p = {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}; + +-- To remove the need for index wrapping, double the permutation table length + +for i=1,#p do + p[i-1] = p[i] + p[i] = nil +end + +for i=1,#Gradients3D do + Gradients3D[i-1] = Gradients3D[i] + Gradients3D[i] = nil +end + +for i=1,#Gradients4D do + Gradients4D[i-1] = Gradients4D[i] + Gradients4D[i] = nil +end + +local perm = {} + +for i=0,255 do + perm[i] = p[i] + perm[i+256] = p[i] +end + +-- A lookup table to traverse the sim around a given point in 4D. +-- Details can be found where this table is used, in the 4D noise method. + +local sim = { +{0,1,2,3},{0,1,3,2},{0,0,0,0},{0,2,3,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,2,3,0}, +{0,2,1,3},{0,0,0,0},{0,3,1,2},{0,3,2,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,3,2,0}, +{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, +{1,2,0,3},{0,0,0,0},{1,3,0,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,3,0,1},{2,3,1,0}, +{1,0,2,3},{1,0,3,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,0,3,1},{0,0,0,0},{2,1,3,0}, +{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, +{2,0,1,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,0,1,2},{3,0,2,1},{0,0,0,0},{3,1,2,0}, +{2,1,0,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,1,0,2},{0,0,0,0},{3,2,0,1},{3,2,1,0}}; + +local function Dot2D(tbl, x, y) + return tbl[1]*x + tbl[2]*y; +end + +local function Dot3D(tbl, x, y, z) + return tbl[1]*x + tbl[2]*y + tbl[3]*z +end + +local function Dot4D( tbl, x,y,z,w) + return tbl[1]*x + tbl[2]*y + tbl[3]*z + tbl[3]*w; +end + +local Prev2D = {} + + +-- 2D simplex noise + +function simplex.Noise2D(xin, yin) + if simplex.internalCache and Prev2D[xin] and Prev2D[xin][yin] then return Prev2D[xin][yin] end + + local n0, n1, n2; -- Noise contributions from the three corners + -- Skew the input space to determine which simplex cell we're in + local F2 = 0.5*(math.sqrt(3.0)-1.0); + local s = (xin+yin)*F2; -- Hairy factor for 2D + local i = math.floor(xin+s); + local j = math.floor(yin+s); + local G2 = (3.0-math.sqrt(3.0))/6.0; + + local t = (i+j)*G2; + local X0 = i-t; -- Unskew the cell origin back to (x,y) space + local Y0 = j-t; + local x0 = xin-X0; -- The x,y distances from the cell origin + local y0 = yin-Y0; + + -- For the 2D case, the simplex shape is an equilateral triangle. + -- Determine which simplex we are in. + local i1, j1; -- Offsets for second (middle) corner of simplex in (i,j) coords + if(x0>y0) then + i1=1 + j1=0 -- lower triangle, XY order: (0,0)->(1,0)->(1,1) + else + i1=0 + j1=1 -- upper triangle, YX order: (0,0)->(0,1)->(1,1) + end + + -- A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and + -- a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where + -- c = (3-sqrt(3))/6 + + local x1 = x0 - i1 + G2; -- Offsets for middle corner in (x,y) unskewed coords + local y1 = y0 - j1 + G2; + local x2 = x0 - 1.0 + 2.0 * G2; -- Offsets for last corner in (x,y) unskewed coords + local y2 = y0 - 1.0 + 2.0 * G2; + + -- Work out the hashed gradient indices of the three simplex corners + local ii = bit.band(i , 255) + local jj = bit.band(j , 255) + local gi0 = perm[ii+perm[jj]] % 12; + local gi1 = perm[ii+i1+perm[jj+j1]] % 12; + local gi2 = perm[ii+1+perm[jj+1]] % 12; + + -- Calculate the contribution from the three corners + local t0 = 0.5 - x0*x0-y0*y0; + if t0<0 then + n0 = 0.0; + else + t0 = t0 * t0 + n0 = t0 * t0 * Dot2D(Gradients3D[gi0], x0, y0); -- (x,y) of Gradients3D used for 2D gradient + end + + local t1 = 0.5 - x1*x1-y1*y1; + if (t1<0) then + n1 = 0.0; + else + t1 = t1*t1 + n1 = t1 * t1 * Dot2D(Gradients3D[gi1], x1, y1); + end + + local t2 = 0.5 - x2*x2-y2*y2; + if (t2<0) then + n2 = 0.0; + else + t2 = t2*t2 + n2 = t2 * t2 * Dot2D(Gradients3D[gi2], x2, y2); + end + + + -- Add contributions from each corner to get the final noise value. + -- The result is scaled to return values in the localerval [-1,1]. + + local retval = 70.0 * (n0 + n1 + n2) + + if simplex.internalCache then + if not Prev2D[xin] then Prev2D[xin] = {} end + Prev2D[xin][yin] = retval + end + + return retval; +end + +local Prev3D = {} + +-- 3D simplex noise +function simplex.Noise3D(xin, yin, zin) + + if simplex.internalCache and Prev3D[xin] and Prev3D[xin][yin] and Prev3D[xin][yin][zin] then return Prev3D[xin][yin][zin] end + + local n0, n1, n2, n3; -- Noise contributions from the four corners + + -- Skew the input space to determine which simplex cell we're in + local F3 = 1.0/3.0; + local s = (xin+yin+zin)*F3; -- Very nice and simple skew factor for 3D + local i = math.floor(xin+s); + local j = math.floor(yin+s); + local k = math.floor(zin+s); + + local G3 = 1.0/6.0; -- Very nice and simple unskew factor, too + local t = (i+j+k)*G3; + + local X0 = i-t; -- Unskew the cell origin back to (x,y,z) space + local Y0 = j-t; + local Z0 = k-t; + + local x0 = xin-X0; -- The x,y,z distances from the cell origin + local y0 = yin-Y0; + local z0 = zin-Z0; + + -- For the 3D case, the simplex shape is a slightly irregular tetrahedron. + -- Determine which simplex we are in. + local i1, j1, k1; -- Offsets for second corner of simplex in (i,j,k) coords + local i2, j2, k2; -- Offsets for third corner of simplex in (i,j,k) coords + + if (x0>=y0) then + if (y0>=z0) then + i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; -- X Y Z order + elseif (x0>=z0) then + i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; -- X Z Y order + else + i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; -- Z X Y order + end + else -- x0 y0) and 32 or 1; + local c2 = (x0 > z0) and 16 or 1; + local c3 = (y0 > z0) and 8 or 1; + local c4 = (x0 > w0) and 4 or 1; + local c5 = (y0 > w0) and 2 or 1; + local c6 = (z0 > w0) and 1 or 1; + local c = c1 + c2 + c3 + c4 + c5 + c6; + local i1, j1, k1, l1; -- The localeger offsets for the second simplex corner + local i2, j2, k2, l2; -- The localeger offsets for the third simplex corner + local i3, j3, k3, l3; -- The localeger offsets for the fourth simplex corner + + -- sim[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. + -- Many values of c will never occur, since e.g. x>y>z>w makes x=3 and 1 or 0; + j1 = sim[c][2]>=3 and 1 or 0; + k1 = sim[c][3]>=3 and 1 or 0; + l1 = sim[c][4]>=3 and 1 or 0; + -- The number 2 in the "sim" array is at the second largest coordinate. + i2 = sim[c][1]>=2 and 1 or 0; + j2 = sim[c][2]>=2 and 1 or 0; + k2 = sim[c][3]>=2 and 1 or 0; + l2 = sim[c][4]>=2 and 1 or 0; + -- The number 1 in the "sim" array is at the second smallest coordinate. + i3 = sim[c][1]>=1 and 1 or 0; + j3 = sim[c][2]>=1 and 1 or 0; + k3 = sim[c][3]>=1 and 1 or 0; + l3 = sim[c][4]>=1 and 1 or 0; + -- The fifth corner has all coordinate offsets = 1, so no need to look that up. + local x1 = x0 - i1 + G4; -- Offsets for second corner in (x,y,z,w) coords + local y1 = y0 - j1 + G4; + local z1 = z0 - k1 + G4; + local w1 = w0 - l1 + G4; + local x2 = x0 - i2 + 2.0*G4; -- Offsets for third corner in (x,y,z,w) coords + local y2 = y0 - j2 + 2.0*G4; + local z2 = z0 - k2 + 2.0*G4; + local w2 = w0 - l2 + 2.0*G4; + local x3 = x0 - i3 + 3.0*G4; -- Offsets for fourth corner in (x,y,z,w) coords + local y3 = y0 - j3 + 3.0*G4; + local z3 = z0 - k3 + 3.0*G4; + local w3 = w0 - l3 + 3.0*G4; + local x4 = x0 - 1.0 + 4.0*G4; -- Offsets for last corner in (x,y,z,w) coords + local y4 = y0 - 1.0 + 4.0*G4; + local z4 = z0 - 1.0 + 4.0*G4; + local w4 = w0 - 1.0 + 4.0*G4; + + -- Work out the hashed gradient indices of the five simplex corners + local ii = bit.band(i , 255) + local jj = bit.band(j , 255) + local kk = bit.band(k , 255) + local ll = bit.band(l , 255) + local gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32; + local gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32; + local gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32; + local gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32; + local gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32; + + + -- Calculate the contribution from the five corners + local t0 = 0.5 - x0*x0 - y0*y0 - z0*z0 - w0*w0; + if (t0<0) then + n0 = 0.0; + else + t0 = t0*t0; + n0 = t0 * t0 * Dot4D(Gradients4D[gi0], x0, y0, z0, w0); + end + + local t1 = 0.5 - x1*x1 - y1*y1 - z1*z1 - w1*w1; + if (t1<0) then + n1 = 0.0; + else + t1 = t1*t1; + n1 = t1 * t1 * Dot4D(Gradients4D[gi1], x1, y1, z1, w1); + end + + local t2 = 0.5 - x2*x2 - y2*y2 - z2*z2 - w2*w2; + if (t2<0) then + n2 = 0.0; + else + t2 = t2*t2; + n2 = t2 * t2 * Dot4D(Gradients4D[gi2], x2, y2, z2, w2); + end + + local t3 = 0.5 - x3*x3 - y3*y3 - z3*z3 - w3*w3; + if (t3<0) then + n3 = 0.0; + else + t3 = t3*t3; + n3 = t3 * t3 * Dot4D(Gradients4D[gi3], x3, y3, z3, w3); + end + + local t4 = 0.5 - x4*x4 - y4*y4 - z4*z4 - w4*w4; + if (t4<0) then + n4 = 0.0; + else + t4 = t4*t4; + n4 = t4 * t4 * Dot4D(Gradients4D[gi4], x4, y4, z4, w4); + end + + -- Sum up and scale the result to cover the range [-1,1] + + local retval = 27.0 * (n0 + n1 + n2 + n3 + n4) + + if simplex.internalCache then + if not Prev4D[x] then Prev4D[x] = {} end + if not Prev4D[x][y] then Prev4D[x][y] = {} end + if not Prev4D[x][y][z] then Prev4D[x][y][z] = {} end + Prev4D[x][y][z][w] = retval + end + + return retval; + + +end + +local e = 2.71828182845904523536 + +local PrevBlur2D = {} + +function simplex.GBlur2D(x,y,stdDev) + if simplex.internalCache and PrevBlur2D[x] and PrevBlur2D[x][y] and PrevBlur2D[x][y][stdDev] then return PrevBlur2D[x][y][stdDev] end + local pwr = ((x^2+y^2)/(2*(stdDev^2)))*-1 + local ret = (1/(2*math.pi*(stdDev^2)))*(e^pwr) + + if simplex.internalCache then + if not PrevBlur2D[x] then PrevBlur2D[x] = {} end + if not PrevBlur2D[x][y] then PrevBlur2D[x][y] = {} end + PrevBlur2D[x][y][stdDev] = ret + end + return ret +end + +local PrevBlur1D = {} + +function simplex.GBlur1D(x,stdDev) + if simplex.internalCache and PrevBlur1D[x] and PrevBlur1D[x][stdDev] then return PrevBlur1D[x][stdDev] end + local pwr = (x^2/(2*stdDev^2))*-1 + local ret = (1/(math.sqrt(2*math.pi)*stdDev))*(e^pwr) + + if simplex.internalCache then + if not PrevBlur1D[x] then PrevBlur1D[x] = {} end + PrevBlur1D[x][stdDev] = ret + end + return ret +end + +function simplex.FractalSum(func, iter, ...) + local ret = func(...) + for i=1,iter do + local power = 2^iter + local s = power/i + + local scaled = {} + for elem in ipairs({...}) do + table.insert(scaled, elem*s) + end + ret = ret + (i/power)*(func(unpack(scaled))) + end + return ret +end + +function simplex.FractalSumAbs(func, iter, ...) + local ret = math.abs(func(...)) + for i=1,iter do + local power = 2^iter + local s = power/i + + local scaled = {} + for elem in ipairs({...}) do + table.insert(scaled, elem*s) + end + ret = ret + (i/power)*(math.abs(func(unpack(scaled)))) + end + return ret +end + +function simplex.Turbulence(func, direction, iter, ...) + local ret = math.abs(func(...)) + for i=1,iter do + local power = 2^iter + local s = power/i + + local scaled = {} + for elem in ipairs({...}) do + table.insert(scaled, elem*s) + end + ret = ret + (i/power)*(math.abs(func(unpack(scaled)))) + end + local args = {...} + local dir_component = args[direction+1] + return math.sin(dir_component+ret) +end + return simplex \ No newline at end of file