Perlin noise
You are encouraged to solve this task according to the task description, using any language you may know.
The Perlin noise is a kind of gradient noise invented by Ken Perlin around the end of the twentieth century and still currently heavily used in computer graphics, most notably to procedurally generate textures or heightmaps.
The Perlin noise is basically a pseudo-random mapping of into with an integer which can be arbitrarily large but which is usually 2, 3, or 4.
Either by using a dedicated library or by implementing the algorithm, show that the Perlin noise (as defined in 2002 in the Java implementation below) of the point in 3D-space with coordinates 3.14, 42, 7 is 0.13691995878400012.
Note: this result assumes 64 bit IEEE-754 floating point calculations. If your language uses a different floating point representation, make a note of it and calculate the value accurate to 15 decimal places, or your languages accuracy threshold if it is less. Trailing zeros need not be displayed.
C
A sign of how close C and Java are is this implementation which differs very little from Perlin's Java implementation. I only removed the static, public and final keywords and the Math class name from the floor calls, and it compiled without errors. Interestingly, in the paper, Perlin says that the benchmark implementation which was used to gauge the algorithm's performance was in C. One important improvement here is that the permutation data is externalized and read from a file. This way different textures and effects can be generated without having to change the source code. <lang C>
- include<stdlib.h>
- include<stdio.h>
- include<math.h>
int p[512];
double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); } double lerp(double t, double a, double b) { return a + t * (b - a); } double grad(int hash, double x, double y, double z) {
int h = hash & 15;
double u = h<8 ? x : y,
v = h<4 ? y : h==12||h==14 ? x : z;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
double noise(double x, double y, double z) {
int X = (int)floor(x) & 255,
Y = (int)floor(y) & 255,
Z = (int)floor(z) & 255;
x -= floor(x);
y -= floor(y);
z -= floor(z);
double u = fade(x),
v = fade(y),
w = fade(z);
int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z,
B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z;
return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ),
grad(p[BA ], x-1, y , z )),
lerp(u, grad(p[AB ], x , y-1, z ),
grad(p[BB ], x-1, y-1, z ))),
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ),
grad(p[BA+1], x-1, y , z-1 )),
lerp(u, grad(p[AB+1], x , y-1, z-1 ),
grad(p[BB+1], x-1, y-1, z-1 ))));
}
void loadPermutation(char* fileName){ FILE* fp = fopen(fileName,"r"); int permutation[256],i;
for(i=0;i<256;i++) fscanf(fp,"%d",&permutation[i]);
fclose(fp);
for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; }
int main(int argC,char* argV[]) { if(argC!=5) printf("Usage : %s <permutation data file> <x,y,z co-ordinates separated by space>"); else{ loadPermutation(argV[1]); printf("Perlin Noise for (%s,%s,%s) is %.17lf",argV[2],argV[3],argV[4],noise(strtod(argV[2],NULL),strtod(argV[3],NULL),strtod(argV[4],NULL))); }
return 0; } </lang> Permutation file, it should have 256 integers in the range [0,255]:
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
Invocation and output :
C:\rosettaCode>perlin.exe perlinData.txt 3.14 42 7 Perlin Noise for (3.14,42,7) is 0.13691995878400012
Common Lisp
<lang lisp>;;;; Translation from: Java
(declaim (optimize (speed 3) (debug 0)))
(defconstant +p+
(let ((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)) (aux (make-array 512 :element-type 'fixnum)))
(dotimes (i 256 aux)
(setf (aref aux i) (aref permutation i))
(setf (aref aux (+ 256 i)) (aref permutation i)))))
(defun fade (te)
(declare (type double-float te)) (the double-float (* te te te (+ (* te (- (* te 6) 15)) 10))))
(defun lerp (te a b)
(declare (type double-float te a b)) (the double-float (+ a (* te (- b a)))))
(defun grad (hash x y z)
(declare (type fixnum hash)
(type double-float x y z))
(let* ((h (logand hash 15)) ;; convert lo 4 bits of hash code into 12 gradient directions
(u (if (< h 8) x y)) (v (cond ((< h 4) y) ((or (= h 12) (= h 14)) x) (t z))))
(the
double-float
(+
(if (zerop (logand h 1)) u (- u))
(if (zerop (logand h 2)) v (- v))))))
(defun noise (x y z)
(declare (type double-float x y z)) ;; find unit cube that contains point. (let ((cx (logand (floor x) 255))
(cy (logand (floor y) 255)) (cz (logand (floor z) 255)))
;; find relative x, y, z of point in cube. (let ((x (- x (floor x)))
(y (- y (floor y))) (z (- z (floor z))))
;; compute fade curves for each of x, y, z.
(let ((u (fade x))
(v (fade y)) (w (fade z))) ;; hash coordinates of the 8 cube corners, (let* ((ca (+ (aref +p+ cx) cy)) (caa (+ (aref +p+ ca) cz)) (cab (+ (aref +p+ (1+ ca)) cz)) (cb (+ (aref +p+ (1+ cx)) cy)) (cba (+ (aref +p+ cb) cz)) (cbb (+ (aref +p+ (1+ cb)) cz))) ;; ... and add blended results from 8 corners of cube (the double-float (lerp w (lerp v (lerp u (grad (aref +p+ caa) x y z) (grad (aref +p+ cba) (1- x) y z)) (lerp u (grad (aref +p+ cab) x (1- y) z) (grad (aref +p+ cbb) (1- x) (1- y) z))) (lerp v (lerp u (grad (aref +p+ (1+ caa)) x y (1- z)) (grad (aref +p+ (1+ cba)) (1- x) y (1- z))) (lerp u (grad (aref +p+ (1+ cab)) x (1- y) (1- z)) (grad (aref +p+ (1+ cbb)) (1- x) (1- y) (1- z)))))))))))
(print (noise 3.14d0 42d0 7d0)) </lang>
- Output:
0.13691995878400012d0
D
<lang d>import std.stdio, std.math;
struct PerlinNoise {
private static double fade(in double t) pure nothrow @safe @nogc {
return t ^^ 3 * (t * (t * 6 - 15) + 10);
}
private static double lerp(in double t, in double a, in double b)
pure nothrow @safe @nogc {
return a + t * (b - a);
}
private static double grad(in ubyte hash,
in double x, in double y, in double z)
pure nothrow @safe @nogc {
// Convert lo 4 bits of hash code into 12 gradient directions.
immutable h = hash & 0xF;
immutable double u = (h < 8) ? x : y,
v = (h < 4) ? y : (h == 12 || h == 14 ? x : z);
return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
}
static immutable ubyte[512] p;
static this() pure nothrow @safe @nogc {
static immutable permutation = cast(ubyte[256])x"97 A0 89 5B 5A
0F 83 0D C9 5F 60 35 C2 E9 07 E1 8C 24 67 1E 45 8E 08 63 25
F0 15 0A 17 BE 06 94 F7 78 EA 4B 00 1A C5 3E 5E FC DB CB 75
23 0B 20 39 B1 21 58 ED 95 38 57 AE 14 7D 88 AB A8 44 AF 4A
A5 47 86 8B 30 1B A6 4D 92 9E E7 53 6F E5 7A 3C D3 85 E6 DC
69 5C 29 37 2E F5 28 F4 66 8F 36 41 19 3F A1 01 D8 50 49 D1
4C 84 BB D0 59 12 A9 C8 C4 87 82 74 BC 9F 56 A4 64 6D C6 AD
BA 03 40 34 D9 E2 FA 7C 7B 05 CA 26 93 76 7E FF 52 55 D4 CF
CE 3B E3 2F 10 3A 11 B6 BD 1C 2A DF B7 AA D5 77 F8 98 02 2C
9A A3 46 DD 99 65 9B A7 2B AC 09 81 16 27 FD 13 62 6C 6E 4F
71 E0 E8 B2 B9 70 68 DA F6 61 E4 FB 22 F2 C1 EE D2 90 0C BF
B3 A2 F1 51 33 91 EB F9 0E EF 6B 31 C0 D6 1F B5 C7 6A 9D B8
54 CC B0 73 79 32 2D 7F 04 96 FE 8A EC CD 5D DE 72 43 1D 18
48 F3 8D 80 C3 4E 42 D7 3D 9C B4";
// Two copies of permutation.
p[0 .. permutation.length] = permutation[];
p[permutation.length .. $] = permutation[];
}
/// x0, y0 and z0 can be any real numbers, but the result is
/// zero if they are all integers.
/// The result is probably in [-1.0, 1.0].
static double opCall(in double x0, in double y0, in double z0)
pure nothrow @safe @nogc {
// Find unit cube that contains point.
immutable ubyte X = cast(int)x0.floor & 0xFF,
Y = cast(int)y0.floor & 0xFF,
Z = cast(int)z0.floor & 0xFF;
// Find relative x,y,z of point in cube.
immutable x = x0 - x0.floor,
y = y0 - y0.floor,
z = z0 - z0.floor;
// Compute fade curves for each of x,y,z.
immutable u = fade(x),
v = fade(y),
w = fade(z);
// Hash coordinates of the 8 cube corners.
immutable A = p[X ] + Y,
AA = p[A] + Z,
AB = p[A + 1] + Z,
B = p[X + 1] + Y,
BA = p[B] + Z,
BB = p[B + 1] + Z;
// And add blended results from 8 corners of cube.
return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ),
grad(p[BA ], x-1, y , z )),
lerp(u, grad(p[AB ], x , y-1, z ),
grad(p[BB ], x-1, y-1, z ))),
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1),
grad(p[BA+1], x-1, y , z-1)),
lerp(u, grad(p[AB+1], x , y-1, z-1),
grad(p[BB+1], x-1, y-1, z-1))));
}
}
void main() {
writefln("%1.17f", PerlinNoise(3.14, 42, 7));
/*
// Generate a demo image using the Gray Scale task module.
import grayscale_image;
enum N = 200;
auto im = new Image!Gray(N, N);
foreach (immutable y; 0 .. N)
foreach (immutable x; 0 .. N) {
immutable p = PerlinNoise(x / 30.0, y / 30.0, 0.1);
im[x, y] = Gray(cast(ubyte)((p + 1) / 2 * 256));
}
im.savePGM("perlin_noise.pgm");
*/
}</lang>
- Output:
0.13691995878400012
Factor
As this is a strict translation of applicative code that makes heavy use of local variables, it is highly non-idiomatic. In idiomatic code, we would never write a word as long as noise or name so many throwaway values. We would also abstract out repetitive patterns such as
<lang>x floor >integer 255 bitand :> X
y floor >integer 255 bitand :> Y
z floor >integer 255 bitand :> Z</lang>
with dataflow combinators:
<lang>[ floor >integer 255 bitand ] tri@</lang>
<lang factor>USING: kernel math math.functions literals locals prettyprint
sequences ;
IN: rosetta-code.perlin-noise
CONSTANT: 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 } dup append
]
- fade ( t -- x ) t 6 * 15 - t * 10 + t * t * t * ;
- lerp ( t a b -- x ) b a - t * a + ;
- grad ( hash x y z -- w )
hash 15 bitand :> h h 8 < x y ? :> u h 4 < y h 12 = h 14 = or x z ? ? :> v h 1 bitand 0 = u u neg ? h 2 bitand 0 = v v neg ? + ;
- noise ( x! y! z! -- noise )
x floor >integer 255 bitand :> X
y floor >integer 255 bitand :> Y
z floor >integer 255 bitand :> Z
x x floor - x!
y y floor - y!
z z floor - z!
x fade :> u
y fade :> v
z fade :> w
X p nth Y + :> A
A p nth Z + :> AA
A 1 + p nth Z + :> AB
X 1 + p nth Y + :> B
B p nth Z + :> BA
B 1 + p nth Z + :> BB
w v u AA p nth x y z grad
BA p nth x 1 - y z grad lerp
u AB p nth x y 1 - z grad
BB p nth x 1 - y 1 - z grad lerp lerp
v u AA 1 + p nth x y z 1 - grad
BA 1 + p nth x 1 - y z 1 - grad lerp
u AB 1 + p nth x y 1 - z 1 - grad
BB 1 + p nth x 1 - y 1 - z 1 - grad lerp lerp lerp ;
- main ( -- ) 3.14 42 7 noise . ;
MAIN: main</lang>
- Output:
0.1369199587840001
GLSL
From https://gist.github.com/patriciogonzalezvivo/670c22f3966e662d2f83 : <lang glsl> float rand(vec2 c){ return fract(sin(dot(c.xy ,vec2(12.9898,78.233))) * 43758.5453); }
float noise(vec2 p, float freq ){ float unit = screenWidth/freq; vec2 ij = floor(p/unit); vec2 xy = mod(p,unit)/unit; //xy = 3.*xy*xy-2.*xy*xy*xy; xy = .5*(1.-cos(PI*xy)); float a = rand((ij+vec2(0.,0.))); float b = rand((ij+vec2(1.,0.))); float c = rand((ij+vec2(0.,1.))); float d = rand((ij+vec2(1.,1.))); float x1 = mix(a, b, xy.x); float x2 = mix(c, d, xy.x); return mix(x1, x2, xy.y); }
float pNoise(vec2 p, int res){ float persistance = .5; float n = 0.; float normK = 0.; float f = 4.; float amp = 1.; int iCount = 0; for (int i = 0; i<50; i++){ n+=amp*noise(p, f); f*=2.; normK+=amp; amp*=persistance; if (iCount == res) break; iCount++; } float nf = n/normK; return nf*nf*nf*nf; } </lang>
Go
<lang go>package main
import (
"fmt" "math"
)
func main() {
fmt.Println(noise(3.14, 42, 7))
}
func noise(x, y, z float64) float64 {
X := int(math.Floor(x)) & 255
Y := int(math.Floor(y)) & 255
Z := int(math.Floor(z)) & 255
x -= math.Floor(x)
y -= math.Floor(y)
z -= math.Floor(z)
u := fade(x)
v := fade(y)
w := fade(z)
A := p[X] + Y
AA := p[A] + Z
AB := p[A+1] + Z
B := p[X+1] + Y
BA := p[B] + Z
BB := p[B+1] + Z
return lerp(w, lerp(v, lerp(u, grad(p[AA], x, y, z),
grad(p[BA], x-1, y, z)),
lerp(u, grad(p[AB], x, y-1, z),
grad(p[BB], x-1, y-1, z))),
lerp(v, lerp(u, grad(p[AA+1], x, y, z-1),
grad(p[BA+1], x-1, y, z-1)),
lerp(u, grad(p[AB+1], x, y-1, z-1),
grad(p[BB+1], x-1, y-1, z-1))))
} func fade(t float64) float64 { return t * t * t * (t*(t*6-15) + 10) } func lerp(t, a, b float64) float64 { return a + t*(b-a) } func grad(hash int, x, y, z float64) float64 {
// Go doesn't have a ternary. Ternaries can be translated directly
// with if statements, but chains of if statements are often better
// expressed with switch statements.
switch hash & 15 {
case 0, 12:
return x + y
case 1, 14:
return y - x
case 2:
return x - y
case 3:
return -x - y
case 4:
return x + z
case 5:
return z - x
case 6:
return x - z
case 7:
return -x - z
case 8:
return y + z
case 9, 13:
return z - y
case 10:
return y - z
}
// case 11, 16:
return -y - z
}
var permutation = []int{
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,
} var p = append(permutation, permutation...)</lang>
- Output:
0.13691995878400012
J
We can trivially copy the java implementation:
<lang J>band=:17 b. ImprovedNoise=:3 :0
'x y z'=. y
X=. (<. x) band 255
Y=. (<. y) band 255
Z=. (<. z) band 255
x=. x-<.!.0 x
y=. y-<.!.0 y
z=. z-<.!.0 z
u=. fade x
v=. fade y
w=. fade z
A=. (p{~X)+Y
AA=.(p{~A)+Z
AB=.(p{~A+1)+Z
B=. (p{~X+1)+Y
BA=.(p{~B)+Z
BB=.(p{~B+1)+Z
t1=. (grad(p{~BB+1),(x-1),(y-1),z-1)
t2=. (lerp u,(grad(p{~AB+1),x,(y-1),z-1),t1)
t3=. (grad(p{~BA+1),(x-1),y,z-1)
t4=. (lerp v,(lerp u,(grad(p{~AA+1),x,y,z-1),t3),t2)
t5=. (grad(p{~BB),(x-1),(y-1),z)
t6=. (lerp u,(grad(p{~AB),x,(y-1),z),t5)
t7=. (grad(p{~BA),(x-1),y,z)
(lerp w,(lerp v,(lerp u,(grad(p{~AA),x,y,z),t7),t6),t4)
)
fade=:3 :0
t=.y t * t * t * ((t * ((t * 6) - 15)) + 10)
)
lerp=:3 :0
't a b'=. y a + t * (b - a)
)
grad=:3 :0
'hash x y z'=. y h =. hash band 15 NB. CONVERT LO 4 BITS OF HASH CODE u =. x [^:(h<8) y NB. INTO 12 GRADIENT DIRECTIONS. v =. y [^:(h<4) x [^:((h=12)+.(h=14)) z (u [^:((h band 1) = 0) -u) + v [^:((h band 2) = 0) -v
)
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
fade=: 0 0 0 10 _15 6&p.
ImprovedNoise=:3 :0
'XYZ xyz'=. |:256 1 #:y
uvw=. fade xyz
hash=. 0 1+/(+ p{~0 1+/])/|. XYZ
t1=. (grad(p{~BB+1),(x-1),(y-1),z-1)
t2=. (lerp u,(grad(p{~AB+1), x, (y-1),z-1),t1)
t3=. (grad(p{~BA+1),(x-1), y, z-1)
t4=. (lerp v,(lerp u,(grad(p{~AA+1), x, y, z-1),t3),t2)
t5=. (grad(p{~BB), (x-1),(y-1),z)
t6=. (lerp u,(grad(p{~AB), x, (y-1),z), t5)
t7=. (grad(p{~BA), (x-1), y, z)
(lerp w,(lerp v,(lerp u,(grad(p{~AA),x, y, z), t7),t6),t4)
) </lang>
And this gives us our desired result:
<lang J> ImprovedNoise 3.14 42 7 0.13692</lang>
Or, asking to see 20 digits after the decimal point:
<lang J>
22j20": ImprovedNoise 3.14 42 7
0.13691995878400012000</lang>
Simplified Expression
It's tempting, though, to express this more concisely. We are limited, there, by some of the arbitrary choices in the algorithm, but we can still exploit regularities in its structure:
<lang J>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
fade=: 0 0 0 10 _15 6&p.
grad=:4 :0
dir=. (16|x){_1+3 3 3#:25 7 19 1 23 5 21 3 17 11 15 9 25 11 7 9
dir+/ .*"1 y
)
lerp=:4 :0
'a b'=. y a + x * (b - a)
)
ImprovedNoise=:3 :0
'XYZ xyz'=. |:256 1 #:y
uvw=. fade xyz
hash=. p{~0 1+/(+ p{~0 1+/])/|. XYZ
g=. hash grad xyz-"1|."1#:i.$hash
u=. (0{uvw) lerp"1 g
v=. (1{uvw) lerp"1 u
w=. (2{uvw) lerp"1 v
)</lang>
And we can see that there's no difference in this result:
<lang J> 0.13691995878400012 - ImprovedNoise 3.14 42 7 0</lang>
It's probably possible to simplify this further.
Java
The original code from Perlin was originally published in java. Note that this does not have a main method so there will be no output. To test, add a main method, call noise() with 3.14,42,7, save the file as ImprovedNoise.java and compile. <lang java>// JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN.
public final class ImprovedNoise {
static public double noise(double x, double y, double z) {
int X = (int)Math.floor(x) & 255, // FIND UNIT CUBE THAT
Y = (int)Math.floor(y) & 255, // CONTAINS POINT.
Z = (int)Math.floor(z) & 255;
x -= Math.floor(x); // FIND RELATIVE X,Y,Z
y -= Math.floor(y); // OF POINT IN CUBE.
z -= Math.floor(z);
double u = fade(x), // COMPUTE FADE CURVES
v = fade(y), // FOR EACH OF X,Y,Z.
w = fade(z);
int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z, // HASH COORDINATES OF
B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z; // THE 8 CUBE CORNERS,
return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD
grad(p[BA ], x-1, y , z )), // BLENDED
lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS
grad(p[BB ], x-1, y-1, z ))),// FROM 8
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS
grad(p[BA+1], x-1, y , z-1 )), // OF CUBE
lerp(u, grad(p[AB+1], x , y-1, z-1 ),
grad(p[BB+1], x-1, y-1, z-1 ))));
}
static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); }
static double lerp(double t, double a, double b) { return a + t * (b - a); }
static double grad(int hash, double x, double y, double z) {
int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? y : h==12||h==14 ? x : z;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
static final int p[] = new int[512], 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
};
static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; }
}</lang>
Julia
<lang julia>const permutation = UInt8[
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]
function grad(h::Integer, x, y, z)
h &= 15 # CONVERT LO 4 BITS OF HASH CODE u = h < 8 ? x : y # INTO 12 GRADIENT DIRECTIONS. v = h < 4 ? y : h == 12 || h == 14 ? x : z (h & 1 == 0 ? u : -u) + (h & 2 == 0 ? v : -v)
end
function perlinsnoise(x, y, z)
p = vcat(permutation, permutation) fade(t) = t * t * t * (t * (t * 6 - 15) + 10) lerp(t, a, b) = a + t * (b - a) floorb(x) = Int(floor(x)) & 0xff X, Y, Z = floorb(x), floorb(y), floorb(z) # FIND UNIT CUBE THAT CONTAINS POINT. x, y, z = x - floor(x), y - floor(y), z - floor(z) # FIND RELATIVE X,Y,Z OF POINT IN CUBE. u, v, w = fade(x), fade(y), fade(z) # COMPUTE FADE CURVES FOR EACH OF X,Y,Z. A = p[X + 1] + Y; AA = p[A + 1] + Z; AB = p[A + 2] + Z B = p[X + 2] + Y; BA = p[B + 1] + Z; BB = p[B + 2] + Z # HASH COORDINATES OF THE 8 CUBE CORNERS
return lerp(w, lerp(v, lerp(u, grad(p[AA + 1], x , y , z ), # AND ADD
grad(p[BA + 1], x - 1, y , z )), # BLENDED
lerp(u, grad(p[AB + 1], x , y - 1, z ), # RESULTS
grad(p[BB + 1], x - 1, y - 1, z ))), # FROM 8
lerp(v, lerp(u, grad(p[AA + 2], x , y , z - 1 ), # CORNERS
grad(p[BA + 2], x - 1, y , z - 1)), # OF CUBE.
lerp(u, grad(p[AB + 2], x , y - 1, z - 1 ),
grad(p[BB + 2], x - 1, y - 1, z - 1))))
end
println("Perlin noise applied to (3.14, 42.0, 7.0) gives ", perlinsnoise(3.14, 42.0, 7.0))
</lang>
- Output:
Perlin noise applied to (3.14, 42.0, 7.0) gives 0.13691995878400012
Kotlin
<lang scala>// version 1.1.3
object Perlin {
private val permutation = intArrayOf(
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
)
private val p = IntArray(512) {
if (it < 256) permutation[it] else permutation[it - 256]
}
fun noise(x: Double, y: Double, z: Double): Double {
// Find unit cube that contains point
val xi = Math.floor(x).toInt() and 255
val yi = Math.floor(y).toInt() and 255
val zi = Math.floor(z).toInt() and 255
// Find relative x, y, z of point in cube
val xx = x - Math.floor(x)
val yy = y - Math.floor(y)
val zz = z - Math.floor(z)
// Compute fade curves for each of xx, yy, zz
val u = fade(xx)
val v = fade(yy)
val w = fade(zz)
// Hash co-ordinates of the 8 cube corners
// and add blended results from 8 corners of cube
val a = p[xi] + yi
val aa = p[a] + zi
val ab = p[a + 1] + zi
val b = p[xi + 1] + yi
val ba = p[b] + zi
val bb = p[b + 1] + zi
return lerp(w, lerp(v, lerp(u, grad(p[aa], xx, yy, zz),
grad(p[ba], xx - 1, yy, zz)),
lerp(u, grad(p[ab], xx, yy - 1, zz),
grad(p[bb], xx - 1, yy - 1, zz))),
lerp(v, lerp(u, grad(p[aa + 1], xx, yy, zz - 1),
grad(p[ba + 1], xx - 1, yy, zz - 1)),
lerp(u, grad(p[ab + 1], xx, yy - 1, zz - 1),
grad(p[bb + 1], xx - 1, yy - 1, zz - 1))))
}
private fun fade(t: Double) = t * t * t * (t * (t * 6 - 15) + 10)
private fun lerp(t: Double, a: Double, b: Double) = a + t * (b - a)
private fun grad(hash: Int, x: Double, y: Double, z: Double): Double {
// Convert low 4 bits of hash code into 12 gradient directions
val h = hash and 15
val u = if (h < 8) x else y
val v = if (h < 4) y else if (h == 12 || h == 14) x else z
return (if ((h and 1) == 0) u else -u) +
(if ((h and 2) == 0) v else -v)
}
}
fun main(args: Array<String>) {
println(Perlin.noise(3.14, 42.0, 7.0))
}</lang>
- Output:
0.13691995878400012
OCaml
<lang ocaml>let 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]
let lerp (t, a, b) = a +. t *. (b -. a)
let fade t =
(t *. t *. t) *. (t *. (t *. 6. -. 15.) +. 10.)
let grad (hash, x, y, z) =
let h = hash land 15 in let u = if (h < 8) then x else y in let v = if (h < 4) then y else (if (h = 12 || h = 14) then x else z) in (if (h land 1 = 0) then u else (0. -. u)) +. (if (h land 2 = 0) then v else (0. -. v))
let perlin_init p =
List.rev (List.fold_left (fun i x -> x :: i) (List.rev p) p);;
let perlin_noise p x y z =
let x1 = (int_of_float x) land 255 and
y1 = (int_of_float y) land 255 and
z1 = (int_of_float z) land 255 and
xi = x -. (float (int_of_float x)) and
yi = y -. (float (int_of_float y)) and
zi = z -. (float (int_of_float z)) in
let u = fade xi and
v = fade yi and
w = fade zi and
a = (List.nth p x1) + y1 in
let aa = (List.nth p a) + z1 and
ab = (List.nth p (a + 1)) + z1 and
b = (List.nth p (x1 + 1)) + y1 in
let ba = (List.nth p b) + z1 and
bb = (List.nth p (b + 1)) + z1 in
lerp(w, lerp(v, lerp(u, (grad ((List.nth p aa), xi, yi, zi)),
(grad ((List.nth p ba), xi -. 1., yi , zi))),
lerp(u, (grad ((List.nth p ab), xi , yi -. 1., zi)),
(grad ((List.nth p bb), xi -. 1., yi -. 1., zi)))),
lerp(v, lerp(u, (grad ((List.nth p (aa + 1)), xi, yi, zi -. 1.)),
(grad ((List.nth p (ba + 1)), xi -. 1., yi , zi -. 1.))),
lerp(u, (grad ((List.nth p (ab + 1)), xi , yi -. 1., zi -. 1.)),
(grad ((List.nth p (bb + 1)), xi -. 1., yi -. 1., zi -. 1.)))))
let p = perlin_init permutation in
print_string ((Printf.sprintf "%0.17f" (perlin_noise p 3.14 42.0 7.0)) ^ "\n")</lang>
- Output:
0.13691995878400012
Pascal
dumb copy of Go minimal adjustments. <lang pascal>program perlinNoise; //Perlin Noise //http://rosettacode.org/mw/index.php?title=Perlin_noise#Go uses
sysutils;
type
float64 = double;
const
p{ermutation} : array[0..255] of byte = (
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);
function fade(t:float64):float64;inline; begin
fade := ((t*6-15)*t + 10) * t*t*t;
end;
function lerp(t, a, b:float64):float64;inline; Begin
lerp := t*(b-a)+a;
end;
function grad(hash:integer; x, y, z: float64):float64; Begin
case (hash AND 15) of
0:
grad := x + y;
1:
grad := y - x;
2:
grad := x - y;
3:
grad := -x - y;
4:
grad := x + z;
5:
grad := z - x;
6:
grad := x - z;
7:
grad := -x - z;
8:
grad := y + z;
9:
grad := z - y;
10:
grad := y - z;
11:
grad := -y - z;
12:
grad := x + y;
13:
grad := z - y;
14:
grad := y - x;
15:
grad := -y - z;
end;
end;
function noise(x, y, z: float64):float64; var
u,v,w : float64; a,b,c,A0,A1,A2,B0,B1,B2 : Integer;
Begin
a := trunc(x) AND 255; b := trunc(y) AND 255; c := trunc(z) AND 255; x := frac(x); y := frac(y); z := frac(z); u := fade(x); v := fade(y); w := fade(z);
A0 := p[ a] + b; A1 := p[A0] + c; A2 := p[A0+1] + c; B0 := p[ a+1] + b; B1 := p[B0] + c; B2 := p[B0+1] + c;
noise:= lerp(w, lerp(v, lerp(u, grad(p[A1], x, y, z),
grad(p[B1], x-1, y, z)),
lerp(u, grad(p[A2], x, y-1, z),
grad(p[B2], x-1, y-1, z))),
lerp(v, lerp(u, grad(p[A1+1], x, y, z-1),
grad(p[B1+1], x-1, y, z-1)),
lerp(u, grad(p[A2+1], x, y-1, z-1),
grad(p[B2+1], x-1, y-1, z-1))))
end;
Begin
writeln(noise(3.14, 42, 7):20:17);
end. </lang>
- Output:
0.13691995878400012
Perl
<lang perl>use strict; use warnings;
use constant permutation => qw{ 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 }; use constant p => (permutation, permutation);
sub floor {
my $x = shift; my $xi = int($x); return $x < $xi ? $xi - 1 : $xi;
}
sub fade { $_ = shift; $_ * $_ * $_ * ($_ * ($_ * 6 - 15) + 10) } sub lerp { $_[1] + $_[0] * ($_[2] - $_[1]) } sub grad {
my ($h, $x, $y, $z) = @_[0..3]; $h &= 15; my $u = $h < 8 ? $x : $y; my $v = $h < 4 ? $y : $h == 12 || $h == 14 ? $x : $z; return (($h & 1) == 0 ? $u : -$u) + (($h & 2) == 0 ? $v : -$v);
}
sub noise {
my ($X, $Y, $Z) = map { floor($_) & 255 }
my ($x, $y, $z) = @_[0,1,2];
my ($u, $v, $w) = map { fade($_) }
$x -= $X, $y -= $Y, $z -= $Z;
my $A = (p)[$X] + $Y;
my ($AA, $AB) = ( (p)[$A] + $Z, (p)[$A + 1] + $Z );
my $B = (p)[$X + 1] + $Y;
my ($BA, $BB) = ( (p)[$B] + $Z, (p)[$B + 1] + $Z );
lerp($w, lerp($v, lerp($u,
grad( (p)[$AA], $x, $y, $z ), grad( (p)[$BA], $x - 1, $y, $z ) ), lerp($u, grad( (p)[$AB], $x, $y - 1, $z ), grad( (p)[$BB], $x - 1, $y - 1, $z ) ) ), lerp($v, lerp($u, grad((p)[$AA + 1], $x, $y, $z - 1 ), grad((p)[$BA + 1], $x - 1, $y, $z - 1 )), lerp($u, grad((p)[$AB + 1], $x, $y - 1, $z - 1 ), grad((p)[$BB + 1], $x - 1, $y - 1, $z - 1 )) )
);
}
print noise 3.14, 42, 7;</lang>
- Output:
0.136919958784
Phix
<lang Phix>constant ph = x"97 A0 89 5B 5A 0F 83 0D C9 5F 60 35 C2 E9 07 E1"&
x"8C 24 67 1E 45 8E 08 63 25 F0 15 0A 17 BE 06 94"&
x"F7 78 EA 4B 00 1A C5 3E 5E FC DB CB 75 23 0B 20"&
x"39 B1 21 58 ED 95 38 57 AE 14 7D 88 AB A8 44 AF"&
x"4A A5 47 86 8B 30 1B A6 4D 92 9E E7 53 6F E5 7A"&
x"3C D3 85 E6 DC 69 5C 29 37 2E F5 28 F4 66 8F 36"&
x"41 19 3F A1 01 D8 50 49 D1 4C 84 BB D0 59 12 A9"&
x"C8 C4 87 82 74 BC 9F 56 A4 64 6D C6 AD BA 03 40"&
x"34 D9 E2 FA 7C 7B 05 CA 26 93 76 7E FF 52 55 D4"&
x"CF CE 3B E3 2F 10 3A 11 B6 BD 1C 2A DF B7 AA D5"&
x"77 F8 98 02 2C 9A A3 46 DD 99 65 9B A7 2B AC 09"&
x"81 16 27 FD 13 62 6C 6E 4F 71 E0 E8 B2 B9 70 68"&
x"DA F6 61 E4 FB 22 F2 C1 EE D2 90 0C BF B3 A2 F1"&
x"51 33 91 EB F9 0E EF 6B 31 C0 D6 1F B5 C7 6A 9D"&
x"B8 54 CC B0 73 79 32 2D 7F 04 96 FE 8A EC CD 5D"&
x"DE 72 43 1D 18 48 F3 8D 80 C3 4E 42 D7 3D 9C B4",
p = ph&ph
function fade(atom t) return t * t * t * (t * (t * 6 - 15) + 10) end function function lerp(atom t, a, b) return a + t * (b - a) end function function grad(int hash, atom x, y, z)
int h = and_bits(hash,15)
atom u = iff(h<8 ? x : y),
v = iff(h<4 ? y : iff(h==12 or h==14 ? x : z))
return iff(and_bits(h,1) == 0 ? u : -u) +
iff(and_bits(h,2) == 0 ? v : -v)
end function
function noise(atom x, y, z)
integer X = and_bits(x,255),
Y = and_bits(y,255),
Z = and_bits(z,255)
x -= floor(x)
y -= floor(y)
z -= floor(z)
atom u = fade(x),
v = fade(y),
w = fade(z)
integer A = p[X+1]+Y, AA = p[A+1]+Z, AB = p[A+2]+Z,
B = p[X+2]+Y, BA = p[B+1]+Z, BB = p[B+2]+Z
return lerp(w,lerp(v,lerp(u,grad(p[AA+1], x , y , z ),
grad(p[BA+1], x-1, y , z )),
lerp(u,grad(p[AB+1], x , y-1, z ),
grad(p[BB+1], x-1, y-1, z ))),
lerp(v,lerp(u,grad(p[AA+2], x , y , z-1 ),
grad(p[BA+2], x-1, y , z-1 )),
lerp(u,grad(p[AB+2], x , y-1, z-1 ),
grad(p[BB+2], x-1, y-1, z-1 ))))
end function
printf(1,"Perlin Noise for (3.14,42,7) is %.17f\n",{noise(3.14,42,7)})</lang>
- Output:
Perlin Noise for (3.14,42,7) is 0.1369199587840001
Python
<lang python>def perlin_noise(x, y, z):
X = int(x) & 255 # FIND UNIT CUBE THAT
Y = int(y) & 255 # CONTAINS POINT.
Z = int(z) & 255
x -= int(x) # FIND RELATIVE X,Y,Z
y -= int(y) # OF POINT IN CUBE.
z -= int(z)
u = fade(x) # COMPUTE FADE CURVES
v = fade(y) # FOR EACH OF X,Y,Z.
w = fade(z)
A = p[X ]+Y; AA = p[A]+Z; AB = p[A+1]+Z # HASH COORDINATES OF
B = p[X+1]+Y; BA = p[B]+Z; BB = p[B+1]+Z # THE 8 CUBE CORNERS,
return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), # AND ADD
grad(p[BA ], x-1, y , z )), # BLENDED
lerp(u, grad(p[AB ], x , y-1, z ), # RESULTS
grad(p[BB ], x-1, y-1, z ))),# FROM 8
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), # CORNERS
grad(p[BA+1], x-1, y , z-1 )), # OF CUBE
lerp(u, grad(p[AB+1], x , y-1, z-1 ),
grad(p[BB+1], x-1, y-1, z-1 ))))
def fade(t):
return t ** 3 * (t * (t * 6 - 15) + 10)
def lerp(t, a, b):
return a + t * (b - a)
def grad(hash, x, y, z):
h = hash & 15 # CONVERT LO 4 BITS OF HASH CODE u = x if h<8 else y # INTO 12 GRADIENT DIRECTIONS. v = y if h<4 else (x if h in (12, 14) else z) return (u if (h&1) == 0 else -u) + (v if (h&2) == 0 else -v)
p = [None] * 512 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]
for i in range(256):
p[256+i] = p[i] = permutation[i]
if __name__ == '__main__':
print("%1.17f" % perlin_noise(3.14, 42, 7))</lang>
- Output:
0.13691995878400012
Racket
-- because we were asked to
<lang racket>#lang racket (define (floor-to-255 x)
(bitwise-and (exact-floor x) #xFF))
(define (fade t)
(* t t t (+ 10 (* t (- (* t 6) 15)))))
(define (lerp t a b)
(+ a (* t (- b a))))
- CONVERT LO 4 BITS OF HASH CODE INTO 12 GRADIENT DIRECTIONS.
(define (grad hsh x y z)
(define h (bitwise-and hsh #x0F)) (define u (if (< h 8) x y)) (define v (cond [(< h 4) y] [(or (= h 12) (= h 14)) x] [else z])) (+ (if (bitwise-bit-set? h 0) (- u) u) (if (bitwise-bit-set? h 1) (- v) v)))
(define permutation
(vector 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))
(define p (make-vector 512)) (for ((offset (in-list '(0 256))))
(vector-copy! p offset permutation))
(define-syntax-rule (p-ref n)
(vector-ref p n))
(define (noise x y z)
(let*
(
;; FIND UNIT CUBE THAT CONTAINS POINT.
(X (floor-to-255 x))
(Y (floor-to-255 y))
(Z (floor-to-255 z))
; FIND RELATIVE X,Y,Z OF POINT IN CUBE.
(x (- x (floor x)))
(y (- y (floor y)))
(z (- z (floor z)))
;; COMPUTE FADE CURVES FOR EACH OF X,Y,Z.
(u (fade x))
(v (fade y))
(w (fade z))
;; HASH COORDINATES OF THE 8 CUBE CORNERS...
(A (+ (p-ref X) Y))
(AA (+ (p-ref A) Z))
(AB (+ (p-ref (add1 A)) Z))
(B (+ (p-ref (add1 X)) Y))
(BA (+ (p-ref B) Z))
(BB (+ (p-ref (add1 B)) Z)))
;; .. AND ADD BLENDED RESULTS FROM 8 CORNERS OF CUBE
(lerp
w
(lerp
v (lerp u (grad (p-ref AA) x y z) (grad (p-ref BA) (sub1 x) y z))
(lerp u (grad (p-ref AB) x (sub1 y) z) (grad (p-ref BB) (sub1 x) (sub1 y) z)))
(lerp
v
(lerp u (grad (p-ref (add1 AA)) x y (sub1 z)) (grad (p-ref (add1 BA)) (sub1 x) y (sub1 z)))
(lerp u (grad (vector-ref p (add1 AB)) x (sub1 y) (sub1 z))
(grad (vector-ref p (add1 BB)) (sub1 x) (sub1 y) (sub1 z)))))))
(module+ test
(noise 3.14 42 7))</lang>
- Output:
0.13691995878400012
Raku
(formerly Perl 6)
<lang perl6>constant @p = map {:36($_)}, flat < 47 4G 3T 2J 2I F 3N D 5L 2N 2O 1H 5E 6H 7 69 3W 10 2V U 1X 3Y 8 2R 11 6O L A N 5A 6 44 6V 3C 6I 23 0 Q 5H 1Q 2M 70 63 5N 39 Z B W 1L 4X X 2G 6L 45 1K 2F 4U K 3H 3S 4R 4O 1W 4V 22 4L 1Z 3Q 3V 1C R 4M 25 42 4E 6F 2B 33 6D 3E 1O 5V 3P 6E 64 2X 2K 15 1J 1A 6T 14 6S 2U 3Z 1I 1T P 1R 4H 1 60 28 21 5T 24 3O 57 5S 2H I 4P 5K 5G 3R 3M 38 58 4F 2E 4K 2S 31 5I 4T 56 3 1S 1G 61 6A 6Y 3G 3F 5 5M 12 43 3A 3I 73 2A 2D 5W 5R 5Q 1N 6B 1B G 1M H 52 59 S 16 67 53 4Q 5X 3B 6W 48 2 18 4A 4J 1Y 65 49 2T 4B 4N 17 4S 9 3L M 13 71 J 2Q 30 32 27 35 68 6G 4Y 55 34 2W 62 6U 2P 6C 6Z Y 6Q 5D 6M 5U 40 C 5B 4Z 4I 6P 29 1F 41 6J 6X E 6N 2Z 1D 5C 5Y V 51 5J 2Y 4D 54 2C 5O 4W 37 3D 1E 19 3J 4 46 72 3U 6K 5P 2L 66 36 1V T O 20 6R 3X 3K 5F 26 1U 5Z 1P 4C 50 > xx 2;
sub fade($_) { $_ * $_ * $_ * ($_ * ($_ * 6 - 15) + 10) } sub lerp($t, $a, $b) { $a + $t * ($b - $a) } sub grad($h is copy, $x, $y, $z) {
$h +&= 15; my $u = $h < 8 ?? $x !! $y; my $v = $h < 4 ?? $y !! $h == 12|14 ?? $x !! $z; ($h +& 1 ?? -$u !! $u) + ($h +& 2 ?? -$v !! $v);
}
sub noise($x is copy, $y is copy, $z is copy) is export {
my ($X, $Y, $Z) = ($x, $y, $z)».floor »+&» 255;
my ($u, $v, $w) = map &fade, $x -= $X, $y -= $Y, $z -= $Z;
my ($AA, $AB) = @p[$_] + $Z, @p[$_ + 1] + $Z given @p[$X] + $Y;
my ($BA, $BB) = @p[$_] + $Z, @p[$_ + 1] + $Z given @p[$X + 1] + $Y;
lerp($w, lerp($v, lerp($u, grad(@p[$AA ], $x , $y , $z ),
grad(@p[$BA ], $x - 1, $y , $z )),
lerp($u, grad(@p[$AB ], $x , $y - 1, $z ),
grad(@p[$BB ], $x - 1, $y - 1, $z ))),
lerp($v, lerp($u, grad(@p[$AA + 1], $x , $y , $z - 1 ),
grad(@p[$BA + 1], $x - 1, $y , $z - 1 )),
lerp($u, grad(@p[$AB + 1], $x , $y - 1, $z - 1 ),
grad(@p[$BB + 1], $x - 1, $y - 1, $z - 1 ))));
}
say noise 3.14, 42, 7;</lang>
- Output:
0.13691995878
REXX
Programming note: the REXX operator // is the remainder for division (not modulus), so the absolute value of the
remainder is used for this task.
The original decimal (data) table was compressed into a single hexadecimal value (without spaces). <lang rexx>/*REXX program implements a Perlin noise algorithm of a point in 3D─space. */ _= 97a0895b5a0f830dc95f6035c2e907e18c24671e458e086325f0150a17be0694f778ea4b001ac53e5efcdbcb75230b2039b12158ed953857ae147d88aba844af,
||4aa547868b301ba64d929ee7536fe57a3cd385e6dc695c29372ef528f4668f3641193fa101d85049d14c84bbd05912a9c8c4878274bc9f56a4646dc6adba0340,
||34d9e2fa7c7b05ca2693767eff5255d4cfce3be32f103a11b6bd1c2adfb7aad577f898022c9aa346dd99659ba72bac09811627fd13626c6e4f71e0e8b2b97068,
||daf661e4fb22f2c1eed2900cbfb3a2f1513391ebf90eef6b31c0d61fb5c76a9db854ccb07379322d7f0496fe8aeccd5dde72431d1848f38d80c34e42d73d9cb4
do j=0 for length(_)%2; @.j= x2d( substr(_, 2 * j + 1, 2) )
end /*j*/ /* [↑] assign an indexed array. */
parse arg x y z d . /*obtain optional arguments from the CL*/ if x== | x=="," then x= 3.14 /*Not specified? Then use the default.*/ if y== | y=="," then y= 42 /* " " " " " " */ if z== | z=="," then z= 7 /* " " " " " " */ if d== | d=="," then d= 100 /* " " " " " " */ numeric digits d /*use D decimal digits for precision.*/ say 'Perlin noise for the 3D point ['space(x y z, 3)"] ───► " PerlinNoise(x, y, z) exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fade: procedure; parse arg t; return t**3 * (t * (t * 6 - 15) + 10) floor: procedure; parse arg x; _= x % 1; return _ - (x < 0) * (x \= _) lerp: procedure; parse arg t,a,b; return a + t * (b - a) pick: _= abs( arg(1) ) // 256; return @._ /*──────────────────────────────────────────────────────────────────────────────────────*/ grad: procedure; parse arg hash,x,y,z; _= abs(hash) // 16 /*force positive remainder*/
select
when _== 0 | _==12 then return x+y; when _== 1 | _==14 then return y-x
when _== 2 then return x-y; when _== 3 then return -x-y
when _== 4 then return x+z; when _== 5 then return z-x
when _== 6 then return x-z; when _== 7 then return -x-z
when _== 8 then return y+z; when _== 9 | _==13 then return z-y
when _==10 then return y-z
otherwise return -y-z /*for cases 11 or 15. */
end /*select*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ PerlinNoise: procedure expose @.; parse arg x,y,z
x$= floor(x) // 256; x = x - floor(x); xm= x-1; u= fade(x)
y$= floor(y) // 256; y = y - floor(y); ym= y-1; v= fade(y)
z$= floor(z) // 256; z = z - floor(z); zm= z-1; w= fade(z)
a = pick(x$ ) + y$; aa= pick(a) + z$; ab= pick(a +1) + z$
b = pick(x$ +1) + y$; ba= pick(b) + z$; bb= pick(b +1) + z$
return lerp(w, lerp(v, lerp(u, grad( pick(aa ), x , y , z ), ,
grad( pick(ba ), xm, y , z )), ,
lerp(u, grad( pick(ab ), x , ym, z ), ,
grad( pick(bb ), xm, ym, z ))), ,
lerp(v, lerp(u, grad( pick(aa+1), x , y , zm ), ,
grad( pick(ba+1), xm, y , zm )), ,
lerp(u, grad( pick(ab+1), x , ym, zm ), ,
grad( pick(bb+1), xm, ym, zm )))) /1</lang>
- output when using the internal default inputs:
(Output note: this REXX program uses 100 decimal digit precision, but 20 decimal digits would've been adequate.)
(Note that REXX uses decimal floating point, not binary.)
Perlin noise for the 3D point [3.14 42 7] ───► 0.136919958784
Rust
<lang rust>fn main() { println!("{}", noise(3.14, 42.0, 7.0)); }
fn noise(x: f64, y: f64, z: f64) -> f64 { let x0 = x.floor() as usize & 255; let y0 = y.floor() as usize & 255; let z0 = z.floor() as usize & 255;
let x = x - x.floor(); let y = y - y.floor(); let z = z - z.floor();
let u = fade(x); let v = fade(y); let w = fade(z);
let a = P[x0] + y0; let aa = P[a] + z0; let ab = P[a + 1] + z0; let b = P[x0 + 1] + y0; let ba = P[b] + z0; let bb = P[b + 1] + z0;
return lerp(w, lerp(v, lerp(u, grad(P[aa], x , y , z), grad(P[ba], x-1.0, y , z)), lerp(u, grad(P[ab], x , y-1.0, z),
grad(P[bb], x-1.0, y-1.0, z))),
lerp(v, lerp(u, grad(P[aa+1], x , y , z-1.0),
grad(P[ba+1], x-1.0, y , z-1.0)),
lerp(u, grad(P[ab+1], x , y-1.0, z-1.0),
grad(P[bb+1], x-1.0, y-1.0, z-1.0))));
}
fn fade(t: f64) -> f64 { t * t * t * ( t * (t * 6.0 - 15.0) + 10.0) }
fn lerp(t: f64, a: f64, b: f64) -> f64 { a + t * (b - a) }
fn grad(hash: usize, x: f64, y: f64, z: f64) -> f64 { let h = hash & 15; let u = if h < 8 { x } else { y }; let v = if h < 4 { y } else { if h == 12 || h == 14 { x } else { z } };
return if h&1 == 0 { u } else { -u } + if h&2 == 0 { v } else { -v }; }
static P: [usize; 512] = [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, 180,151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103,30,69 ,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];</lang> Output:
0.13691995878400012
Sidef
<lang ruby>const p = (%w'47 4G 3T 2J 2I F 3N D 5L 2N 2O 1H 5E 6H 7 69 3W 10 2V U 1X 3Y 8 2R 11 6O L A N 5A 6 44 6V 3C 6I 23 0 Q 5H 1Q 2M 70 63 5N 39 Z B W 1L 4X X 2G 6L 45 1K 2F 4U K 3H 3S 4R 4O 1W 4V 22 4L 1Z 3Q 3V 1C R 4M 25 42 4E 6F 2B 33 6D 3E 1O 5V 3P 6E 64 2X 2K 15 1J 1A 6T 14 6S 2U 3Z 1I 1T P 1R 4H 1 60 28 21 5T 24 3O 57 5S 2H I 4P 5K 5G 3R 3M 38 58 4F 2E 4K 2S 31 5I 4T 56 3 1S 1G 61 6A 6Y 3G 3F 5 5M 12 43 3A 3I 73 2A 2D 5W 5R 5Q 1N 6B 1B G 1M H 52 59 S 16 67 53 4Q 5X 3B 6W 48 2 18 4A 4J 1Y 65 49 2T 4B 4N 17 4S 9 3L M 13 71 J 2Q 30 32 27 35 68 6G 4Y 55 34 2W 62 6U 2P 6C 6Z Y 6Q 5D 6M 5U 40 C 5B 4Z 4I 6P 29 1F 41 6J 6X E 6N 2Z 1D 5C 5Y V 51 5J 2Y 4D 54 2C 5O 4W 37 3D 1E 19 3J 4 46 72 3U 6K 5P 2L 66 36 1V T O 20 6R 3X 3K 5F 26 1U 5Z 1P 4C 50' * 2 -> map {|n| Num(n, 36) })
func fade(n) { n * n * n * (n * (n * 6 - 15) + 10) } func lerp(t, a, b) { a + t*(b-a) }
func grad(h, x, y, z) {
h &= 15 var u = (h < 8 ? x : y) var v = (h < 4 ? y : (h ~~ [12,14] ? x : z)) (h&1 ? -u : u) + (h&2 ? -v : v)
}
func noise(x, y, z) {
var(X, Y, Z) = [x, y, z].map { .floor & 255 }...
var (u, v, w) = [x-=X, y-=Y, z-=Z].map { fade(_) }...
var (AA, AB) = with(p[X] + Y) {|i| (p[i] + Z, p[i+1] + Z) }
var (BA, BB) = with(p[X+1] + Y) {|i| (p[i] + Z, p[i+1] + Z) }
lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ),
grad(p[BA ], x-1, y , z )),
lerp(u, grad(p[AB ], x , y-1, z ),
grad(p[BB ], x-1, y-1, z ))),
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1),
grad(p[BA+1], x-1, y , z-1)),
lerp(u, grad(p[AB+1], x , y-1, z-1),
grad(p[BB+1], x-1, y-1, z-1))))
}
say noise(3.14, 42, 7)</lang>
- Output:
0.136919958784
Swift
<lang swift>import Foundation
struct Perlin {
private static let 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 ]
private static let p = (0..<512).map({i -> Int in
if i < 256 {
return permutation[i]
} else {
return permutation[i - 256]
}
})
private static func fade(_ t: Double) -> Double { t * t * t * (t * (t * 6 - 15) + 10) }
private static func lerp(_ t: Double, _ a: Double, _ b: Double) -> Double { a + t * (b - a) }
private static func grad(_ hash: Int, _ x: Double, _ y: Double, _ z: Double) -> Double {
let h = hash & 15
let u = h < 8 ? x : y
let v = h < 4 ? y : h == 12 || h == 14 ? x : z
return (h & 1 == 0 ? u : -u) + (h & 2 == 0 ? v : -v) }
static func noise(x: Double, y: Double, z: Double) -> Double {
let xi = Int(x) & 255
let yi = Int(y) & 255
let zi = Int(z) & 255
let xx = x - floor(x) let yy = y - floor(y) let zz = z - floor(z)
let u = fade(xx) let v = fade(yy) let w = fade(zz)
let a = p[xi] + yi let aa = p[a] + zi let b = p[xi + 1] + yi let ba = p[b] + zi let ab = p[a + 1] + zi let bb = p[b + 1] + zi
return lerp(w, lerp(v, lerp(u, grad(p[aa], xx, yy, zz),
grad(p[ba], xx - 1, yy, zz)),
lerp(u, grad(p[ab], xx, yy - 1, zz),
grad(p[bb], xx - 1, yy - 1, zz))),
lerp(v, lerp(u, grad(p[aa + 1], xx, yy, zz - 1),
grad(p[ba + 1], xx - 1, yy, zz - 1)),
lerp(u, grad(p[ab + 1], xx, yy - 1, zz - 1),
grad(p[bb + 1], xx - 1, yy - 1, zz - 1))))
}
}
print(Perlin.noise(x: 3.14, y: 42, z: 7))</lang>
- Output:
0.13691995878400012
Tcl
<lang tcl>namespace eval perlin {
proc noise {x y z} {
# Find unit cube that contains point. set X [expr {int(floor($x)) & 255}] set Y [expr {int(floor($y)) & 255}] set Z [expr {int(floor($z)) & 255}]
# Find relative x,y,z of point in cube. set x [expr {$x - floor($x)}] set y [expr {$y - floor($y)}] set z [expr {$z - floor($z)}]
# Compute fade curves for each of x,y,z. set u [expr {fade($x)}] set v [expr {fade($y)}] set w [expr {fade($z)}]
# Hash coordinates of the 8 cube corners... variable p set A [expr {p($X) + $Y}] set AA [expr {p($A) + $Z}] set AB [expr {p($A+1) + $Z}] set B [expr {p($X+1) + $Y}] set BA [expr {p($B) + $Z}] set BB [expr {p($B+1) + $Z}]
# And add blended results from 8 corners of cube return [expr { lerp($w, lerp($v, lerp($u, grad(p($AA), $x, $y, $z ), grad(p($BA), $x-1, $y, $z )), lerp($u, grad(p($AB), $x, $y-1, $z ), grad(p($BB), $x-1, $y-1, $z ))), lerp($v, lerp($u, grad(p($AA+1), $x, $y, $z-1 ), grad(p($BA+1), $x-1, $y, $z-1 )), lerp($u, grad(p($AB+1), $x, $y-1, $z-1 ), grad(p($BB+1), $x-1, $y-1, $z-1 )))) }]
}
namespace eval tcl::mathfunc {
proc p {idx} {lindex $::perlin::permutation $idx} proc fade {t} {expr { $t**3 * ($t * ($t * 6 - 15) + 10) }} proc lerp {t a b} {expr { $a + $t * ($b - $a) }} proc grad {hash x y z} { # Convert low 4 bits of hash code into 12 gradient directions set h [expr { $hash & 15 }] set u [expr { $h<8 ? $x : $y }] set v [expr { $h<4 ? $y : ($h==12 || $h==14) ? $x : $z }] expr { (($h&1)==0 ? $u : -$u) + (($h&2)==0 ? $v : -$v) } }
}
apply {{} {
binary scan [binary format H* [join { 97A0895B5A0F830DC95F6035C2E907E18C24671E458E086325F0150A17BE0694F7 78EA4B001AC53E5EFCDBCB75230B2039B12158ED953857AE147D88ABA844AF4AA5
47868B301BA64D929EE7536FE57A3CD385E6DC695C29372EF528F4668F3641193F
A101D85049D14C84BBD05912A9C8C4878274BC9F56A4646DC6ADBA034034D9E2FA
7C7B05CA2693767EFF5255D4CFCE3BE32F103A11B6BD1C2ADFB7AAD577F898022C
9AA346DD99659BA72BAC09811627FD13626C6E4F71E0E8B2B97068DAF661E4FB22
F2C1EED2900CBFB3A2F1513391EBF90EEF6B31C0D61FB5C76A9DB854CCB0737932
2D7F0496FE8AECCD5DDE72431D1848F38D80C34E42D73D9CB4 } ""]] cu* p variable ::perlin::permutation [concat $p $p]
}}
}
puts [perlin::noise 3.14 42 7]</lang>
- Output:
0.13691995878400012
zkl
<lang zkl>class [static] ImprovedNoise{ // a container, not an object
fcn noise(xyz){ xyz=vm.arglist.apply("toFloat");
X,Y,Z:= // FIND UNIT CUBE THAT CONTAINS POINT.
xyz.apply(fcn(x){ x.floor().toInt().bitAnd(255) });
xyz= // FIND RELATIVE X,Y,Z OF POINT IN CUBE.
xyz.apply(fcn(x){ x - x.floor() });
u,v,w:= xyz.apply(fade); // COMPUTE FADE CURVES FOR EACH OF X,Y,Z.
A,AA,AB:= p[X ]+Y, p[A]+Z, p[A+1]+Z; // HASH COORDINATES OF
B,BA,BB:= p[X+1]+Y, p[B]+Z, p[B+1]+Z; // THE 8 CUBE CORNERS,
x,y,z:=xyz;
lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD
grad(p[BA ], x-1, y , z )), // BLENDED
lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS
grad(p[BB ], x-1, y-1, z ))),// FROM 8
lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS
grad(p[BA+1], x-1, y , z-1 )), // OF CUBE
lerp(u, grad(p[AB+1], x , y-1, z-1 ),
grad(p[BB+1], x-1, y-1, z-1 ))));
}
fcn [private] fade(t){ t*t*t*(t*(t*6 - 15) + 10) }
fcn [private] lerp(t,a,b){ a + t*(b - a) }
fcn [private] grad(hash,x,y,z){
h:=hash.bitAnd(15); // CONVERT LO 4 BITS OF HASH CODE
u:=(if(h<8) x else y); // INTO 12 GRADIENT DIRECTIONS.
v:=(if(h<4) y else ((h==12 or h==14) and x or z));
(if(h.isEven) u else -u) + (if(h.bitAnd(2)==0) v else -v)
}
var [const,private] permutation=Data(Void, 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),
p=Data(Void,permutation,permutation);
}</lang> <lang zkl>ImprovedNoise.noise(3.14, 42, 7).println();</lang>
- Output:
0.13692