How to resolve the algorithm Perlin noise step by step in the OCaml programming language

Published on 12 May 2024 09:40 PM
#Ocaml

How to resolve the algorithm Perlin noise step by step in the OCaml programming language

Table of Contents

Problem Statement

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

R

d

{\displaystyle \mathbb {R} ^{d}}

into

R

{\displaystyle \mathbb {R} }

with an integer

d

{\displaystyle d}

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.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Perlin noise step by step in the OCaml programming language

Source code in the ocaml programming language

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")

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