How to resolve the algorithm Perlin noise step by step in the V (Vlang) programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Perlin noise step by step in the V (Vlang) 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 V (Vlang) programming language
Source code in the v programming language
import math
// vlang doesn't have globals
const (
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,
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 ]
)
fn main() {
println(noise(3.14, 42, 7))
}
fn noise(x1 f64, y1 f64, z1 f64) f64 {
bx := int(math.floor(x1)) & 255
by := int(math.floor(y1)) & 255
bz := int(math.floor(z1)) & 255
x := x1 - math.floor(x1)
y := y1 - math.floor(y1)
z := z1 - math.floor(z1)
u := fade(x)
v := fade(y)
w := fade(z)
ba := p[bx] + by
baa := p[ba] + bz
bab := p[ba+1] + bz
bb := p[bx+1] + by
bba := p[bb] + bz
bbb := p[bb+1] + bz
return lerp(w, lerp(v, lerp(u, grad(p[baa], x, y, z),
grad(p[bba], x-1, y, z)),
lerp(u, grad(p[bab], x, y-1, z),
grad(p[bbb], x-1, y-1, z))),
lerp(v, lerp(u, grad(p[baa+1], x, y, z-1),
grad(p[bba+1], x-1, y, z-1)),
lerp(u, grad(p[bab+1], x, y-1, z-1),
grad(p[bbb+1], x-1, y-1, z-1))))
}
fn fade(t f64) f64 { return t * t * t * (t*(t*6-15) + 10) }
fn lerp(t f64, a f64, b f64) f64 { return a + t*(b-a) }
fn grad(hash int, x f64, y f64, z f64) f64 {
// Vlang doesn't have a ternary. Ternaries can be translated directly
// with if statements, but chains of if statements are often better
// expressed with match statements.
match hash & 15 {
0 {
return x + y
}
1 {
return y - x
}
2 {
return x - y
}
3 {
return -x - y
}
4 {
return x + z
}
5 {
return z - x
}
6{
return x - z
}
7{
return -x - z
}
8 {
return y + z
}
9 {
return z - y
}
10 {
return y - z
}
12 {
return x + y
}
13 {
return z - y
}
14 {
return y - x
}
else {
// case 11, 16:
return -y - z
}
}
}
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