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Yoplitein/opensimplex2.rs

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Port of OpenSimplex to Rust
Raw
opensimplex2.rs
// Port of https://github.com/KdotJPG/OpenSimplex2/blob/e09a94744b3d69e4c58ce615445f18712cb50104/java/OpenSimplex2.java
#![allow(non_snake_case)]
/*!
K.jpg's OpenSimplex 2, faster variant
*/
use std::{num::Wrapping, sync::Once};
const PRIME_X: i64 = 0x5205402B9270C86F;
const PRIME_Y: i64 = 0x598CD327003817B5;
const PRIME_Z: i64 = 0x5BCC226E9FA0BACB;
const PRIME_W: i64 = 0x56CC5227E58F554B;
const HASH_MULTIPLIER: i64 = 0x53A3F72DEEC546F5;
const SEED_FLIP_3D: i64 = -0x52D547B2E96ED629;
const SEED_OFFSET_4D: i64 = 0xE83DC3E0DA7164D;
const ROOT2OVER2: f64 = 0.7071067811865476;
const SKEW_2D: f64 = 0.366025403784439;
const UNSKEW_2D: f64 = -0.21132486540518713;
const ROOT3OVER3: f64 = 0.577350269189626;
const FALLBACK_ROTATE_3D: f64 = 2.0 / 3.0;
const ROTATE_3D_ORTHOGONALIZER: f64 = UNSKEW_2D;
const SKEW_4D: f32 = -0.138196601125011;
const UNSKEW_4D: f32 = 0.309016994374947;
const LATTICE_STEP_4D: f32 = 0.2;
const N_GRADS_2D_EXPONENT: i32 = 7;
const N_GRADS_3D_EXPONENT: i32 = 8;
const N_GRADS_4D_EXPONENT: i32 = 9;
const N_GRADS_2D: i32 = 1 << N_GRADS_2D_EXPONENT;
const N_GRADS_3D: i32 = 1 << N_GRADS_3D_EXPONENT;
const N_GRADS_4D: i32 = 1 << N_GRADS_4D_EXPONENT;
const NORMALIZER_2D: f64 = 0.01001634121365712;
const NORMALIZER_3D: f64 = 0.07969837668935331;
const NORMALIZER_4D: f64 = 0.0220065933241897;
const RSQUARED_2D: f32 = 0.5;
const RSQUARED_3D: f32 = 0.6;
const RSQUARED_4D: f32 = 0.6;
/*
Noise Evaluators
*/
/**
2D Simplex noise, standard lattice orientation.
*/
pub fn noise2(seed: i64, x: f64, y: f64) -> f32 {
// Get points for A2* lattice
let s = SKEW_2D * (x + y);
let xs = x + s;
let ys = y + s;
noise2_UnskewedBase(seed, xs, ys)
}
/**
2D Simplex noise, with Y pointing down the main diagonal.
Might be better for a 2D sandbox style game, where Y is vertical.
Probably slightly less optimal for heightmaps or continent maps,
unless your map is centered around an equator. It's a subtle
difference, but the option is here to make it an easy choice.
*/
pub fn noise2_ImproveX(seed: i64, x: f64, y: f64) -> f32 {
// Skew transform and rotation baked into one.
let xx = x * ROOT2OVER2;
let yy = y * (ROOT2OVER2 * (1.0 + 2.0 * SKEW_2D));
noise2_UnskewedBase(seed, yy + xx, yy - xx)
}
/**
2D Simplex noise base.
*/
fn noise2_UnskewedBase(seed: i64, xs: f64, ys: f64) -> f32 {
let seed = Wrapping(seed);
// Get base points and offsets.
let xsb = fastFloor(xs);
let ysb = fastFloor(ys);
let xi = (xs - xsb as f64) as f32;
let yi = (ys - ysb as f64) as f32;
// Prime pre-multiplication for hash.
let xsbp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
let ysbp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);
// Unskew.
let t = (xi + yi) * UNSKEW_2D as f32;
let dx0 = xi + t;
let dy0 = yi + t;
// First vertex.
let mut value = 0.0;
let a0 = RSQUARED_2D - dx0 * dx0 - dy0 * dy0;
if a0 > 0.0 {
value = (a0 * a0) * (a0 * a0) * grad2(seed, xsbp, ysbp, dx0, dy0);
}
// Second vertex.
let a1 = (2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 / UNSKEW_2D + 2.0)) as f32 * t
+ ((-2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 + 2.0 * UNSKEW_2D)) as f32 + a0);
if a1 > 0.0 {
let dx1 = dx0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
let dy1 = dy0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
value += (a1 * a1)
* (a1 * a1)
* grad2(
seed,
xsbp + Wrapping(PRIME_X),
ysbp + Wrapping(PRIME_Y),
dx1,
dy1,
);
}
// Third vertex.
if dy0 > dx0 {
let dx2 = dx0 - UNSKEW_2D as f32;
let dy2 = dy0 - (UNSKEW_2D + 1.0) as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value += (a2 * a2) * (a2 * a2) * grad2(seed, xsbp, ysbp + Wrapping(PRIME_Y), dx2, dy2);
}
} else {
let dx2 = dx0 - (UNSKEW_2D + 1.0) as f32;
let dy2 = dy0 - UNSKEW_2D as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value += (a2 * a2) * (a2 * a2) * grad2(seed, xsbp + Wrapping(PRIME_X), ysbp, dx2, dy2);
}
}
value
}
/**
3D OpenSimplex2 noise, with better visual isotropy in (X, Y).
Recommended for 3D terrain and time-varied animations.
The Z coordinate should always be the "different" coordinate in whatever your use case is.
If Y is vertical in world coordinates, call noise3_ImproveXZ(x, z, Y) or use noise3_XZBeforeY.
If Z is vertical in world coordinates, call noise3_ImproveXZ(x, y, Z).
For a time varied animation, call noise3_ImproveXY(x, y, T).
*/
pub fn noise3_ImproveXY(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices without skewing, so Z points up the main lattice diagonal,
// and the planes formed by XY are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
let xy = x + y;
let s2 = xy * ROTATE_3D_ORTHOGONALIZER;
let zz = z * ROOT3OVER3;
let xr = x + s2 + zz;
let yr = y + s2 + zz;
let zr = xy * -ROOT3OVER3 + zz;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
3D OpenSimplex2 noise, with better visual isotropy in (X, Z).
Recommended for 3D terrain and time-varied animations.
The Y coordinate should always be the "different" coordinate in whatever your use case is.
If Y is vertical in world coordinates, call noise3_ImproveXZ(x, Y, z).
If Z is vertical in world coordinates, call noise3_ImproveXZ(x, Z, y) or use noise3_ImproveXY.
For a time varied animation, call noise3_ImproveXZ(x, T, y) or use noise3_ImproveXY.
*/
pub fn noise3_ImproveXZ(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices without skewing, so Y points up the main lattice diagonal,
// and the planes formed by XZ are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
let xz = x + z;
let s2 = xz * ROTATE_3D_ORTHOGONALIZER;
let yy = y * ROOT3OVER3;
let xr = x + s2 + yy;
let zr = z + s2 + yy;
let yr = xz * -ROOT3OVER3 + yy;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
3D OpenSimplex2 noise, fallback rotation option
Use noise3_ImproveXY or noise3_ImproveXZ instead, wherever appropriate.
They have less diagonal bias. This function's best use is as a fallback.
*/
pub fn noise3_Fallback(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices via rotation, to produce a familiar look.
// Orthonormal rotation. Not a skew transform.
let r = FALLBACK_ROTATE_3D * (x + y + z);
let xr = r - x;
let yr = r - y;
let zr = r - z;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
Generate overlapping cubic lattices for 3D OpenSimplex2 noise.
*/
fn noise3_UnrotatedBase(seed: i64, xr: f64, yr: f64, zr: f64) -> f32 {
let mut seed = Wrapping(seed);
// Get base points and offsets.
let xrb = fastRound(xr);
let yrb = fastRound(yr);
let zrb = fastRound(zr);
let mut xri = (xr - xrb as f64) as f32;
let mut yri = (yr - yrb as f64) as f32;
let mut zri = (zr - zrb as f64) as f32;
// -1 if positive, 1 if negative.
let mut xNSign = (-1.0 - xri) as i32 | 1;
let mut yNSign = (-1.0 - yri) as i32 | 1;
let mut zNSign = (-1.0 - zri) as i32 | 1;
// Compute absolute values, using the above as a shortcut. This was faster in my tests for some reason.
let mut ax0 = xNSign as f32 * -xri;
let mut ay0 = yNSign as f32 * -yri;
let mut az0 = zNSign as f32 * -zri;
// Prime pre-multiplication for hash.
let mut xrbp = Wrapping(xrb as i64) * Wrapping(PRIME_X);
let mut yrbp = Wrapping(yrb as i64) * Wrapping(PRIME_Y);
let mut zrbp = Wrapping(zrb as i64) * Wrapping(PRIME_Z);
// Loop: Pick an edge on each lattice copy.
let mut value = 0.0;
let mut a = (RSQUARED_3D - xri * xri) - (yri * yri + zri * zri);
for l in 0.. {
// Closest point on cube.
if a > 0.0 {
value += (a * a) * (a * a) * grad3(seed, xrbp, yrbp, zrbp, xri, yri, zri);
}
// Second-closest point.
if ax0 >= ay0 && ax0 >= az0 {
let mut b = a + ax0 + ax0;
if b > 1.0 {
b -= 1.0;
value += (b * b)
* (b * b)
* grad3(
seed,
xrbp - Wrapping(xNSign as i64) * Wrapping(PRIME_X),
yrbp,
zrbp,
xri + xNSign as f32,
yri,
zri,
);
}
} else if ay0 > ax0 && ay0 >= az0 {
let mut b = a + ay0 + ay0;
if b > 1.0 {
b -= 1.0;
value += (b * b)
* (b * b)
* grad3(
seed,
xrbp,
yrbp - Wrapping(yNSign as i64) * Wrapping(PRIME_Y),
zrbp,
xri,
yri + yNSign as f32,
zri,
);
}
} else {
let mut b = a + az0 + az0;
if b > 1.0 {
b -= 1.0;
value += (b * b)
* (b * b)
* grad3(
seed,
xrbp,
yrbp,
zrbp - Wrapping(zNSign as i64) * Wrapping(PRIME_Z),
xri,
yri,
zri + zNSign as f32,
);
}
}
// Break from loop if we're done, skipping updates below.
if l == 1 {
break;
}
// Update absolute value.
ax0 = 0.5 - ax0;
ay0 = 0.5 - ay0;
az0 = 0.5 - az0;
// Update relative coordinate.
xri = xNSign as f32 * ax0;
yri = yNSign as f32 * ay0;
zri = zNSign as f32 * az0;
// Update falloff.
a += (0.75 - ax0) - (ay0 + az0);
// Update prime for hash.
xrbp += (xNSign as i64 >> 1) & PRIME_X;
yrbp += (yNSign as i64 >> 1) & PRIME_Y;
zrbp += (zNSign as i64 >> 1) & PRIME_Z;
// Update the reverse sign indicators.
xNSign = -xNSign;
yNSign = -yNSign;
zNSign = -zNSign;
// And finally update the seed for the other lattice copy.
seed ^= SEED_FLIP_3D;
}
value
}
/**
4D OpenSimplex2 noise, with XYZ oriented like noise3_ImproveXY
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
in a space where Z is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXY(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xy = x + y;
let s2 = xy * -0.21132486540518699998;
let zz = z * 0.28867513459481294226;
let ww = w * 0.2236067977499788;
let xr = x + (zz + ww + s2);
let yr = y + (zz + ww + s2);
let zr = xy * -0.57735026918962599998 + (zz + ww);
let wr = z * -0.866025403784439 + ww;
noise4_UnskewedBase(seed, xr, yr, zr, wr)
}
/**
4D OpenSimplex2 noise, with XYZ oriented like noise3_ImproveXZ
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
in a space where Y is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xz = x + z;
let s2 = xz * -0.21132486540518699998;
let yy = y * 0.28867513459481294226;
let ww = w * 0.2236067977499788;
let xr = x + (yy + ww + s2);
let zr = z + (yy + ww + s2);
let yr = xz * -0.57735026918962599998 + (yy + ww);
let wr = y * -0.866025403784439 + ww;
noise4_UnskewedBase(seed, xr, yr, zr, wr)
}
/**
4D OpenSimplex2 noise, with XYZ oriented like noise3_Fallback
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
where there isn't a clear distinction between horizontal and vertical
*/
pub fn noise4_ImproveXYZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xyz = x + y + z;
let ww = w * 0.2236067977499788;
let s2 = xyz * -0.16666666666666666 + ww;
let xs = x + s2;
let ys = y + s2;
let zs = z + s2;
let ws = -0.5 * xyz + ww;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D OpenSimplex2 noise, with XY and ZW forming orthogonal triangular-based planes.
Recommended for 3D terrain, where X and Y (or Z and W) are horizontal.
Recommended for noise(x, y, sin(time), cos(time)) trick.
*/
pub fn noise4_ImproveXY_ImproveZW(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let s2 = (x + y) * -0.178275657951399372 + (z + w) * 0.215623393288842828;
let t2 = (z + w) * -0.403949762580207112 + (x + y) * -0.375199083010075342;
let xs = x + s2;
let ys = y + s2;
let zs = z + t2;
let ws = w + t2;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D OpenSimplex2 noise, fallback lattice orientation.
*/
pub fn noise4_Fallback(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
// Get points for A4 lattice
let s = SKEW_4D as f64 * (x + y + z + w);
let xs = x + s;
let ys = y + s;
let zs = z + s;
let ws = w + s;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D OpenSimplex2 noise base.
*/
fn noise4_UnskewedBase(seed: i64, xs: f64, ys: f64, zs: f64, ws: f64) -> f32 {
let mut seed = Wrapping(seed);
// Get base points and offsets
let xsb = fastFloor(xs);
let ysb = fastFloor(ys);
let zsb = fastFloor(zs);
let wsb = fastFloor(ws);
let mut xsi = (xs - xsb as f64) as f32;
let mut ysi = (ys - ysb as f64) as f32;
let mut zsi = (zs - zsb as f64) as f32;
let mut wsi = (ws - wsb as f64) as f32;
// Determine which lattice we can be confident has a contributing point its corresponding cell's base simplex.
// We only look at the spaces between the diagonal planes. This proved effective in all of my tests.
let siSum = (xsi + ysi) + (zsi + wsi);
let startingLattice = (siSum * 1.25) as i32;
// Offset for seed based on first lattice copy.
seed += Wrapping(startingLattice as i64) * Wrapping(SEED_OFFSET_4D);
// Offset for lattice point relative positions (skewed)
let startingLatticeOffset = startingLattice as f32 * -LATTICE_STEP_4D;
xsi += startingLatticeOffset;
ysi += startingLatticeOffset;
zsi += startingLatticeOffset;
wsi += startingLatticeOffset;
// Prep for vertex contributions.
let mut ssi = (siSum + startingLatticeOffset * 4.0) * UNSKEW_4D;
// Prime pre-multiplication for hash.
let mut xsvp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
let mut ysvp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);
let mut zsvp = Wrapping(zsb as i64) * Wrapping(PRIME_Z);
let mut wsvp = Wrapping(wsb as i64) * Wrapping(PRIME_W);
// Five points to add, total, from five copies of the A4 lattice.
let mut value = 0.0;
for i in 0.. {
// Next point is the closest vertex on the 4-simplex whose base vertex is the aforementioned vertex.
let score0 = 1.0 + ssi * (-1.0 / UNSKEW_4D); // Seems slightly faster than 1.0-xsi-ysi-zsi-wsi
if xsi >= ysi && xsi >= zsi && xsi >= wsi && xsi >= score0 {
xsvp += PRIME_X;
xsi -= 1.0;
ssi -= UNSKEW_4D;
} else if ysi > xsi && ysi >= zsi && ysi >= wsi && ysi >= score0 {
ysvp += PRIME_Y;
ysi -= 1.0;
ssi -= UNSKEW_4D;
} else if zsi > xsi && zsi > ysi && zsi >= wsi && zsi >= score0 {
zsvp += PRIME_Z;
zsi -= 1.0;
ssi -= UNSKEW_4D;
} else if wsi > xsi && wsi > ysi && wsi > zsi && wsi >= score0 {
wsvp += PRIME_W;
wsi -= 1.0;
ssi -= UNSKEW_4D;
}
// gradient contribution with falloff.
let dx = xsi + ssi;
let dy = ysi + ssi;
let dz = zsi + ssi;
let dw = wsi + ssi;
let mut a = (dx * dx + dy * dy) + (dz * dz + dw * dw);
if a < RSQUARED_4D {
a -= RSQUARED_4D;
a *= a;
value += a * a * grad4(seed, xsvp, ysvp, zsvp, wsvp, dx, dy, dz, dw);
}
// Break from loop if we're done, skipping updates below.
if i == 4 {
break;
}
// Update for next lattice copy shifted down by <-0.2, -0.2, -0.2, -0.2>.
xsi += LATTICE_STEP_4D;
ysi += LATTICE_STEP_4D;
zsi += LATTICE_STEP_4D;
wsi += LATTICE_STEP_4D;
ssi += LATTICE_STEP_4D * 4.0 * UNSKEW_4D;
seed -= SEED_OFFSET_4D;
// Because we don't always start on the same lattice copy, there's a special reset case.
if i == startingLattice {
xsvp -= PRIME_X;
ysvp -= PRIME_Y;
zsvp -= PRIME_Z;
wsvp -= PRIME_W;
seed += SEED_OFFSET_4D * 5;
}
}
value
}
/*
Utility
*/
fn grad2(seed: Wrapping<i64>, xsvp: Wrapping<i64>, ysvp: Wrapping<i64>, dx: f32, dy: f32) -> f32 {
let mut hash = seed ^ xsvp ^ ysvp;
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_2D_EXPONENT + 1);
let gi = (hash.0 as i32 & ((N_GRADS_2D - 1) << 1)) as usize;
let grads = &getGradients().gradients2D;
grads[gi | 0] * dx + grads[gi | 1] * dy
}
fn grad3(
seed: Wrapping<i64>,
xrvp: Wrapping<i64>,
yrvp: Wrapping<i64>,
zrvp: Wrapping<i64>,
dx: f32,
dy: f32,
dz: f32,
) -> f32 {
let mut hash = (seed ^ xrvp) ^ (yrvp ^ zrvp);
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_3D_EXPONENT + 2);
let gi = (hash.0 as i32 & ((N_GRADS_3D - 1) << 2)) as usize;
let grads = &getGradients().gradients3D;
grads[gi | 0] * dx + grads[gi | 1] * dy + grads[gi | 2] * dz
}
fn grad4(
seed: Wrapping<i64>,
xsvp: Wrapping<i64>,
ysvp: Wrapping<i64>,
zsvp: Wrapping<i64>,
wsvp: Wrapping<i64>,
dx: f32,
dy: f32,
dz: f32,
dw: f32,
) -> f32 {
let mut hash = seed ^ (xsvp ^ ysvp) ^ (zsvp ^ wsvp);
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_4D_EXPONENT + 2);
let gi = (hash.0 as i32 & ((N_GRADS_4D - 1) << 2)) as usize;
let grads = &getGradients().gradients4D;
(grads[gi | 0] * dx + grads[gi | 1] * dy) + (grads[gi | 2] * dz + grads[gi | 3] * dw)
}
fn fastFloor(x: f64) -> i32 {
let xi = x as i32;
if x < xi as f64 {
xi - 1
} else {
xi
}
}
fn fastRound(x: f64) -> i32 {
if x < 0.0 {
(x - 0.5) as i32
} else {
(x + 0.5) as i32
}
}
/*
gradients
*/
struct Gradients {
gradients2D: Vec<f32>,
gradients3D: Vec<f32>,
gradients4D: Vec<f32>,
}
static mut GRADIENTS: (Once, Option<Gradients>) = (Once::new(), None);
fn getGradients() -> &'static Gradients {
unsafe {
GRADIENTS.0.call_once(|| {
GRADIENTS.1 = Some(initGradients());
});
GRADIENTS.1.as_ref().unwrap()
}
}
fn initGradients() -> Gradients {
let grad2Src = [
0.38268343236509,
0.923879532511287,
0.923879532511287,
0.38268343236509,
0.923879532511287,
-0.38268343236509,
0.38268343236509,
-0.923879532511287,
-0.38268343236509,
-0.923879532511287,
-0.923879532511287,
-0.38268343236509,
-0.923879532511287,
0.38268343236509,
-0.38268343236509,
0.923879532511287,
0.130526192220052,
0.99144486137381,
0.608761429008721,
0.793353340291235,
0.793353340291235,
0.608761429008721,
0.99144486137381,
0.130526192220051,
0.99144486137381,
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];
let gradients2D: Vec<_> = grad2Src
.into_iter()
.map(|v| (v / NORMALIZER_2D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_2D * 2) as usize)
.collect();
let grad3Src = [
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];
let gradients3D: Vec<_> = grad3Src
.into_iter()
.map(|v| (v / NORMALIZER_3D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_3D * 4) as usize)
.collect();
let grad4Src = [
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0.3239847771997537,
0.5794684678643381,
-0.3239847771997537,
-0.3239847771997537,
-0.6740059517812944,
0.5029860367700724,
-0.4004672082940195,
0.15296486218853164,
-0.7504883828755602,
0.5029860367700724,
0.15296486218853164,
-0.4004672082940195,
-0.7504883828755602,
0.4553054119602712,
0.08164729285680945,
0.08164729285680945,
-0.8828161875373585,
0.8828161875373585,
-0.08164729285680945,
-0.08164729285680945,
-0.4553054119602712,
0.7504883828755602,
-0.15296486218853164,
0.4004672082940195,
-0.5029860367700724,
0.7504883828755602,
0.4004672082940195,
-0.15296486218853164,
-0.5029860367700724,
0.6740059517812944,
0.3239847771997537,
0.3239847771997537,
-0.5794684678643381,
0.03381941603233842,
0.03381941603233842,
0.03381941603233842,
0.9982828964265062,
-0.044802370851755174,
-0.044802370851755174,
0.508629699630796,
0.8586508742123365,
-0.044802370851755174,
0.508629699630796,
-0.044802370851755174,
0.8586508742123365,
-0.12128480194602098,
0.4321472685365301,
0.4321472685365301,
0.7821684431180708,
0.508629699630796,
-0.044802370851755174,
-0.044802370851755174,
0.8586508742123365,
0.4321472685365301,
-0.12128480194602098,
0.4321472685365301,
0.7821684431180708,
0.4321472685365301,
0.4321472685365301,
-0.12128480194602098,
0.7821684431180708,
0.37968289875261624,
0.37968289875261624,
0.37968289875261624,
0.753341017856078,
0.03381941603233842,
0.03381941603233842,
0.9982828964265062,
0.03381941603233842,
-0.044802370851755174,
0.044802370851755174,
0.8586508742123365,
0.508629699630796,
-0.044802370851755174,
0.508629699630796,
0.8586508742123365,
-0.044802370851755174,
-0.12128480194602098,
0.4321472685365301,
0.7821684431180708,
0.4321472685365301,
0.508629699630796,
-0.044802370851755174,
0.8586508742123365,
-0.044802370851755174,
0.4321472685365301,
-0.12128480194602098,
0.7821684431180708,
0.4321472685365301,
0.4321472685365301,
0.4321472685365301,
0.7821684431180708,
-0.12128480194602098,
0.37968289875261624,
0.37968289875261624,
0.753341017856078,
0.37968289875261624,
0.03381941603233842,
0.9982828964265062,
0.03381941603233842,
0.03381941603233842,
-0.044802370851755174,
0.8586508742123365,
-0.044802370851755174,
0.508629699630796,
-0.044802370851755174,
0.8586508742123365,
0.508629699630796,
-0.044802370851755174,
-0.12128480194602098,
0.7821684431180708,
0.4321472685365301,
0.4321472685365301,
0.508629699630796,
0.8586508742123365,
-0.044802370851755174,
-0.044802370851755174,
0.4321472685365301,
0.7821684431180708,
-0.12128480194602098,
0.4321472685365301,
0.4321472685365301,
0.7821684431180708,
0.4321472685365301,
-0.12128480194602098,
0.37968289875261624,
0.753341017856078,
0.37968289875261624,
0.37968289875261624,
0.9982828964265062,
0.03381941603233842,
0.03381941603233842,
0.03381941603233842,
0.8586508742123365,
-0.044802370851755174,
-0.044802370851755174,
0.508629699630796,
0.8586508742123365,
-0.044802370851755174,
0.508629699630796,
-0.044802370851755174,
0.7821684431180708,
-0.12128480194602098,
0.4321472685365301,
0.4321472685365301,
0.8586508742123365,
0.508629699630796,
-0.044802370851755174,
-0.044802370851755174,
0.7821684431180708,
0.4321472685365301,
-0.12128480194602098,
0.4321472685365301,
0.7821684431180708,
0.4321472685365301,
0.4321472685365301,
-0.12128480194602098,
0.753341017856078,
0.37968289875261624,
0.37968289875261624,
0.37968289875261624,
];
let gradients4D: Vec<_> = grad4Src
.into_iter()
.map(|v| (v / NORMALIZER_4D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_4D * 4) as usize)
.collect();
Gradients { gradients2D, gradients3D, gradients4D }
}
Raw
opensimplex2s.rs
// Port of https://github.com/KdotJPG/OpenSimplex2/blob/e09a94744b3d69e4c58ce615445f18712cb50104/java/OpenSimplex2S.java
#![allow(non_snake_case)]
/*!
K.jpg's OpenSimplex 2, smooth variant ("SuperSimplex")
*/
use std::{num::Wrapping, sync::Once};
const PRIME_X: i64 = 0x5205402B9270C86F;
const PRIME_Y: i64 = 0x598CD327003817B5;
const PRIME_Z: i64 = 0x5BCC226E9FA0BACB;
const PRIME_W: i64 = 0x56CC5227E58F554B;
const HASH_MULTIPLIER: i64 = 0x53A3F72DEEC546F5;
// const SEED_FLIP_3D: i64 = -0x52D547B2E96ED629; // unused
const ROOT2OVER2: f64 = 0.7071067811865476;
const SKEW_2D: f64 = 0.366025403784439;
const UNSKEW_2D: f64 = -0.21132486540518713;
const ROOT3OVER3: f64 = 0.577350269189626;
const FALLBACK_ROTATE3: f64 = 2.0 / 3.0;
const ROTATE3_ORTHOGONALIZER: f64 = UNSKEW_2D;
const SKEW_4D: f32 = 0.309016994374947;
const UNSKEW_4D: f32 = -0.138196601125011;
const N_GRADS_2D_EXPONENT: i32 = 7;
const N_GRADS_3D_EXPONENT: i32 = 8;
const N_GRADS_4D_EXPONENT: i32 = 9;
const N_GRADS_2D: i32 = 1 << N_GRADS_2D_EXPONENT;
const N_GRADS_3D: i32 = 1 << N_GRADS_3D_EXPONENT;
const N_GRADS_4D: i32 = 1 << N_GRADS_4D_EXPONENT;
const NORMALIZER_2D: f64 = 0.05481866495625118;
const NORMALIZER_3D: f64 = 0.2781926117527186;
const NORMALIZER_4D: f64 = 0.11127401889945551;
const RSQUARED_2D: f32 = 2.0 / 3.0;
const RSQUARED_3D: f32 = 3.0 / 4.0;
const RSQUARED_4D: f32 = 4.0 / 5.0;
/*
Noise Evaluators
*/
/**
2D OpenSimplex2S/SuperSimplex noise, standard lattice orientation.
*/
pub fn noise2(seed: i64, x: f64, y: f64) -> f32 {
// Get points for A2* lattice
let s = SKEW_2D * (x + y);
let xs = x + s;
let ys = y + s;
noise2_UnskewedBase(seed, xs, ys)
}
/**
2D OpenSimplex2S/SuperSimplex noise, with Y pointing down the main diagonal.
Might be better for a 2D sandbox style game, where Y is vertical.
Probably slightly less optimal for heightmaps or continent maps,
unless your map is centered around an equator. It's a slight
difference, but the option is here to make it easy.
*/
pub fn noise2_ImproveX(seed: i64, x: f64, y: f64) -> f32 {
// Skew transform and rotation baked into one.
let xx = x * ROOT2OVER2;
let yy = y * (ROOT2OVER2 * (1.0 + 2.0 * SKEW_2D));
noise2_UnskewedBase(seed, yy + xx, yy - xx)
}
/**
2D OpenSimplex2S/SuperSimplex noise base.
*/
fn noise2_UnskewedBase(seed: i64, xs: f64, ys: f64) -> f32 {
let seed = Wrapping(seed);
// Get base points and offsets.
let xsb = fastFloor(xs);
let ysb = fastFloor(ys);
let xi = (xs - xsb as f64) as f32;
let yi = (ys - ysb as f64) as f32;
// Prime pre-multiplication for hash.
let xsbp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
let ysbp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);
// Unskew.
let t = (xi + yi) * UNSKEW_2D as f32;
let dx0 = xi + t;
let dy0 = yi + t;
// First vertex.
let a0 = RSQUARED_2D - dx0 * dx0 - dy0 * dy0;
let mut value = (a0 * a0) * (a0 * a0) * grad2(seed, xsbp, ysbp, dx0, dy0);
// Second vertex.
let a1 = (2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 / UNSKEW_2D + 2.0)) as f32 * t
+ ((-2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 + 2.0 * UNSKEW_2D)) as f32 + a0);
let dx1 = dx0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
let dy1 = dy0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
value += (a1 * a1)
* (a1 * a1)
* grad2(
seed,
xsbp + Wrapping(PRIME_X),
ysbp + Wrapping(PRIME_Y),
dx1,
dy1,
);
// Third and fourth vertices.
// Nested conditionals were faster than compact bit logic/arithmetic.
let xmyi = xi - yi;
if t < UNSKEW_2D as f32 {
if xi + xmyi > 1.0 {
let dx2 = dx0 - (3.0 * UNSKEW_2D + 2.0) as f32;
let dy2 = dy0 - (3.0 * UNSKEW_2D + 1.0) as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value += (a2 * a2)
* (a2 * a2)
* grad2(
seed,
xsbp + Wrapping(PRIME_X << 1),
ysbp + Wrapping(PRIME_Y),
dx2,
dy2,
);
}
} else {
let dx2 = dx0 - UNSKEW_2D as f32;
let dy2 = dy0 - (UNSKEW_2D + 1.0) as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value +=
(a2 * a2) * (a2 * a2) * grad2(seed, xsbp, ysbp + Wrapping(PRIME_Y), dx2, dy2);
}
}
if yi - xmyi > 1.0 {
let dx3 = dx0 - (3.0 * UNSKEW_2D + 1.0) as f32;
let dy3 = dy0 - (3.0 * UNSKEW_2D + 2.0) as f32;
let a3 = RSQUARED_2D - dx3 * dx3 - dy3 * dy3;
if a3 > 0.0 {
value += (a3 * a3)
* (a3 * a3)
* grad2(
seed,
xsbp + Wrapping(PRIME_X),
ysbp + Wrapping(PRIME_Y << 1),
dx3,
dy3,
);
}
} else {
let dx3 = dx0 - (UNSKEW_2D + 1.0) as f32;
let dy3 = dy0 - UNSKEW_2D as f32;
let a3 = RSQUARED_2D - dx3 * dx3 - dy3 * dy3;
if a3 > 0.0 {
value +=
(a3 * a3) * (a3 * a3) * grad2(seed, xsbp + Wrapping(PRIME_X), ysbp, dx3, dy3);
}
}
} else {
if xi + xmyi < 0.0 {
let dx2 = dx0 + (1.0 + UNSKEW_2D) as f32;
let dy2 = dy0 + UNSKEW_2D as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value +=
(a2 * a2) * (a2 * a2) * grad2(seed, xsbp - Wrapping(PRIME_X), ysbp, dx2, dy2);
}
} else {
let dx2 = dx0 - (UNSKEW_2D + 1.0) as f32;
let dy2 = dy0 - UNSKEW_2D as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value +=
(a2 * a2) * (a2 * a2) * grad2(seed, xsbp + Wrapping(PRIME_X), ysbp, dx2, dy2);
}
}
if yi < xmyi {
let dx2 = dx0 + UNSKEW_2D as f32;
let dy2 = dy0 + (UNSKEW_2D + 1.0) as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value +=
(a2 * a2) * (a2 * a2) * grad2(seed, xsbp, ysbp - Wrapping(PRIME_Y), dx2, dy2);
}
} else {
let dx2 = dx0 - UNSKEW_2D as f32;
let dy2 = dy0 - (UNSKEW_2D + 1.0) as f32;
let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
if a2 > 0.0 {
value +=
(a2 * a2) * (a2 * a2) * grad2(seed, xsbp, ysbp + Wrapping(PRIME_Y), dx2, dy2);
}
}
}
value
}
/**
3D OpenSimplex2S/SuperSimplex noise, with better visual isotropy in (X, Y).
Recommended for 3D terrain and time-varied animations.
The Z coordinate should always be the "different" coordinate in whatever your use case is.
If Y is vertical in world coordinates, call noise3_ImproveXZ(x, z, Y) or use noise3_XZBeforeY.
If Z is vertical in world coordinates, call noise3_ImproveXZ(x, y, Z).
For a time varied animation, call noise3_ImproveXY(x, y, T).
*/
pub fn noise3_ImproveXY(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices without skewing, so Z points up the main lattice diagonal,
// and the planes formed by XY are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
let xy = x + y;
let s2 = xy * ROTATE3_ORTHOGONALIZER;
let zz = z * ROOT3OVER3;
let xr = x + s2 + zz;
let yr = y + s2 + zz;
let zr = xy * -ROOT3OVER3 + zz;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
3D OpenSimplex2S/SuperSimplex noise, with better visual isotropy in (X, Z).
Recommended for 3D terrain and time-varied animations.
The Y coordinate should always be the "different" coordinate in whatever your use case is.
If Y is vertical in world coordinates, call noise3_ImproveXZ(x, Y, z).
If Z is vertical in world coordinates, call noise3_ImproveXZ(x, Z, y) or use noise3_ImproveXY.
For a time varied animation, call noise3_ImproveXZ(x, T, y) or use noise3_ImproveXY.
*/
pub fn noise3_ImproveXZ(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices without skewing, so Y points up the main lattice diagonal,
// and the planes formed by XZ are moved far out of alignment with the cube faces.
// Orthonormal rotation. Not a skew transform.
let xz = x + z;
let s2 = xz * -0.211324865405187;
let yy = y * ROOT3OVER3;
let xr = x + s2 + yy;
let zr = z + s2 + yy;
let yr = xz * -ROOT3OVER3 + yy;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
3D OpenSimplex2S/SuperSimplex noise, fallback rotation option
Use noise3_ImproveXY or noise3_ImproveXZ instead, wherever appropriate.
They have less diagonal bias. This function's best use is as a fallback.
*/
pub fn noise3_Fallback(seed: i64, x: f64, y: f64, z: f64) -> f32 {
// Re-orient the cubic lattices via rotation, to produce a familiar look.
// Orthonormal rotation. Not a skew transform.
let r = FALLBACK_ROTATE3 * (x + y + z);
let xr = r - x;
let yr = r - y;
let zr = r - z;
// Evaluate both lattices to form a BCC lattice.
noise3_UnrotatedBase(seed, xr, yr, zr)
}
/**
Generate overlapping cubic lattices for 3D Re-oriented BCC noise.
Lookup table implementation inspired by DigitalShadow.
It was actually faster to narrow down the points in the loop itself,
than to build up the index with enough info to isolate 8 points.
*/
fn noise3_UnrotatedBase(seed: i64, xr: f64, yr: f64, zr: f64) -> f32 {
let seed = Wrapping(seed);
// Get base points and offsets.
let xrb = fastFloor(xr);
let yrb = fastFloor(yr);
let zrb = fastFloor(zr);
let xi = (xr - xrb as f64) as f32;
let yi = (yr - yrb as f64) as f32;
let zi = (zr - zrb as f64) as f32;
// Prime pre-multiplication for hash. Also flip seed for second lattice copy.
let xrbp = Wrapping(xrb as i64) * Wrapping(PRIME_X);
let yrbp = Wrapping(yrb as i64) * Wrapping(PRIME_Y);
let zrbp = Wrapping(zrb as i64) * Wrapping(PRIME_Z);
let seed2 = seed ^ Wrapping(-0x52D547B2E96ED629);
// -1 if positive, 0 if negative.
let xNMask = (-0.5 - xi) as i32;
let yNMask = (-0.5 - yi) as i32;
let zNMask = (-0.5 - zi) as i32;
// First vertex.
let x0 = xi + xNMask as f32;
let y0 = yi + yNMask as f32;
let z0 = zi + zNMask as f32;
let a0 = RSQUARED_3D - x0 * x0 - y0 * y0 - z0 * z0;
let mut value = (a0 * a0)
* (a0 * a0)
* grad3(
seed,
xrbp + Wrapping(xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(zNMask as i64) & Wrapping(PRIME_Z),
x0,
y0,
z0,
);
// Second vertex.
let x1 = xi - 0.5;
let y1 = yi - 0.5;
let z1 = zi - 0.5;
let a1 = RSQUARED_3D - x1 * x1 - y1 * y1 - z1 * z1;
value += (a1 * a1)
* (a1 * a1)
* grad3(
seed2,
xrbp + Wrapping(PRIME_X),
yrbp + Wrapping(PRIME_Y),
zrbp + Wrapping(PRIME_Z),
x1,
y1,
z1,
);
// Shortcuts for building the remaining falloffs.
// Derived by subtracting the polynomials with the offsets plugged in.
let xAFlipMask0 = ((xNMask | 1) << 1) as f32 * x1;
let yAFlipMask0 = ((yNMask | 1) << 1) as f32 * y1;
let zAFlipMask0 = ((zNMask | 1) << 1) as f32 * z1;
let xAFlipMask1 = (-2 - (xNMask << 2)) as f32 * x1 - 1.0;
let yAFlipMask1 = (-2 - (yNMask << 2)) as f32 * y1 - 1.0;
let zAFlipMask1 = (-2 - (zNMask << 2)) as f32 * z1 - 1.0;
let mut skip5 = false;
let a2 = xAFlipMask0 + a0;
if a2 > 0.0 {
let x2 = x0 - (xNMask | 1) as f32;
let y2 = y0;
let z2 = z0;
value += (a2 * a2)
* (a2 * a2)
* grad3(
seed,
xrbp + Wrapping(!xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(zNMask as i64) & Wrapping(PRIME_Z),
x2,
y2,
z2,
);
} else {
let a3 = yAFlipMask0 + zAFlipMask0 + a0;
if a3 > 0.0 {
let x3 = x0;
let y3 = y0 - (yNMask | 1) as f32;
let z3 = z0 - (zNMask | 1) as f32;
value += (a3 * a3)
* (a3 * a3)
* grad3(
seed,
xrbp + Wrapping(xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(!yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(!zNMask as i64) & Wrapping(PRIME_Z),
x3,
y3,
z3,
);
}
let a4 = xAFlipMask1 + a1;
if a4 > 0.0 {
let x4 = (xNMask | 1) as f32 + x1;
let y4 = y1;
let z4 = z1;
value += (a4 * a4)
* (a4 * a4)
* grad3(
seed2,
xrbp + (Wrapping(xNMask as i64) & (Wrapping(PRIME_X) * Wrapping(2))),
yrbp + Wrapping(PRIME_Y),
zrbp + Wrapping(PRIME_Z),
x4,
y4,
z4,
);
skip5 = true;
}
}
let mut skip9 = false;
let a6 = yAFlipMask0 + a0;
if a6 > 0.0 {
let x6 = x0;
let y6 = y0 - (yNMask | 1) as f32;
let z6 = z0;
value += (a6 * a6)
* (a6 * a6)
* grad3(
seed,
xrbp + Wrapping(xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(!yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(zNMask as i64) & Wrapping(PRIME_Z),
x6,
y6,
z6,
);
} else {
let a7 = xAFlipMask0 + zAFlipMask0 + a0;
if a7 > 0.0 {
let x7 = x0 - (xNMask | 1) as f32;
let y7 = y0;
let z7 = z0 - (zNMask | 1) as f32;
value += (a7 * a7)
* (a7 * a7)
* grad3(
seed,
xrbp + Wrapping(!xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(!zNMask as i64) & Wrapping(PRIME_Z),
x7,
y7,
z7,
);
}
let a8 = yAFlipMask1 + a1;
if a8 > 0.0 {
let x8 = x1;
let y8 = (yNMask | 1) as f32 + y1;
let z8 = z1;
value += (a8 * a8)
* (a8 * a8)
* grad3(
seed2,
xrbp + Wrapping(PRIME_X),
yrbp + (Wrapping(yNMask as i64) & (Wrapping(PRIME_Y) << 1)),
zrbp + Wrapping(PRIME_Z),
x8,
y8,
z8,
);
skip9 = true;
}
}
let mut skipD = false;
let aA = zAFlipMask0 + a0;
if aA > 0.0 {
let xA = x0;
let yA = y0;
let zA = z0 - (zNMask | 1) as f32;
value += (aA * aA)
* (aA * aA)
* grad3(
seed,
xrbp + Wrapping(xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(!zNMask as i64) & Wrapping(PRIME_Z),
xA,
yA,
zA,
);
} else {
let aB = xAFlipMask0 + yAFlipMask0 + a0;
if aB > 0.0 {
let xB = x0 - (xNMask | 1) as f32;
let yB = y0 - (yNMask | 1) as f32;
let zB = z0;
value += (aB * aB)
* (aB * aB)
* grad3(
seed,
xrbp + Wrapping(!xNMask as i64) & Wrapping(PRIME_X),
yrbp + Wrapping(!yNMask as i64) & Wrapping(PRIME_Y),
zrbp + Wrapping(zNMask as i64) & Wrapping(PRIME_Z),
xB,
yB,
zB,
);
}
let aC = zAFlipMask1 + a1;
if aC > 0.0 {
let xC = x1;
let yC = y1;
let zC = (zNMask | 1) as f32 + z1;
value += (aC * aC)
* (aC * aC)
* grad3(
seed2,
xrbp + Wrapping(PRIME_X),
yrbp + Wrapping(PRIME_Y),
zrbp + (Wrapping(zNMask as i64) & (Wrapping(PRIME_Z) << 1)),
xC,
yC,
zC,
);
skipD = true;
}
}
if !skip5 {
let a5 = yAFlipMask1 + zAFlipMask1 + a1;
if a5 > 0.0 {
let x5 = x1;
let y5 = (yNMask | 1) as f32 + y1;
let z5 = (zNMask | 1) as f32 + z1;
value += (a5 * a5)
* (a5 * a5)
* grad3(
seed2,
xrbp + Wrapping(PRIME_X),
yrbp + (Wrapping(yNMask as i64) & (Wrapping(PRIME_Y) << 1)),
zrbp + (Wrapping(zNMask as i64) & (Wrapping(PRIME_Z) << 1)),
x5,
y5,
z5,
);
}
}
if !skip9 {
let a9 = xAFlipMask1 + zAFlipMask1 + a1;
if a9 > 0.0 {
let x9 = (xNMask | 1) as f32 + x1;
let y9 = y1;
let z9 = (zNMask | 1) as f32 + z1;
value += (a9 * a9)
* (a9 * a9)
* grad3(
seed2,
xrbp + (Wrapping(xNMask as i64) & (Wrapping(PRIME_X) * Wrapping(2))),
yrbp + Wrapping(PRIME_Y),
zrbp + (Wrapping(zNMask as i64) & (Wrapping(PRIME_Z) << 1)),
x9,
y9,
z9,
);
}
}
if !skipD {
let aD = xAFlipMask1 + yAFlipMask1 + a1;
if aD > 0.0 {
let xD = (xNMask | 1) as f32 + x1;
let yD = (yNMask | 1) as f32 + y1;
let zD = z1;
value += (aD * aD)
* (aD * aD)
* grad3(
seed2,
xrbp + (Wrapping(xNMask as i64) & (Wrapping(PRIME_X) << 1)),
yrbp + (Wrapping(yNMask as i64) & (Wrapping(PRIME_Y) << 1)),
zrbp + Wrapping(PRIME_Z),
xD,
yD,
zD,
);
}
}
value
}
/**
4D SuperSimplex noise, with XYZ oriented like noise3_ImproveXY
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
in a space where Z is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXY(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xy = x + y;
let s2 = xy * -0.21132486540518699998;
let zz = z * 0.28867513459481294226;
let ww = w * 1.118033988749894;
let xr = x + (zz + ww + s2);
let yr = y + (zz + ww + s2);
let zr = xy * -0.57735026918962599998 + (zz + ww);
let wr = z * -0.866025403784439 + ww;
noise4_UnskewedBase(seed, xr, yr, zr, wr)
}
/**
4D SuperSimplex noise, with XYZ oriented like noise3_ImproveXZ
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
in a space where Y is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xz = x + z;
let s2 = xz * -0.21132486540518699998;
let yy = y * 0.28867513459481294226;
let ww = w * 1.118033988749894;
let xr = x + (yy + ww + s2);
let zr = z + (yy + ww + s2);
let yr = xz * -0.57735026918962599998 + (yy + ww);
let wr = y * -0.866025403784439 + ww;
noise4_UnskewedBase(seed, xr, yr, zr, wr)
}
/**
4D SuperSimplex noise, with XYZ oriented like noise3_Fallback
and W for an extra degree of freedom. W repeats eventually.
Recommended for time-varied animations which texture a 3D object (W=time)
where there isn't a clear distinction between horizontal and vertical
*/
pub fn noise4_ImproveXYZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let xyz = x + y + z;
let ww = w * 1.118033988749894;
let s2 = xyz * -0.16666666666666666 + ww;
let xs = x + s2;
let ys = y + s2;
let zs = z + s2;
let ws = -0.5 * xyz + ww;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D SuperSimplex noise, with XY and ZW forming orthogonal triangular-based planes.
Recommended for 3D terrain, where X and Y (or Z and W) are horizontal.
Recommended for noise(x, y, sin(time), cos(time)) trick.
*/
pub fn noise4_ImproveXY_ImproveZW(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
let s2 = (x + y) * -0.28522513987434876941 + (z + w) * 0.83897065470611435718;
let t2 = (z + w) * 0.21939749883706435719 + (x + y) * -0.48214856493302476942;
let xs = x + s2;
let ys = y + s2;
let zs = z + t2;
let ws = w + t2;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D SuperSimplex noise, fallback lattice orientation.
*/
pub fn noise4_Fallback(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
// Get points for A4 lattice
let s = SKEW_4D as f64 * (x + y + z + w);
let xs = x + s;
let ys = y + s;
let zs = z + s;
let ws = w + s;
noise4_UnskewedBase(seed, xs, ys, zs, ws)
}
/**
4D SuperSimplex noise base.
Using ultra-simple 4x4x4x4 lookup partitioning.
This isn't as elegant or SIMD/GPU/etc. portable as other approaches,
but it competes performance-wise with optimized 2014 OpenSimplex.
*/
fn noise4_UnskewedBase(seed: i64, xs: f64, ys: f64, zs: f64, ws: f64) -> f32 {
let seed = Wrapping(seed);
// Get base points and offsets
let xsb = fastFloor(xs);
let ysb = fastFloor(ys);
let zsb = fastFloor(zs);
let wsb = fastFloor(ws);
let xsi = (xs - xsb as f64) as f32;
let ysi = (ys - ysb as f64) as f32;
let zsi = (zs - zsb as f64) as f32;
let wsi = (ws - wsb as f64) as f32;
// Unskewed offsets
let ssi = (xsi + ysi + zsi + wsi) * UNSKEW_4D;
let xi = xsi + ssi;
let yi = ysi + ssi;
let zi = zsi + ssi;
let wi = wsi + ssi;
// Prime pre-multiplication for hash.
let xsvp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
let ysvp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);
let zsvp = Wrapping(zsb as i64) * Wrapping(PRIME_Z);
let wsvp = Wrapping(wsb as i64) * Wrapping(PRIME_W);
// Index into initial table.
let index = ((fastFloor(xs * 4.0) & 3) << 0)
| ((fastFloor(ys * 4.0) & 3) << 2)
| ((fastFloor(zs * 4.0) & 3) << 4)
| ((fastFloor(ws * 4.0) & 3) << 6);
// Point contributions
let staticData = getStaticData();
let mut value = 0.0;
let secondaryIndexStartAndStop = staticData.lookup4DA[index as usize];
let secondaryIndexStart = secondaryIndexStartAndStop & 0xFFFF;
let secondaryIndexStop = secondaryIndexStartAndStop >> 16;
for i in secondaryIndexStart..secondaryIndexStop {
let c = &staticData.lookup4DB[i];
let dx = xi + c.dx;
let dy = yi + c.dy;
let dz = zi + c.dz;
let dw = wi + c.dw;
let mut a = (dx * dx + dy * dy) + (dz * dz + dw * dw);
if a < RSQUARED_4D {
a -= RSQUARED_4D;
a *= a;
value += a
* a
* grad4(
seed,
xsvp + Wrapping(c.xsvp),
ysvp + Wrapping(c.ysvp),
zsvp + Wrapping(c.zsvp),
wsvp + Wrapping(c.wsvp),
dx,
dy,
dz,
dw,
);
}
}
value
}
/*
Utility
*/
fn grad2(seed: Wrapping<i64>, xsvp: Wrapping<i64>, ysvp: Wrapping<i64>, dx: f32, dy: f32) -> f32 {
let mut hash = seed ^ xsvp ^ ysvp;
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_2D_EXPONENT + 1);
let gi = (hash.0 as i32 & ((N_GRADS_2D - 1) << 1)) as usize;
let grads = &getStaticData().gradients2D;
grads[gi | 0] * dx + grads[gi | 1] * dy
}
fn grad3(
seed: Wrapping<i64>,
xrvp: Wrapping<i64>,
yrvp: Wrapping<i64>,
zrvp: Wrapping<i64>,
dx: f32,
dy: f32,
dz: f32,
) -> f32 {
let mut hash = (seed ^ xrvp) ^ (yrvp ^ zrvp);
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_3D_EXPONENT + 2);
let gi = (hash.0 as i32 & ((N_GRADS_3D - 1) << 2)) as usize;
let grads = &getStaticData().gradients3D;
grads[gi | 0] * dx + grads[gi | 1] * dy + grads[gi | 2] * dz
}
fn grad4(
seed: Wrapping<i64>,
xsvp: Wrapping<i64>,
ysvp: Wrapping<i64>,
zsvp: Wrapping<i64>,
wsvp: Wrapping<i64>,
dx: f32,
dy: f32,
dz: f32,
dw: f32,
) -> f32 {
let mut hash = seed ^ (xsvp ^ ysvp) ^ (zsvp ^ wsvp);
hash *= HASH_MULTIPLIER;
hash ^= hash.0 >> (64 - N_GRADS_4D_EXPONENT + 2);
let gi = (hash.0 as i32 & ((N_GRADS_4D - 1) << 2)) as usize;
let grads = &getStaticData().gradients4D;
(grads[gi | 0] * dx + grads[gi | 1] * dy) + (grads[gi | 2] * dz + grads[gi | 3] * dw)
}
fn fastFloor(x: f64) -> i32 {
let xi = x as i32;
if x < xi as f64 {
xi - 1
} else {
xi
}
}
/*
Lookup Tables & Gradients
*/
struct StaticData {
gradients2D: Vec<f32>,
gradients3D: Vec<f32>,
gradients4D: Vec<f32>,
lookup4DA: Vec<usize>,
lookup4DB: Vec<LatticeVertex4D>,
}
static mut STATIC_DATA: (Once, Option<StaticData>) = (Once::new(), None);
fn getStaticData() -> &'static StaticData {
unsafe {
STATIC_DATA.0.call_once(|| {
STATIC_DATA.1 = Some(initStaticData());
});
STATIC_DATA.1.as_ref().unwrap()
}
}
fn initStaticData() -> StaticData {
let grad2Src = &[
0.38268343236509,
0.923879532511287,
0.923879532511287,
0.38268343236509,
0.923879532511287,
-0.38268343236509,
0.38268343236509,
-0.923879532511287,
-0.38268343236509,
-0.923879532511287,
-0.923879532511287,
-0.38268343236509,
-0.923879532511287,
0.38268343236509,
-0.38268343236509,
0.923879532511287,
0.130526192220052,
0.99144486137381,
0.608761429008721,
0.793353340291235,
0.793353340291235,
0.608761429008721,
0.99144486137381,
0.130526192220051,
0.99144486137381,
-0.130526192220051,
0.793353340291235,
-0.60876142900872,
0.608761429008721,
-0.793353340291235,
0.130526192220052,
-0.99144486137381,
-0.130526192220052,
-0.99144486137381,
-0.608761429008721,
-0.793353340291235,
-0.793353340291235,
-0.608761429008721,
-0.99144486137381,
-0.130526192220052,
-0.99144486137381,
0.130526192220051,
-0.793353340291235,
0.608761429008721,
-0.608761429008721,
0.793353340291235,
-0.130526192220052,
0.99144486137381,
][..];
let gradients2D: Vec<_> = grad2Src
.into_iter()
.map(|v| (v / NORMALIZER_2D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_2D * 2) as usize)
.collect();
let grad3Src = &[
2.22474487139,
2.22474487139,
-1.0,
0.0,
2.22474487139,
2.22474487139,
1.0,
0.0,
3.0862664687972017,
1.1721513422464978,
0.0,
0.0,
1.1721513422464978,
3.0862664687972017,
0.0,
0.0,
-2.22474487139,
2.22474487139,
-1.0,
0.0,
-2.22474487139,
2.22474487139,
1.0,
0.0,
-1.1721513422464978,
3.0862664687972017,
0.0,
0.0,
-3.0862664687972017,
1.1721513422464978,
0.0,
0.0,
-1.0,
-2.22474487139,
-2.22474487139,
0.0,
1.0,
-2.22474487139,
-2.22474487139,
0.0,
0.0,
-3.0862664687972017,
-1.1721513422464978,
0.0,
0.0,
-1.1721513422464978,
-3.0862664687972017,
0.0,
-1.0,
-2.22474487139,
2.22474487139,
0.0,
1.0,
-2.22474487139,
2.22474487139,
0.0,
0.0,
-1.1721513422464978,
3.0862664687972017,
0.0,
0.0,
-3.0862664687972017,
1.1721513422464978,
0.0,
-2.22474487139,
-2.22474487139,
-1.0,
0.0,
-2.22474487139,
-2.22474487139,
1.0,
0.0,
-3.0862664687972017,
-1.1721513422464978,
0.0,
0.0,
-1.1721513422464978,
-3.0862664687972017,
0.0,
0.0,
-2.22474487139,
-1.0,
-2.22474487139,
0.0,
-2.22474487139,
1.0,
-2.22474487139,
0.0,
-1.1721513422464978,
0.0,
-3.0862664687972017,
0.0,
-3.0862664687972017,
0.0,
-1.1721513422464978,
0.0,
-2.22474487139,
-1.0,
2.22474487139,
0.0,
-2.22474487139,
1.0,
2.22474487139,
0.0,
-3.0862664687972017,
0.0,
1.1721513422464978,
0.0,
-1.1721513422464978,
0.0,
3.0862664687972017,
0.0,
-1.0,
2.22474487139,
-2.22474487139,
0.0,
1.0,
2.22474487139,
-2.22474487139,
0.0,
0.0,
1.1721513422464978,
-3.0862664687972017,
0.0,
0.0,
3.0862664687972017,
-1.1721513422464978,
0.0,
-1.0,
2.22474487139,
2.22474487139,
0.0,
1.0,
2.22474487139,
2.22474487139,
0.0,
0.0,
3.0862664687972017,
1.1721513422464978,
0.0,
0.0,
1.1721513422464978,
3.0862664687972017,
0.0,
2.22474487139,
-2.22474487139,
-1.0,
0.0,
2.22474487139,
-2.22474487139,
1.0,
0.0,
1.1721513422464978,
-3.0862664687972017,
0.0,
0.0,
3.0862664687972017,
-1.1721513422464978,
0.0,
0.0,
2.22474487139,
-1.0,
-2.22474487139,
0.0,
2.22474487139,
1.0,
-2.22474487139,
0.0,
3.0862664687972017,
0.0,
-1.1721513422464978,
0.0,
1.1721513422464978,
0.0,
-3.0862664687972017,
0.0,
2.22474487139,
-1.0,
2.22474487139,
0.0,
2.22474487139,
1.0,
2.22474487139,
0.0,
1.1721513422464978,
0.0,
3.0862664687972017,
0.0,
3.0862664687972017,
0.0,
1.1721513422464978,
0.0,
][..];
let gradients3D: Vec<_> = grad3Src
.into_iter()
.map(|v| (v / NORMALIZER_3D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_3D * 4) as usize)
.collect();
let grad4Src = &[
-0.6740059517812944,
-0.3239847771997537,
-0.3239847771997537,
0.5794684678643381,
-0.7504883828755602,
-0.4004672082940195,
0.15296486218853164,
0.5029860367700724,
-0.7504883828755602,
0.15296486218853164,
-0.4004672082940195,
0.5029860367700724,
-0.8828161875373585,
0.08164729285680945,
0.08164729285680945,
0.4553054119602712,
-0.4553054119602712,
-0.08164729285680945,
-0.08164729285680945,
0.8828161875373585,
-0.5029860367700724,
-0.15296486218853164,
0.4004672082940195,
0.7504883828755602,
-0.5029860367700724,
0.4004672082940195,
-0.15296486218853164,
0.7504883828755602,
-0.5794684678643381,
0.3239847771997537,
0.3239847771997537,
0.6740059517812944,
-0.6740059517812944,
-0.3239847771997537,
0.5794684678643381,
-0.3239847771997537,
-0.7504883828755602,
-0.4004672082940195,
0.5029860367700724,
0.15296486218853164,
-0.7504883828755602,
0.15296486218853164,
0.5029860367700724,
-0.4004672082940195,
-0.8828161875373585,
0.08164729285680945,
0.4553054119602712,
0.08164729285680945,
-0.4553054119602712,
-0.08164729285680945,
0.8828161875373585,
-0.08164729285680945,
-0.5029860367700724,
-0.15296486218853164,
0.7504883828755602,
0.4004672082940195,
-0.5029860367700724,
0.4004672082940195,
0.7504883828755602,
-0.15296486218853164,
-0.5794684678643381,
0.3239847771997537,
0.6740059517812944,
0.3239847771997537,
-0.6740059517812944,
0.5794684678643381,
-0.3239847771997537,
-0.3239847771997537,
-0.7504883828755602,
0.5029860367700724,
-0.4004672082940195,
0.15296486218853164,
-0.7504883828755602,
0.5029860367700724,
0.15296486218853164,
-0.4004672082940195,
-0.8828161875373585,
0.4553054119602712,
0.08164729285680945,
0.08164729285680945,
-0.4553054119602712,
0.8828161875373585,
-0.08164729285680945,
-0.08164729285680945,
-0.5029860367700724,
0.7504883828755602,
-0.15296486218853164,
0.4004672082940195,
-0.5029860367700724,
0.7504883828755602,
0.4004672082940195,
-0.15296486218853164,
-0.5794684678643381,
0.6740059517812944,
0.3239847771997537,
0.3239847771997537,
0.5794684678643381,
-0.6740059517812944,
-0.3239847771997537,
-0.3239847771997537,
0.5029860367700724,
-0.7504883828755602,
-0.4004672082940195,
0.15296486218853164,
0.5029860367700724,
-0.7504883828755602,
0.15296486218853164,
-0.4004672082940195,
0.4553054119602712,
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][..];
let gradients4D: Vec<_> = grad4Src
.into_iter()
.map(|v| (v / NORMALIZER_4D) as f32)
.collect::<Vec<_>>() // cache divisions
.into_iter()
.cycle()
.take((N_GRADS_4D * 4) as usize)
.collect();
let lookup4DVertexCodes = &[
&[
0x15, 0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96,
0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA,
][..],
&[
0x15, 0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6,
0xAA,
],
&[
0x01, 0x05, 0x11, 0x15, 0x41, 0x45, 0x51, 0x55, 0x56, 0x5A, 0x66, 0x6A, 0x96, 0x9A,
0xA6, 0xAA,
],
&[
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0xA6, 0xAA, 0xAB,
],
&[
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0xAA,
],
&[
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0x9A, 0xAA,
],
&[
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],
&[
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0xAB,
],
&[
0x04, 0x05, 0x14, 0x15, 0x44, 0x45, 0x54, 0x55, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A,
0xA9, 0xAA,
],
&[
0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA,
],
&[0x05, 0x15, 0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x9A, 0xAA],
&[
0x05, 0x15, 0x16, 0x45, 0x46, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x6A, 0x9A, 0xAA, 0xAB,
],
&[
0x04, 0x15, 0x19, 0x45, 0x49, 0x54, 0x55, 0x58, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A,
0xA9, 0xAA, 0xAE,
],
&[
0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x99, 0x9A, 0xAA,
0xAE,
],
&[
0x05, 0x15, 0x19, 0x45, 0x49, 0x55, 0x56, 0x59, 0x5A, 0x5E, 0x6A, 0x9A, 0xAA, 0xAE,
],
&[
0x05, 0x15, 0x1A, 0x45, 0x4A, 0x55, 0x56, 0x59, 0x5A, 0x5B, 0x5E, 0x6A, 0x9A, 0xAA,
0xAB, 0xAE, 0xAF,
],
&[
0x15, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9,
0xAA,
],
&[
0x11, 0x15, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5,
0xA6, 0xAA,
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0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA,
],
&[
0x51, 0x52, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA6, 0xA7, 0xAA, 0xAB,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x45, 0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9,
0xAA, 0xEA,
],
&[
0x45, 0x51, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5,
0xA6, 0xA9, 0xAA, 0xAB, 0xEA,
],
&[
0x55, 0x56, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA,
],
&[
0x45, 0x54, 0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5,
0xA6, 0xA9, 0xAA, 0xAE, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xAB,
],
&[
0x54, 0x55, 0x58, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAD, 0xAE,
],
&[
0x55, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xAE,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x6A, 0x96, 0x99, 0x9A, 0xAA, 0xAB, 0xAE, 0xAF,
],
&[0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA,
],
&[0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA],
&[
0x51, 0x52, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA,
],
&[
0x51, 0x54, 0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5,
0xA6, 0xA9, 0xAA, 0xBA, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA,
],
&[
0x51, 0x55, 0x56, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB,
],
&[0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6,
0xA9, 0xAA,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB,
],
&[
0x54, 0x55, 0x58, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE,
],
&[
0x54, 0x55, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAE,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x66, 0x69, 0x6A, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB,
0xAE, 0xAF,
],
&[
0x50, 0x51, 0x54, 0x55, 0x61, 0x64, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB5, 0xBA,
],
&[
0x51, 0x55, 0x61, 0x65, 0x66, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA,
],
&[
0x51, 0x55, 0x56, 0x61, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xB6, 0xBA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA,
0xBB,
],
&[
0x54, 0x55, 0x64, 0x65, 0x69, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA,
],
&[
0x55, 0x65, 0x66, 0x69, 0x6A, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x6A, 0x96, 0xA5, 0xA6, 0xAA, 0xAB, 0xBA, 0xBB,
],
&[
0x54, 0x55, 0x59, 0x64, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xB9, 0xBA,
],
&[
0x54, 0x55, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA,
],
&[
0x55, 0x56, 0x59, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA,
],
&[
0x55, 0x56, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB,
0xBA, 0xBB,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA,
0xBE,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x6A, 0x99, 0xA5, 0xA9, 0xAA, 0xAE, 0xBA, 0xBE,
],
&[
0x55, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE,
0xBA, 0xBE,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE,
0xBA,
],
&[
0x40, 0x45, 0x51, 0x54, 0x55, 0x85, 0x91, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6,
0xA9, 0xAA, 0xEA,
],
&[
0x41, 0x45, 0x51, 0x55, 0x56, 0x85, 0x91, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xAA,
0xEA,
],
&[
0x41, 0x45, 0x51, 0x55, 0x56, 0x85, 0x91, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xD6, 0xEA,
],
&[
0x41, 0x45, 0x51, 0x55, 0x56, 0x86, 0x92, 0x95, 0x96, 0x97, 0x9A, 0xA6, 0xAA, 0xAB,
0xD6, 0xEA, 0xEB,
],
&[
0x44, 0x45, 0x54, 0x55, 0x59, 0x85, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA9, 0xAA,
0xEA,
],
&[
0x45, 0x55, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xDA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xDA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x86, 0x95, 0x96, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB, 0xDA, 0xEA, 0xEB,
],
&[
0x44, 0x45, 0x54, 0x55, 0x59, 0x85, 0x94, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xD9, 0xEA,
],
&[
0x45, 0x55, 0x59, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xDA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x85, 0x95, 0x96, 0x99, 0x9A, 0xAA, 0xDA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9B, 0xA6, 0xAA, 0xAB, 0xDA, 0xEA,
0xEB,
],
&[
0x44, 0x45, 0x54, 0x55, 0x59, 0x89, 0x95, 0x98, 0x99, 0x9A, 0x9D, 0xA9, 0xAA, 0xAE,
0xD9, 0xEA, 0xEE,
],
&[
0x45, 0x55, 0x59, 0x89, 0x95, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE, 0xDA, 0xEA, 0xEE,
],
&[
0x45, 0x55, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9E, 0xA9, 0xAA, 0xAE, 0xDA, 0xEA,
0xEE,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0x9B, 0x9E, 0xAA, 0xAB, 0xAE,
0xDA, 0xEA, 0xEF,
],
&[
0x50, 0x51, 0x54, 0x55, 0x65, 0x91, 0x94, 0x95, 0x96, 0x99, 0xA5, 0xA6, 0xA9, 0xAA,
0xEA,
],
&[
0x51, 0x55, 0x91, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xE6, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x91, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xE6, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x92, 0x95, 0x96, 0x9A, 0xA6, 0xA7, 0xAA, 0xAB, 0xE6, 0xEA, 0xEB,
],
&[
0x54, 0x55, 0x94, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xE9, 0xEA,
],
&[0x55, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA],
&[
0x55, 0x56, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[0x55, 0x56, 0x95, 0x96, 0x9A, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB],
&[
0x54, 0x55, 0x59, 0x94, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xE9, 0xEA,
],
&[
0x55, 0x59, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x45, 0x55, 0x56, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB,
],
&[
0x54, 0x55, 0x59, 0x95, 0x98, 0x99, 0x9A, 0xA9, 0xAA, 0xAD, 0xAE, 0xE9, 0xEA, 0xEE,
],
&[0x55, 0x59, 0x95, 0x99, 0x9A, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE],
&[
0x45, 0x55, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x95, 0x96, 0x99, 0x9A, 0xAA, 0xAB, 0xAE, 0xEA, 0xEF,
],
&[
0x50, 0x51, 0x54, 0x55, 0x65, 0x91, 0x94, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xE5, 0xEA,
],
&[
0x51, 0x55, 0x65, 0x91, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xE6, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x91, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xE6, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xE6, 0xEA,
0xEB,
],
&[
0x54, 0x55, 0x65, 0x94, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xE9, 0xEA,
],
&[
0x55, 0x65, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x51, 0x55, 0x56, 0x66, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xAA, 0xAB, 0xEA, 0xEB,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x94, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xE9, 0xEA,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x55, 0x56, 0x59, 0x65, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xEA,
],
&[
0x55, 0x56, 0x5A, 0x66, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB,
0xEA, 0xEB,
],
&[
0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xE9, 0xEA,
0xEE,
],
&[
0x54, 0x55, 0x59, 0x69, 0x95, 0x99, 0x9A, 0xA5, 0xA9, 0xAA, 0xAE, 0xEA, 0xEE,
],
&[
0x55, 0x59, 0x5A, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE,
0xEA, 0xEE,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA6, 0xA9, 0xAA, 0xAB, 0xAE,
0xEA,
],
&[
0x50, 0x51, 0x54, 0x55, 0x65, 0x95, 0xA1, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB5, 0xBA,
0xE5, 0xEA, 0xFA,
],
&[
0x51, 0x55, 0x65, 0x95, 0xA1, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA, 0xFA,
],
&[
0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xB6, 0xBA, 0xE6, 0xEA,
0xFA,
],
&[
0x51, 0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA7, 0xAA, 0xAB, 0xB6, 0xBA,
0xE6, 0xEA, 0xFB,
],
&[
0x54, 0x55, 0x65, 0x95, 0xA4, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA, 0xFA,
],
&[0x55, 0x65, 0x95, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA],
&[
0x51, 0x55, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA,
],
&[
0x55, 0x56, 0x65, 0x66, 0x95, 0x96, 0xA5, 0xA6, 0xAA, 0xAB, 0xBA, 0xEA, 0xFB,
],
&[
0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xB9, 0xBA, 0xE9, 0xEA,
0xFA,
],
&[
0x54, 0x55, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA, 0xEA, 0xFA,
],
&[
0x55, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xBA,
0xEA, 0xFA,
],
&[
0x55, 0x56, 0x65, 0x66, 0x6A, 0x95, 0x96, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAB, 0xBA,
0xEA,
],
&[
0x54, 0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAD, 0xAE, 0xB9, 0xBA,
0xE9, 0xEA, 0xFE,
],
&[
0x55, 0x59, 0x65, 0x69, 0x95, 0x99, 0xA5, 0xA9, 0xAA, 0xAE, 0xBA, 0xEA, 0xFE,
],
&[
0x55, 0x59, 0x65, 0x69, 0x6A, 0x95, 0x99, 0x9A, 0xA5, 0xA6, 0xA9, 0xAA, 0xAE, 0xBA,
0xEA,
],
&[
0x55, 0x56, 0x59, 0x5A, 0x65, 0x66, 0x69, 0x6A, 0x95, 0x96, 0x99, 0x9A, 0xA5, 0xA6,
0xA9, 0xAA, 0xAB, 0xAE, 0xBA, 0xEA,
],
][..];
let nLatticeVerticesTotal = lookup4DVertexCodes.iter().map(|v| v.len()).sum();
let latticeVerticesByCode: Vec<_> = (0..256)
.map(|i| {
let cx = ((i >> 0) & 3) - 1;
let cy = ((i >> 2) & 3) - 1;
let cz = ((i >> 4) & 3) - 1;
let cw = ((i >> 6) & 3) - 1;
LatticeVertex4D::new(cx, cy, cz, cw)
})
.collect();
let mut lookup4DA = vec![0; 256];
let mut lookup4DB = vec![Default::default(); nLatticeVerticesTotal];
let mut j = 0;
for i in 0..256 {
lookup4DA[i] = j | ((j + lookup4DVertexCodes[i].len()) << 16);
for k in 0..lookup4DVertexCodes[i].len() {
lookup4DB[j] = latticeVerticesByCode[lookup4DVertexCodes[i][k]].clone();
j += 1;
}
}
StaticData {
gradients2D,
gradients3D,
gradients4D,
lookup4DA,
lookup4DB,
}
}
#[derive(Clone, Default)]
struct LatticeVertex4D {
pub dx: f32,
pub dy: f32,
pub dz: f32,
pub dw: f32,
pub xsvp: i64,
pub ysvp: i64,
pub zsvp: i64,
pub wsvp: i64,
}
impl LatticeVertex4D {
pub fn new(xsv: i32, ysv: i32, zsv: i32, wsv: i32) -> Self {
let ssv = (xsv + ysv + zsv + wsv) as f32 * UNSKEW_4D;
Self {
xsvp: (Wrapping(xsv as i64) * Wrapping(PRIME_X)).0,
ysvp: (Wrapping(ysv as i64) * Wrapping(PRIME_Y)).0,
zsvp: (Wrapping(zsv as i64) * Wrapping(PRIME_Z)).0,
wsvp: (Wrapping(wsv as i64) * Wrapping(PRIME_W)).0,
dx: -xsv as f32 - ssv,
dy: -ysv as f32 - ssv,
dz: -zsv as f32 - ssv,
dw: -wsv as f32 - ssv,
}
}
}
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