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Add new **Noise** library for C++/C#/VisualScript/HLSL utilities

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This commit is contained in:
Wojtek Figat
2022-07-31 22:20:38 +02:00
parent 1fdc43699c
commit 2104dbc682
10 changed files with 786 additions and 131 deletions
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63
Content/Editor/MaterialTemplates/GPUParticles.shader
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@@ -5,6 +5,7 @@
#include "./Flax/Common.hlsl"
#include "./Flax/GBufferCommon.hlsl"
#include "./Flax/Matrix.hlsl"
#include "./Flax/Noise.hlsl"
@7
// Primary constant buffer
META_CB_BEGIN(0, Data)
@@ -62,68 +63,6 @@ float Rand(inout uint seed)
return asfloat((seed >> 9) | 0x3f800000) - 1.0f;
}
float4 Mod289(float4 x)
{
return x - floor(x * (1.0 / 289.0)) * 289.0;
}
float4 Perm(float4 x)
{
return Mod289(((x * 34.0) + 1.0) * x);
}
float Noise(float3 p)
{
float3 a = floor(p);
float3 d = p - a;
d = d * d * (3.0 - 2.0 * d);
float4 b = a.xxyy + float4(0.0, 1.0, 0.0, 1.0);
float4 k1 = Perm(b.xyxy);
float4 k2 = Perm(k1.xyxy + b.zzww);
float4 c = k2 + a.zzzz;
float4 k3 = Perm(c);
float4 k4 = Perm(c + 1.0);
float4 o1 = frac(k3 * (1.0 / 41.0));
float4 o2 = frac(k4 * (1.0 / 41.0));
float4 o3 = o2 * d.z + o1 * (1.0 - d.z);
float2 o4 = o3.yw * d.x + o3.xz * (1.0 - d.x);
return o4.y * d.y + o4.x * (1.0 - d.y);
}
float3 Noise3D(float3 p)
{
float o = Noise(p);
float a = Noise(p + float3(0.0001f, 0.0f, 0.0f));
float b = Noise(p + float3(0.0f, 0.0001f, 0.0f));
float c = Noise(p + float3(0.0f, 0.0f, 0.0001f));
float3 grad = float3(o - a, o - b, o - c);
float3 other = abs(grad.zxy);
return normalize(cross(grad,other));
}
float3 Noise3D(float3 position, int octaves, float roughness)
{
float weight = 0.0f;
float3 noise = float3(0.0, 0.0, 0.0);
float scale = 1.0f;
for (int i = 0; i < octaves; i++)
{
float curWeight = pow((1.0-((float)i / octaves)), lerp(2.0, 0.2, roughness));
noise += Noise3D(position * scale) * curWeight;
weight += curWeight;
scale *= 1.72531;
}
return noise / weight;
}
// Reprojects the world space position from the given UV and raw device depth
float3 ReprojectPosition(float2 uv, float rawDepth)
{

5
Source/Engine/Core/Math/Math.h
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@@ -172,6 +172,11 @@ namespace Math
return modff(a, b);
}
static FORCE_INLINE float Frac(float value)
{
return value - Floor(value);
}
/// <summary>
/// Returns signed fractional part of a float.
/// </summary>

5
Source/Engine/Core/Math/Mathd.h
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@@ -130,6 +130,11 @@ namespace Math
return modf(a, b);
}
static FORCE_INLINE double Frac(double value)
{
return value - Floor(value);
}
/// <summary>
/// Returns signed fractional part of a double.
/// </summary>

2
Source/Engine/Core/Math/Vector2.h
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@@ -469,7 +469,7 @@ public:
static Vector2Base Frac(const Vector2Base& v)
{
return Vector3(v.X - (int32)v.X, v.Y - (int32)v.Y);
return Vector2Base(v.X - (int32)v.X, v.Y - (int32)v.Y);
}
static Vector2Base Round(const Vector2Base& v)

65
Source/Engine/Particles/Graph/CPU/ParticleEmitterGraph.CPU.ParticleModules.cpp
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@@ -2,6 +2,7 @@
#include "ParticleEmitterGraph.CPU.h"
#include "Engine/Core/Random.h"
#include "Engine/Utilities/Noise.h"
// ReSharper disable CppCStyleCast
// ReSharper disable CppClangTidyClangDiagnosticCastAlign
@@ -25,68 +26,6 @@
namespace
{
FORCE_INLINE Float4 Mod289(Float4 x)
{
return x - Float4::Floor(x * (1.0f / 289.0f)) * 289.0f;
}
FORCE_INLINE Float4 Perm(Float4 x)
{
return Mod289((x * 34.0f + 1.0f) * x);
}
float Noise(Float3 p)
{
Float3 a = Float3::Floor(p);
Float3 d = p - a;
d = d * d * (3.0f - 2.0f * d);
Float4 b(a.X, a.X + 1.0f, a.Y, a.Y + 1.0f);
Float4 k1 = Perm(Float4(b.X, b.Y, b.X, b.Y));
Float4 k2 = Perm(Float4(k1.X + b.Z, k1.Y + b.Z, k1.X + b.W, k1.Y + b.W));
Float4 c = k2 + Float4(a.Z);
Float4 k3 = Perm(c);
Float4 k4 = Perm(c + 1.0f);
Float4 o1 = Float4::Frac(k3 * (1.0f / 41.0f));
Float4 o2 = Float4::Frac(k4 * (1.0f / 41.0f));
Float4 o3 = o2 * d.Z + o1 * (1.0f - d.Z);
Float2 o4 = Float2(o3.Y, o3.W) * d.X + Float2(o3.X, o3.Z) * (1.0f - d.X);
return o4.Y * d.Y + o4.X * (1.0f - d.Y);
}
Float3 Noise3D(Float3 p)
{
const float o = Noise(p);
const float a = Noise(p + Float3(0.0001f, 0.0f, 0.0f));
const float b = Noise(p + Float3(0.0f, 0.0001f, 0.0f));
const float c = Noise(p + Float3(0.0f, 0.0f, 0.0001f));
const Float3 grad(o - a, o - b, o - c);
const Float3 other = Float3::Abs(Float3(grad.Z, grad.X, grad.Y));
return Float3::Normalize(Float3::Cross(grad, other));
}
Float3 Noise3D(Float3 position, int32 octaves, float roughness)
{
float weight = 0.0f;
Float3 noise = Float3::Zero;
float scale = 1.0f;
for (int32 i = 0; i < octaves; i++)
{
const float curWeight = Math::Pow(1.0f - ((float)i / (float)octaves), Math::Lerp(2.0f, 0.2f, roughness));
noise += Noise3D(position * scale) * curWeight;
weight += curWeight;
scale *= 1.72531f;
}
return noise / Math::Max(weight, ZeroTolerance);
}
VariantType::Types GetVariantType(ParticleAttribute::ValueTypes type)
{
switch (type)
@@ -570,7 +509,7 @@ void ParticleEmitterGraphCPUExecutor::ProcessModule(ParticleEmitterGraphCPUNode*
const int32 octavesCount = (int)GetValue(octavesCountBox, 7)
#define LOGIC() \
Float3 vectorFieldUVW = Float3::Transform(*((Float3*)positionPtr), invFieldTransformMatrix); \
Float3 force = Noise3D(vectorFieldUVW + 0.5f, octavesCount, roughness); \
Float3 force = Noise::CustomNoise3D(vectorFieldUVW + 0.5f, octavesCount, roughness); \
force = Float3::Transform(force, fieldTransformMatrix) * intensity; \
*((Float3*)velocityPtr) += force * (context.DeltaTime / Math::Max(*(float*)massPtr, ZeroTolerance)); \
positionPtr += stride; \

3
Source/Engine/Particles/Graph/GPU/ParticleEmitterGraph.GPU.ParticleModules.cpp
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@@ -207,6 +207,7 @@ void ParticleEmitterGPUGenerator::ProcessModule(Node* node)
auto roughness = tryGetValue(node->GetBox(3), 5, Value::Zero).AsFloat();
auto intensity = tryGetValue(node->GetBox(4), 6, Value::Zero).AsFloat();
auto octavesCount = tryGetValue(node->GetBox(5), 7, Value::Zero).AsInt();
_includes.Add(TEXT("./Flax/Noise.hlsl"));
// TODO: build fieldTransformMatrix and invFieldTransformMatrix on CPU and pass in constant buffer - no need to support field transform per particle
_writer.Write(
TEXT(
@@ -218,7 +219,7 @@ void ParticleEmitterGPUGenerator::ProcessModule(Node* node)
" fieldTransformMatrix = mul(fieldTransformMatrix, scaleMatrix);\n"
" float4x4 invFieldTransformMatrix = Inverse(fieldTransformMatrix);\n"
" float3 vectorFieldUVW = mul(invFieldTransformMatrix, float4({0}, 1.0f)).xyz;\n"
" float3 force = Noise3D(vectorFieldUVW + 0.5f, {8}, {6});\n"
" float3 force = CustomNoise3D(vectorFieldUVW + 0.5f, {8}, {6});\n"
" force = mul(fieldTransformMatrix, float4(force, 0.0f)).xyz * {7};\n"
" {1} += force * (DeltaTime / max({2}, PARTICLE_THRESHOLD));\n"
" }}\n"

343
Source/Engine/Utilities/Noise.cpp Normal file
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@@ -0,0 +1,343 @@
// Copyright (c) 2012-2022 Wojciech Figat. All rights reserved.
// Copyright (c) 2011 Stefan Gustavson. All rights reserved.
// Distributed under the MIT license.
// https://github.com/stegu/webgl-noise
#include "Noise.h"
#include "Engine/Core/Math/Vector4.h"
namespace
{
FORCE_INLINE Float2 Mod289(const Float2& x)
{
return x - Float2::Floor(x * (1.0f / 289.0f)) * 289.0f;
}
FORCE_INLINE Float3 Mod289(const Float3& x)
{
return x - Float3::Floor(x * (1.0f / 289.0f)) * 289.0f;
}
FORCE_INLINE Float4 Mod289(const Float4& x)
{
return x - Float4::Floor(x * (1.0f / 289.0f)) * 289.0f;
}
FORCE_INLINE Float3 Mod7(const Float3& x)
{
return x - Float3::Floor(x * (1.0f / 7.0f)) * 7.0f;
}
FORCE_INLINE Float3 Permute(const Float3& x)
{
return Mod289((x * 34.0f + 1.0f) * x);
}
FORCE_INLINE Float4 Permute(const Float4& x)
{
return Mod289((x * 34.0f + 1.0f) * x);
}
FORCE_INLINE Float4 TaylorInvSqrt(const Float4& r)
{
return 1.79284291400159f - 0.85373472095314f * r;
}
FORCE_INLINE Float2 PerlinNoiseFade(const Float2& t)
{
return t * t * t * (t * (t * 6.0 - 15.0) + 10.0);
}
float rand2dTo1d(const Float2& value, const Float2& dotDir)
{
// https://www.ronja-tutorials.com/post/024-white-noise/
const Float2 smallValue(Math::Sin(value.X), Math::Sin(value.Y));
const float random = Float2::Dot(smallValue, dotDir);
return Math::Frac(Math::Sin(random) * 143758.5453f);
}
float rand2dTo1d(const Float2& value)
{
// https://www.ronja-tutorials.com/post/024-white-noise/
return rand2dTo1d(value, Float2(12.9898f, 78.233f));
}
Float2 rand2dTo2d(const Float2& value)
{
// https://www.ronja-tutorials.com/post/024-white-noise/
return Float2(
rand2dTo1d(value, Float2(12.989f, 78.233f)),
rand2dTo1d(value, Float2(39.346f, 11.135f))
);
}
}
float Noise::PerlinNoise(const Float2& p)
{
Float4 Pxy(p.X, p.Y, p.X, p.Y);
Float4 Pi = Float4::Floor(Pxy) + Float4(0.0, 0.0, 1.0, 1.0);
Float4 Pf = Float4::Frac(Pxy) - Float4(0.0, 0.0, 1.0, 1.0);
Pi = Mod289(Pi);
Float4 ix(Pi.X, Pi.Z, Pi.X, Pi.Z);
Float4 iy(Pi.Y, Pi.Y, Pi.W, Pi.W);
Float4 fx(Pf.X, Pf.Z, Pf.X, Pf.Z);
Float4 fy(Pf.Y, Pf.Y, Pf.W, Pf.W);
Float4 i = Permute(Permute(ix) + iy);
Float4 gx = Float4::Frac(i * (1.0 / 41.0)) * 2.0 - 1.0;
Float4 gy = Float4::Abs(gx) - 0.5;
Float4 tx = Float4::Floor(gx + 0.5);
gx = gx - tx;
Float2 g00(gx.X, gy.X);
Float2 g10(gx.Y, gy.Y);
Float2 g01(gx.Z, gy.Z);
Float2 g11(gx.W, gy.W);
Float4 norm = TaylorInvSqrt(Float4(Float2::Dot(g00, g00), Float2::Dot(g01, g01), Float2::Dot(g10, g10), Float2::Dot(g11, g11)));
g00 *= norm.X;
g01 *= norm.Y;
g10 *= norm.Z;
g11 *= norm.W;
float n00 = Float2::Dot(g00, Float2(fx.X, fy.X));
float n10 = Float2::Dot(g10, Float2(fx.Y, fy.Y));
float n01 = Float2::Dot(g01, Float2(fx.Z, fy.Z));
float n11 = Float2::Dot(g11, Float2(fx.W, fy.W));
Float2 fade_xy = PerlinNoiseFade(Float2(Pf));
Float2 n_x = Float2::Lerp(Float2(n00, n01), Float2(n10, n11), fade_xy.X);
float n_xy = Math::Lerp(n_x.X, n_x.Y, fade_xy.Y);
return Math::Saturate(2.3f * n_xy);
}
float Noise::PerlinNoise(const Float2& p, const Float2& rep)
{
Float4 Pxy(p.X, p.Y, p.X, p.Y);
Float4 Repxy(rep.X, rep.Y, rep.X, rep.Y);
Float4 Pi = Float4::Floor(Pxy) + Float4(0.0, 0.0, 1.0, 1.0);
Float4 Pf = Float4::Frac(Pxy) - Float4(0.0, 0.0, 1.0, 1.0);
Pi = Float4::Mod(Pi, Repxy);
Pi = Mod289(Pi);
Float4 ix(Pi.X, Pi.Z, Pi.X, Pi.Z);
Float4 iy(Pi.Y, Pi.Y, Pi.W, Pi.W);
Float4 fx(Pf.X, Pf.Z, Pf.X, Pf.Z);
Float4 fy(Pf.Y, Pf.Y, Pf.W, Pf.W);
Float4 i = Permute(Permute(ix) + iy);
Float4 gx = Float4::Frac(i * (1.0 / 41.0)) * 2.0 - 1.0;
Float4 gy = Float4::Abs(gx) - 0.5;
Float4 tx = Float4::Floor(gx + 0.5);
gx = gx - tx;
Float2 g00(gx.X, gy.X);
Float2 g10(gx.Y, gy.Y);
Float2 g01(gx.Z, gy.Z);
Float2 g11(gx.W, gy.W);
Float4 norm = TaylorInvSqrt(Float4(Float2::Dot(g00, g00), Float2::Dot(g01, g01), Float2::Dot(g10, g10), Float2::Dot(g11, g11)));
g00 *= norm.X;
g01 *= norm.Y;
g10 *= norm.Z;
g11 *= norm.W;
float n00 = Float2::Dot(g00, Float2(fx.X, fy.X));
float n10 = Float2::Dot(g10, Float2(fx.Y, fy.Y));
float n01 = Float2::Dot(g01, Float2(fx.Z, fy.Z));
float n11 = Float2::Dot(g11, Float2(fx.W, fy.W));
Float2 fade_xy = PerlinNoiseFade(Float2(Pf));
Float2 n_x = Float2::Lerp(Float2(n00, n01), Float2(n10, n11), fade_xy.X);
float n_xy = Math::Lerp(n_x.X, n_x.Y, fade_xy.Y);
return Math::Saturate(2.3f * n_xy);
}
float Noise::SimplexNoise(const Float2& p)
{
Float4 C(0.211324865405187f, // (3.0-math.sqrt(3.0))/6.0
0.366025403784439f, // 0.5*(math.sqrt(3.0)-1.0)
-0.577350269189626f, // -1.0 + 2.0 * C.x
0.024390243902439f); // 1.0 / 41.0
// First corner
Float2 i = Float2::Floor(p + Float2::Dot(p, Float2(C.Y, C.Y)));
Float2 x0 = p - i + Float2::Dot(i, Float2(C.X, C.X));
// Other corners
Float2 i1 = x0.X > x0.Y ? Float2(1.0f, 0.0f) : Float2(0.0f, 1.0f);
Float4 x12 = Float4(x0.X, x0.Y, x0.X, x0.Y) + Float4(C.X, C.X, C.Z, C.Z);
x12.X -= i1.X;
x12.Y -= i1.Y;
// Permutations
i = Mod289(i);
Float3 perm = Permute(Permute(i.Y + Float3(0.0f, i1.Y, 1.0f)) + i.X + Float3(0.0f, i1.X, 1.0f));
Float2 x12xy(x12.X, x12.Y);
Float2 x12zw(x12.Z, x12.W);
Float3 m = Float3::Max(0.5f - Float3(Float2::Dot(x0, x0), Float2::Dot(x12xy, x12xy), Float2::Dot(x12zw, x12zw)), 0.0f);
m = m * m;
m = m * m;
// Gradients: 41 points uniformly over a line, mapped onto a diamond.
// The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
Float3 x = 2.0f * Float3::Frac(perm * C.W) - 1.0f;
Float3 h = Float3::Abs(x) - 0.5f;
Float3 ox = Float3::Floor(x + 0.5f);
Float3 a0 = x - ox;
// Normalise gradients implicitly by scaling m
// Approximation of: m *= inversemath.sqrt( a0*a0 + h*h );
m *= 1.79284291400159f - 0.85373472095314f * (a0 * a0 + h * h);
// Compute final noise value at P
float gx = a0.X * x0.X + h.X * x0.Y;
Float2 gyz = Float2(a0.Y, a0.Z) * Float2(x12.X, x12.Z) + Float2(h.Y, h.Z) * Float2(x12.Y, x12.W);
Float3 g(gx, gyz.X, gyz.Y);
return Math::Saturate(130.0f * Float3::Dot(m, g));
}
Float2 Noise::WorleyNoise(const Float2& p)
{
const float K = 0.142857142857f; // 1/7
const float Ko = 0.428571428571f; // 3/7
const float jitter = 1.0f; // Less gives more regular pattern
Float2 Pi = Mod289(Float2::Floor(p));
Float2 Pf = Float2::Frac(p);
Float3 oi = Float3(-1.0f, 0.0f, 1.0f);
Float3 of = Float3(-0.5f, 0.5f, 1.5f);
Float3 px = Permute(Pi.X + oi);
Float3 pp = Permute(px.X + Pi.Y + oi); // p11, p12, p13
Float3 ox = Float3::Frac(pp * K) - Ko;
Float3 oy = Mod7(Float3::Floor(pp * K)) * K - Ko;
Float3 dx = Pf.X + 0.5f + jitter * ox;
Float3 dy = Pf.Y - of + jitter * oy;
Float3 d1 = dx * dx + dy * dy; // d11, d12 and d13, squared
pp = Permute(px.Y + Pi.Y + oi); // p21, p22, p23
ox = Float3::Frac(pp * K) - Ko;
oy = Mod7(Float3::Floor(pp * K)) * K - Ko;
dx = Pf.X - 0.5f + jitter * ox;
dy = Pf.Y - of + jitter * oy;
Float3 d2 = dx * dx + dy * dy; // d21, d22 and d23, squared
pp = Permute(px.Z + Pi.Y + oi); // p31, p32, p33
ox = Float3::Frac(pp * K) - Ko;
oy = Mod7(Float3::Floor(pp * K)) * K - Ko;
dx = Pf.X - 1.5f + jitter * ox;
dy = Pf.Y - of + jitter * oy;
Float3 d3 = dx * dx + dy * dy; // d31, d32 and d33, squared
Float3 d1a = Float3::Min(d1, d2); // Sort out the two smallest distances (F1, F2)
d2 = Float3::Max(d1, d2); // Swap to keep candidates for F2
d2 = Float3::Min(d2, d3); // neither F1 nor F2 are now in d3
d1 = Float3::Min(d1a, d2); // F1 is now in d1
d2 = Float3::Max(d1a, d2); // Swap to keep candidates for F2
d1.X = d1.X < d1.Y ? d1.X : d1.Y; // Swap if smaller
d1.Y = d1.X < d1.Y ? d1.Y : d1.X;
d1.X = d1.X < d1.Z ? d1.X : d1.Z; // F1 is in d1.x
d1.Z = d1.X < d1.Z ? d1.Z : d1.X;
d1.Y = Math::Min(d1.Y, d2.Y); // F2 is now not in d2.yz
d1.Z = Math::Min(d1.Z, d2.Z);
d1.Y = Math::Min(d1.Y, d1.Z); // nor in d1.z
d1.Y = Math::Min(d1.Y, d2.X); // F2 is in d1.y, we're done.
return Float2(Math::Saturate(Math::Sqrt(d1.X)), Math::Saturate(Math::Sqrt(d1.Y)));
}
Float3 Noise::VoronoiNoise(const Float2& p)
{
// Reference: https://www.ronja-tutorials.com/post/028-voronoi-noise/
const Float2 baseCell = Float2::Floor(p);
// first pass to find the closest cell
float minDistToCell = 10.0;
Float2 toClosestCell;
Float2 closestCell;
for (int32 x1 = -1; x1 <= 1; x1++)
{
for (int32 y1 = -1; y1 <= 1; y1++)
{
Float2 cell = baseCell + Float2((float)x1, (float)y1);
Float2 cellPosition = cell + rand2dTo2d(cell);
Float2 toCell = cellPosition - p;
const float distToCell = toCell.Length();
if (distToCell < minDistToCell)
{
minDistToCell = distToCell;
closestCell = cell;
toClosestCell = toCell;
}
}
}
// second pass to find the distance to the closest edge
float minEdgeDistance = 10.0;
for (int32 x2 = -1; x2 <= 1; x2++)
{
for (int32 y2 = -1; y2 <= 1; y2++)
{
Float2 cell = baseCell + Float2((float)x2, (float)y2);
Float2 cellPosition = cell + rand2dTo2d(cell);
Float2 toCell = cellPosition - p;
const Float2 diffToClosestCell = Float2::Abs(closestCell - cell);
if (diffToClosestCell.X + diffToClosestCell.Y >= 0.1f)
{
Float2 toCenter = (toClosestCell + toCell) * 0.5;
Float2 cellDifference = Float2::Normalize(toCell - toClosestCell);
minEdgeDistance = Math::Min(minEdgeDistance, Float2::Dot(toCenter, cellDifference));
}
}
}
float random = rand2dTo1d(closestCell);
return Float3(Math::Saturate(minDistToCell), Math::Saturate(random), Math::Saturate(minEdgeDistance));
}
float Noise::CustomNoise(const Float3& p)
{
Float3 a = Float3::Floor(p);
Float3 d = p - a;
d = d * d * (3.0f - 2.0f * d);
Float4 b(a.X, a.X + 1.0f, a.Y, a.Y + 1.0f);
Float4 k1 = Permute(Float4(b.X, b.Y, b.X, b.Y));
Float4 k2 = Permute(Float4(k1.X + b.Z, k1.Y + b.Z, k1.X + b.W, k1.Y + b.W));
Float4 c = k2 + Float4(a.Z);
Float4 k3 = Permute(c);
Float4 k4 = Permute(c + 1.0f);
Float4 o1 = Float4::Frac(k3 * (1.0f / 41.0f));
Float4 o2 = Float4::Frac(k4 * (1.0f / 41.0f));
Float4 o3 = o2 * d.Z + o1 * (1.0f - d.Z);
Float2 o4 = Float2(o3.Y, o3.W) * d.X + Float2(o3.X, o3.Z) * (1.0f - d.X);
return o4.Y * d.Y + o4.X * (1.0f - d.Y);
}
Float3 Noise::CustomNoise3D(const Float3& p)
{
const float o = CustomNoise(p);
const float a = CustomNoise(p + Float3(0.0001f, 0.0f, 0.0f));
const float b = CustomNoise(p + Float3(0.0f, 0.0001f, 0.0f));
const float c = CustomNoise(p + Float3(0.0f, 0.0f, 0.0001f));
const Float3 grad(o - a, o - b, o - c);
const Float3 other = Float3::Abs(Float3(grad.Z, grad.X, grad.Y));
return Float3::Normalize(Float3::Cross(grad, other));
}
Float3 Noise::CustomNoise3D(const Float3& p, int32 octaves, float roughness)
{
float weight = 0.0f;
Float3 noise = Float3::Zero;
float scale = 1.0f;
for (int32 i = 0; i < octaves; i++)
{
const float curWeight = Math::Pow(1.0f - (float)i / (float)octaves, Math::Lerp(2.0f, 0.2f, roughness));
noise += CustomNoise3D(p * scale) * curWeight;
weight += curWeight;
scale *= 1.72531f;
}
return noise / Math::Max(weight, ZeroTolerance);
}

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// Copyright (c) 2012-2022 Wojciech Figat. All rights reserved.
#pragma once
#include "Engine/Core/Math/Vector2.h"
#include "Engine/Core/Math/Vector3.h"
/// <summary>
/// Collection of various noise functions (eg. Perlin, Worley, Voronoi).
/// </summary>
API_CLASS(Static, Namespace="FlaxEngine.Utilities") class FLAXENGINE_API Noise
{
DECLARE_SCRIPTING_TYPE_MINIMAL(Noise);
public:
/// <summary>
/// Classic Perlin noise.
/// </summary>
/// <param name="p">Point on a 2D grid to sample noise at.</param>
/// <returns>Noise value (range 0-1).</returns>
API_FUNCTION() static float PerlinNoise(const Float2& p);
/// <summary>
/// Classic Perlin noise with periodic variant (tiling).
/// </summary>
/// <param name="p">Point on a 2D grid to sample noise at.</param>
/// <param name="rep">Periodic variant of the noise - period of the noise.</param>
/// <returns>Noise value (range 0-1).</returns>
API_FUNCTION() static float PerlinNoise(const Float2& p, const Float2& rep);
/// <summary>
/// Simplex noise.
/// </summary>
/// <param name="p">Point on a 2D grid to sample noise at.</param>
/// <returns>Noise value (range 0-1).</returns>
API_FUNCTION() static float SimplexNoise(const Float2& p);
/// <summary>
/// Worley noise (cellar noise with standard 3x3 search window for F1 and F2 values).
/// </summary>
/// <param name="p">Point on a 2D grid to sample noise at.</param>
/// <returns>Noise value with: F1 and F2 feature points.</returns>
API_FUNCTION() static Float2 WorleyNoise(const Float2& p);
/// <summary>
/// Voronoi noise.
/// </summary>
/// <param name="p">Point on a 2D grid to sample noise at.</param>
/// <returns>Noise result with: X=minDistToCell, Y=randomColor, Z=minEdgeDistance.</returns>
API_FUNCTION() static Float3 VoronoiNoise(const Float2& p);
/// <summary>
/// Custom noise function (3D -> 1D).
/// </summary>
/// <param name="p">Point on a 3D grid to sample noise at.</param>
/// <returns>Noise result.</returns>
API_FUNCTION() static float CustomNoise(const Float3& p);
/// <summary>
/// Custom noise function (3D -> 3D).
/// </summary>
/// <param name="p">Point on a 3D grid to sample noise at.</param>
/// <returns>Noise result.</returns>
API_FUNCTION() static Float3 CustomNoise3D(const Float3& p);
/// <summary>
/// Custom noise function for forces.
/// </summary>
/// <param name="p">Point on a 3D grid to sample noise at.</param>
/// <param name="octaves">Noise octaves count.</param>
/// <param name="roughness">Noise roughness (in range 0-1).</param>
/// <returns>Noise result.</returns>
API_FUNCTION() static Float3 CustomNoise3D(const Float3& p, int32 octaves, float roughness);
};

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Source/Engine/Utilities/PerlinNoise.cs
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/// <summary>
/// The base value.
/// </summary>
private float Base;
public float Base = 0.0f;
/// <summary>
/// The noise scale parameter.
/// </summary>
public float NoiseScale;
public float NoiseScale = 1.0f;
/// <summary>
/// The noise amount parameter.
/// </summary>
public float NoiseAmount;
public float NoiseAmount = 1.0f;
/// <summary>
/// The noise octaves count.
/// </summary>
public int Octaves;
public int Octaves = 4;
/// <summary>
/// Initializes a new instance of the <see cref="PerlinNoise"/> class.
/// </summary>
public PerlinNoise()
{
}
/// <summary>
/// Initializes a new instance of the <see cref="PerlinNoise"/> class.

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// Copyright (c) 2012-2022 Wojciech Figat. All rights reserved.
// Copyright (c) 2011 Stefan Gustavson. All rights reserved.
// Distributed under the MIT license.
// https://github.com/stegu/webgl-noise
#ifndef __NOISE__
#define __NOISE__
#include "./Flax/Common.hlsl"
float2 Mod289(float2 x)
{
return x - floor(x * (1.0 / 289.0)) * 289.0;
}
float3 Mod289(float3 x)
{
return x - floor(x * (1.0 / 289.0)) * 289.0;
}
float4 Mod289(float4 x)
{
return x - floor(x * (1.0 / 289.0)) * 289.0;
}
float3 Mod7(float3 x)
{
return x - floor(x * (1.0f / 7.0f)) * 7.0f;
}
float2 Permute(float2 x)
{
return Mod289(((x * 34.0) + 1.0) * x);
}
float3 Permute(float3 x)
{
return Mod289(((x * 34.0) + 1.0) * x);
}
float4 Permute(float4 x)
{
return Mod289(((x * 34.0) + 1.0) * x);
}
float4 TaylorInvSqrt(float4 r)
{
return 1.79284291400159 - 0.85373472095314 * r;
}
float2 PerlinNoiseFade(float2 t)
{
return t * t * t * (t * (t * 6.0 - 15.0) + 10.0);
}
float rand2dTo1d(float2 value, float2 dotDir = float2(12.9898, 78.233))
{
// https://www.ronja-tutorials.com/post/024-white-noise/
float2 smallValue = sin(value);
float random = dot(smallValue, dotDir);
return frac(sin(random) * 143758.5453);
}
float2 rand2dTo2d(float2 value)
{
// https://www.ronja-tutorials.com/post/024-white-noise/
return float2(
rand2dTo1d(value, float2(12.989, 78.233)),
rand2dTo1d(value, float2(39.346, 11.135))
);
}
// Classic Perlin noise
float PerlinNoise(float2 p)
{
float4 Pi = floor(p.xyxy) + float4(0.0, 0.0, 1.0, 1.0);
float4 Pf = frac(p.xyxy) - float4(0.0, 0.0, 1.0, 1.0);
Pi = Mod289(Pi);
float4 ix = Pi.xzxz;
float4 iy = Pi.yyww;
float4 fx = Pf.xzxz;
float4 fy = Pf.yyww;
float4 i = Permute(Permute(ix) + iy);
float4 gx = frac(i * (1.0 / 41.0)) * 2.0 - 1.0;
float4 gy = abs(gx) - 0.5;
float4 tx = floor(gx + 0.5);
gx = gx - tx;
float2 g00 = float2(gx.x, gy.x);
float2 g10 = float2(gx.y, gy.y);
float2 g01 = float2(gx.z, gy.z);
float2 g11 = float2(gx.w, gy.w);
float4 norm = TaylorInvSqrt(float4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
g00 *= norm.x;
g01 *= norm.y;
g10 *= norm.z;
g11 *= norm.w;
float n00 = dot(g00, float2(fx.x, fy.x));
float n10 = dot(g10, float2(fx.y, fy.y));
float n01 = dot(g01, float2(fx.z, fy.z));
float n11 = dot(g11, float2(fx.w, fy.w));
float2 fade_xy = PerlinNoiseFade(Pf.xy);
float2 n_x = lerp(float2(n00, n01), float2(n10, n11), fade_xy.x);
float n_xy = lerp(n_x.x, n_x.y, fade_xy.y);
return saturate(2.3 * n_xy);
}
// Classic Perlin noise with periodic variant
float PerlinNoise(float2 p, float2 rep)
{
float4 Pi = floor(p.xyxy) + float4(0.0, 0.0, 1.0, 1.0);
float4 Pf = frac(p.xyxy) - float4(0.0, 0.0, 1.0, 1.0);
Pi = fmod(Pi, rep.xyxy);
Pi = Mod289(Pi);
float4 ix = Pi.xzxz;
float4 iy = Pi.yyww;
float4 fx = Pf.xzxz;
float4 fy = Pf.yyww;
float4 i = Permute(Permute(ix) + iy);
float4 gx = frac(i * (1.0 / 41.0)) * 2.0 - 1.0;
float4 gy = abs(gx) - 0.5;
float4 tx = floor(gx + 0.5);
gx = gx - tx;
float2 g00 = float2(gx.x, gy.x);
float2 g10 = float2(gx.y, gy.y);
float2 g01 = float2(gx.z, gy.z);
float2 g11 = float2(gx.w, gy.w);
float4 norm = TaylorInvSqrt(float4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
g00 *= norm.x;
g01 *= norm.y;
g10 *= norm.z;
g11 *= norm.w;
float n00 = dot(g00, float2(fx.x, fy.x));
float n10 = dot(g10, float2(fx.y, fy.y));
float n01 = dot(g01, float2(fx.z, fy.z));
float n11 = dot(g11, float2(fx.w, fy.w));
float2 fade_xy = PerlinNoiseFade(Pf.xy);
float2 n_x = lerp(float2(n00, n01), float2(n10, n11), fade_xy.x);
float n_xy = lerp(n_x.x, n_x.y, fade_xy.y);
return saturate(2.3 * n_xy);
}
// Simplex noise
float SimplexNoise(float2 p)
{
float4 C = float4(0.211324865405187f, // (3.0-math.sqrt(3.0))/6.0
0.366025403784439f, // 0.5*(math.sqrt(3.0)-1.0)
-0.577350269189626f, // -1.0 + 2.0 * C.x
0.024390243902439f); // 1.0 / 41.0
// First corner
float2 i = floor(p + dot(p, C.yy));
float2 x0 = p - i + dot(i, C.xx);
// Other corners
float2 i1 = (x0.x > x0.y) ? float2(1.0f, 0.0f) : float2(0.0f, 1.0f);
float4 x12 = x0.xyxy + C.xxzz;
x12.xy -= i1;
// Permutations
i = Mod289(i);
float3 perm = Permute(Permute(i.y + float3(0.0f, i1.y, 1.0f)) + i.x + float3(0.0f, i1.x, 1.0f));
float3 m = max(0.5f - float3(dot(x0, x0), dot(x12.xy, x12.xy), dot(x12.zw, x12.zw)), 0.0f);
m = m * m;
m = m * m;
// Gradients: 41 points uniformly over a line, mapped onto a diamond.
// The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
float3 x = 2.0f * frac(perm * C.www) - 1.0f;
float3 h = abs(x) - 0.5f;
float3 ox = floor(x + 0.5f);
float3 a0 = x - ox;
// Normalise gradients implicitly by scaling m
// Approximation of: m *= inversemath.sqrt( a0*a0 + h*h );
m *= 1.79284291400159f - 0.85373472095314f * (a0 * a0 + h * h);
// Compute final noise value at P
float gx = a0.x * x0.x + h.x * x0.y;
float2 gyz = a0.yz * x12.xz + h.yz * x12.yw;
float3 g = float3(gx, gyz);
return saturate(130.0f * dot(m, g));
}
// Worley noise (cellar noise with standard 3x3 search window for F1 and F2 values)
float2 WorleyNoise(float2 p)
{
const float K = 0.142857142857f; // 1/7
const float Ko = 0.428571428571f; // 3/7
const float jitter = 1.0f; // Less gives more regular pattern
float2 Pi = Mod289(floor(p));
float2 Pf = frac(p);
float3 oi = float3(-1.0f, 0.0f, 1.0f);
float3 of = float3(-0.5f, 0.5f, 1.5f);
float3 px = Permute(Pi.x + oi);
float3 pp = Permute(px.x + Pi.y + oi); // p11, p12, p13
float3 ox = frac(pp * K) - Ko;
float3 oy = Mod7(floor(pp * K)) * K - Ko;
float3 dx = Pf.x + 0.5f + jitter * ox;
float3 dy = Pf.y - of + jitter * oy;
float3 d1 = dx * dx + dy * dy; // d11, d12 and d13, squared
pp = Permute(px.y + Pi.y + oi); // p21, p22, p23
ox = frac(pp * K) - Ko;
oy = Mod7(floor(pp * K)) * K - Ko;
dx = Pf.x - 0.5f + jitter * ox;
dy = Pf.y - of + jitter * oy;
float3 d2 = dx * dx + dy * dy; // d21, d22 and d23, squared
pp = Permute(px.z + Pi.y + oi); // p31, p32, p33
ox = frac(pp * K) - Ko;
oy = Mod7(floor(pp * K)) * K - Ko;
dx = Pf.x - 1.5f + jitter * ox;
dy = Pf.y - of + jitter * oy;
float3 d3 = dx * dx + dy * dy; // d31, d32 and d33, squared
float3 d1a = min(d1, d2); // Sort out the two smallest distances (F1, F2)
d2 = max(d1, d2); // Swap to keep candidates for F2
d2 = min(d2, d3); // neither F1 nor F2 are now in d3
d1 = min(d1a, d2); // F1 is now in d1
d2 = max(d1a, d2); // Swap to keep candidates for F2
d1.xy = (d1.x < d1.y) ? d1.xy : d1.yx; // Swap if smaller
d1.xz = (d1.x < d1.z) ? d1.xz : d1.zx; // F1 is in d1.x
d1.yz = min(d1.yz, d2.yz); // F2 is now not in d2.yz
d1.y = min(d1.y, d1.z); // nor in d1.z
d1.y = min(d1.y, d2.x); // F2 is in d1.y, we're done.
return saturate(sqrt(d1.xy));
}
// Voronoi noise (X=minDistToCell, Y=randomColor, Z=minEdgeDistance)
float3 VoronoiNoise(float2 p)
{
// Reference: https://www.ronja-tutorials.com/post/028-voronoi-noise/
float2 baseCell = floor(p);
// first pass to find the closest cell
float minDistToCell = 10;
float2 toClosestCell;
float2 closestCell;
UNROLL
for (int x1 = -1; x1 <= 1; x1++)
{
UNROLL
for (int y1 = -1; y1 <= 1; y1++)
{
float2 cell = baseCell + float2(x1, y1);
float2 cellPosition = cell + rand2dTo2d(cell);
float2 toCell = cellPosition - p;
float distToCell = length(toCell);
if (distToCell < minDistToCell)
{
minDistToCell = distToCell;
closestCell = cell;
toClosestCell = toCell;
}
}
}
// second pass to find the distance to the closest edge
float minEdgeDistance = 10;
UNROLL
for (int x2 = -1; x2 <= 1; x2++)
{
UNROLL
for (int y2 = -1; y2 <= 1; y2++)
{
float2 cell = baseCell + float2(x2, y2);
float2 cellPosition = cell + rand2dTo2d(cell);
float2 toCell = cellPosition - p;
float2 diffToClosestCell = abs(closestCell - cell);
if (diffToClosestCell.x + diffToClosestCell.y >= 0.1)
{
float2 toCenter = (toClosestCell + toCell) * 0.5;
float2 cellDifference = normalize(toCell - toClosestCell);
minEdgeDistance = min(minEdgeDistance, dot(toCenter, cellDifference));
}
}
}
float random = rand2dTo1d(closestCell);
return saturate(float3(minDistToCell, random, minEdgeDistance));
}
float CustomNoise(float3 p)
{
float3 a = floor(p);
float3 d = p - a;
d = d * d * (3.0 - 2.0 * d);
float4 b = a.xxyy + float4(0.0, 1.0, 0.0, 1.0);
float4 k1 = Permute(b.xyxy);
float4 k2 = Permute(k1.xyxy + b.zzww);
float4 c = k2 + a.zzzz;
float4 k3 = Permute(c);
float4 k4 = Permute(c + 1.0);
float4 o1 = frac(k3 * (1.0 / 41.0));
float4 o2 = frac(k4 * (1.0 / 41.0));
float4 o3 = o2 * d.z + o1 * (1.0 - d.z);
float2 o4 = o3.yw * d.x + o3.xz * (1.0 - d.x);
return o4.y * d.y + o4.x * (1.0 - d.y);
}
float3 CustomNoise3D(float3 p)
{
float o = CustomNoise(p);
float a = CustomNoise(p + float3(0.0001f, 0.0f, 0.0f));
float b = CustomNoise(p + float3(0.0f, 0.0001f, 0.0f));
float c = CustomNoise(p + float3(0.0f, 0.0f, 0.0001f));
float3 grad = float3(o - a, o - b, o - c);
float3 other = abs(grad.zxy);
return normalize(cross(grad,other));
}
float3 CustomNoise3D(float3 position, int octaves, float roughness)
{
float weight = 0.0f;
float3 noise = float3(0.0, 0.0, 0.0);
float scale = 1.0f;
for (int i = 0; i < octaves; i++)
{
float curWeight = pow((1.0 - ((float)i / octaves)), lerp(2.0, 0.2, roughness));
noise += CustomNoise3D(position * scale) * curWeight;
weight += curWeight;
scale *= 1.72531;
}
return noise / weight;
}
#endif