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An example of procedurally generating a cloudy pattern out of hand typed octaves of simplex noise. There may be an error in here, I can't quite remember if this is what the end image should look like or not. I feel like the darks should be darker and the lights lighter, but either way this is the general idea. The traditional approach is to writ…
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Program.cs
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using SimplexNoise;
using System.Drawing;
namespace SimplexExample
{
class Program
{
static void Main(string[] args)
{
int dimensions = 300;
int[,] noise = new int[dimensions, dimensions];
for (int i = 0; i < dimensions; i++)
{
for (int j = 0; j < dimensions; j++)
{
var value = 0f;
value += Noise.Generate(i * 0.005f, j * 0.005f) * 0.125f;
value += Noise.Generate(i * 0.01f, j * 0.01f) * 0.125f;
value += Noise.Generate(i * 0.02f, j * 0.02f) * 0.125f;
value += Noise.Generate(i * 0.04f, j * 0.04f) * 0.125f;
value += Noise.Generate(i * 0.08f, j * 0.08f) * 0.125f;
value += Noise.Generate(i * 0.16f, j * 0.16f) * 0.125f;
value += Noise.Generate(i * 0.32f, j * 0.32f) * 0.125f;
value += Noise.Generate(i * 0.64f, j * 0.64f) * 0.125f;
noise[i, j] = ConvertTo255(value);
}
}
Save2DArrayAsGrayscalePNG(noise, @"C:\temp\simplex-noise.png");
Console.WriteLine("All operations complete. Hit enter to exit");
Console.ReadLine();
}
static void Save2DArrayAsGrayscalePNG(int[,] array, string filepath)
{
// these might be inverted, but in this example it won't matter
int xLength = array.GetLength(0);
int yLength = array.GetLength(1);
Bitmap bitmap = new Bitmap(xLength, yLength);
for (var i = 0; i < xLength; i++)
{
for (var j = 0; j < yLength; j++)
{
var value = array[i, j];
bitmap.SetPixel(i, j, Color.FromArgb(value, value, value));
}
}
bitmap.Save(filepath);
}
/// Converts a float from the range -1.0 to 1.0, to an int from 0-255, so that it can be
/// used in Color.FromArgb to make grayscale
static int ConvertTo255(float n)
{
return (int)ScaleToRange(n, -1.0f, 1.0f, 0.0f, 255.0f);
}
/// <summary>
/// Converts a number n from within the range a-b, to a new number within the range c-d
/// </summary>
/// <param name="n">value to be converted</param>
/// <param name="a">start of source range</param>
/// <param name="b">end of source range</param>
/// <param name="c">start of destination range</param>
/// <param name="d">end of destination range</param>
/// <returns>n's new value</returns>
static float ScaleToRange(float n, float a, float b, float c, float d)
{
return (d - c) * (n - a) / (b - a) + c;
}
}
}
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SimplexNoise.cs
// SimplexNoise for C#
// Author: Heikki Törmälä
//This is free and unencumbered software released into the public domain.
//Anyone is free to copy, modify, publish, use, compile, sell, or
//distribute this software, either in source code form or as a compiled
//binary, for any purpose, commercial or non-commercial, and by any
//means.
//In jurisdictions that recognize copyright laws, the author or authors
//of this software dedicate any and all copyright interest in the
//software to the public domain. We make this dedication for the benefit
//of the public at large and to the detriment of our heirs and
//successors. We intend this dedication to be an overt act of
//relinquishment in perpetuity of all present and future rights to this
//software under copyright law.
//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
//EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
//MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
//IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
//OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
//ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
//OTHER DEALINGS IN THE SOFTWARE.
//For more information, please refer to <http://unlicense.org/>
namespace SimplexNoise
{
/// <summary>
/// Implementation of the Perlin simplex noise, an improved Perlin noise algorithm.
/// Based loosely on SimplexNoise1234 by Stefan Gustavson <http://staffwww.itn.liu.se/~stegu/aqsis/aqsis-newnoise/>
///
/// </summary>
public class Noise
{
/// <summary>
/// 1D simplex noise
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
public static float Generate(float x)
{
int i0 = FastFloor(x);
int i1 = i0 + 1;
float x0 = x - i0;
float x1 = x0 - 1.0f;
float n0, n1;
float t0 = 1.0f - x0 * x0;
t0 *= t0;
n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);
float t1 = 1.0f - x1 * x1;
t1 *= t1;
n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
// The maximum value of this noise is 8*(3/4)^4 = 2.53125
// A factor of 0.395 scales to fit exactly within [-1,1]
return 0.395f * (n0 + n1);
}
/// <summary>
/// 2D simplex noise
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public static float Generate(float x, float y)
{
const float F2 = 0.366025403f; // F2 = 0.5*(sqrt(3.0)-1.0)
const float G2 = 0.211324865f; // G2 = (3.0-Math.sqrt(3.0))/6.0
float n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float s = (x + y) * F2; // Hairy factor for 2D
float xs = x + s;
float ys = y + s;
int i = FastFloor(xs);
int j = FastFloor(ys);
float t = (float)(i + j) * G2;
float X0 = i - t; // Unskew the cell origin back to (x,y) space
float Y0 = j - t;
float x0 = x - X0; // The x,y distances from the cell origin
float y0 = y - Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if (x0 > y0) { i1 = 1; j1 = 0; } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else { i1 = 0; j1 = 1; } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * G2;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0.0f) n0 = 0.0f;
else
{
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii + perm[jj]], x0, y0);
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0.0f) n1 = 0.0f;
else
{
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii + i1 + perm[jj + j1]], x1, y1);
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0.0f) n2 = 0.0f;
else
{
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii + 1 + perm[jj + 1]], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
}
public static float Generate(float x, float y, float z)
{
// Simple skewing factors for the 3D case
const float F3 = 0.333333333f;
const float G3 = 0.166666667f;
float n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
float s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
float xs = x + s;
float ys = y + s;
float zs = z + s;
int i = FastFloor(xs);
int j = FastFloor(ys);
int k = FastFloor(zs);
float t = (float)(i + j + k) * G3;
float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
float Y0 = j - t;
float Z0 = k - t;
float x0 = x - X0; // The x,y,z distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
/* This code would benefit from a backport from the GLSL version! */
if (x0 >= y0)
{
if (y0 >= z0)
{ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0; } // X Y Z order
else if (x0 >= z0) { i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1; } // X Z Y order
else { i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1; } // Z X Y order
}
else
{ // x0<y0
if (y0 < z0) { i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1; } // Z Y X order
else if (x0 < z0) { i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1; } // Y Z X order
else { i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0; } // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
float y2 = y0 - j2 + 2.0f * G3;
float z2 = z0 - k2 + 2.0f * G3;
float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
float y3 = y0 - 1.0f + 3.0f * G3;
float z3 = z0 - 1.0f + 3.0f * G3;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = Mod(i, 256);
int jj = Mod(j, 256);
int kk = Mod(k, 256);
// Calculate the contribution from the four corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0.0f) n0 = 0.0f;
else
{
t0 *= t0;
n0 = t0 * t0 * grad(perm[ii + perm[jj + perm[kk]]], x0, y0, z0);
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0.0f) n1 = 0.0f;
else
{
t1 *= t1;
n1 = t1 * t1 * grad(perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], x1, y1, z1);
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0.0f) n2 = 0.0f;
else
{
t2 *= t2;
n2 = t2 * t2 * grad(perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], x2, y2, z2);
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0.0f) n3 = 0.0f;
else
{
t3 *= t3;
n3 = t3 * t3 * grad(perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary!
}
public static byte[] perm = new byte[512] { 151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
};
private static int FastFloor(float x)
{
return (x > 0) ? ((int)x) : (((int)x) - 1);
}
private static int Mod(int x, int m)
{
int a = x % m;
return a < 0 ? a + m : a;
}
private static float grad(int hash, float x)
{
int h = hash & 15;
float grad = 1.0f + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0
if ((h & 8) != 0) grad = -grad; // Set a random sign for the gradient
return (grad * x); // Multiply the gradient with the distance
}
private static float grad(int hash, float x, float y)
{
int h = hash & 7; // Convert low 3 bits of hash code
float u = h < 4 ? x : y; // into 8 simple gradient directions,
float v = h < 4 ? y : x; // and compute the dot product with (x,y).
return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -2.0f * v : 2.0f * v);
}
private static float grad(int hash, float x, float y, float z)
{
int h = hash & 15; // Convert low 4 bits of hash code into 12 simple
float u = h < 8 ? x : y; // gradient directions, and compute dot product.
float v = h < 4 ? y : h == 12 || h == 14 ? x : z; // Fix repeats at h = 12 to 15
return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -v : v);
}
private static float grad(int hash, float x, float y, float z, float t)
{
int h = hash & 31; // Convert low 5 bits of hash code into 32 simple
float u = h < 24 ? x : y; // gradient directions, and compute dot product.
float v = h < 16 ? y : z;
float w = h < 8 ? z : t;
return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -v : v) + ((h & 4) != 0 ? -w : w);
}
}
}
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