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⬅️ Previous capture (2021-11-30)
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I've been working on testing some realtime data visualisation architecture (SignalR / In-Memory Caching vs Ajax / Redis Queue) and I needed some test data.
I needed a smooth-ish curve (i.e. not totally random numbers), but something that didn't contain too much repetition (e.g. a sine wave) and Perlin Noise seemed like a good fit for this.
Until a few weeks ago I'd never heard of Perlin Noise, but I've just read the first couple of chapters of Nature of Code [0] which has a chapter on using pseudo-random numbers to simulate physical forces and generate textures.
The book uses Processing [1] which has a built-in function for generating Perlin Noise. You can try it out yourself on Khan Academy's [2] Programming Natural Simulations [3] course. It's also worth having a read about it on Ken Perlin's Website: [4]
C# implementations I found were 2d or 3d so I minimally ported Ken Perlin's 1983 C code to C# (LinqPad script below). Maybe you'll find it useful...
1d noise:
2d noise:
void Main()
{
// Uses Oxyplot.WindowsForms.
var noise = new PerlinNoise();
var results = new List<double>();
for(double i = 0.0d; i < 100; i += 0.01d)
{
results.Add(noise.Noise(i));
}
var scatterSeries = new ScatterSeries();
scatterSeries.Points.AddRange(results.Select((r, i) => new ScatterPoint(i, r, 1d)));
var chart = new PlotModel();
chart.Series.Add(scatterSeries);
var view = new PlotView()
{
Model = chart,
};
view.Dump();
CreateRandomTexture(1366, 300).Dump();
}
public static class OxyPlotExtensions
{
public static void AddScatterSeries(this PlotModel model, IEnumerable<double> xSeries, IEnumerable<double> ySeries)
{
model.AddScatterSeries(xSeries, ySeries, OxyColors.Automatic);
}
public static void AddScatterSeries(this PlotModel model, IEnumerable<double> xSeries, IEnumerable<double> ySeries, OxyColor color)
{
var scatterSeries = new ScatterSeries()
{
MarkerFill = color,
MarkerSize = 1,
};
foreach (var item in xSeries.Zip(ySeries, (x, y) => new { x, y }))
{
scatterSeries.Points.Add(new ScatterPoint(item.x, item.y));
}
model.Series.Add(scatterSeries);
}
}
public Bitmap CreateRandomTexture(int width, int height)
{
var noise = new PerlinNoise();
var bmp = new Bitmap(width, height);
var xOffset = 30d;
for(int x = 0; x < width; x ++)
{
var yOffset = 500d;
for(int y = 0; y < height; y ++)
{
var noiseValue = noise.Noise(xOffset, yOffset);
var rgb = (int)Math.Abs(Map(noiseValue, -1d, 1d, 100, 255));
bmp.SetPixel(x, y, Color.FromArgb(rgb, rgb, rgb));
yOffset += 0.01d;
}
xOffset += 0.01d;
}
return bmp;
}
public double Map(double value, double sourceRangeMinimum, double sourceRangeMaximum, double targetRangeMinimum, double targetRangeMaximum)
{
if ((sourceRangeMaximum - sourceRangeMinimum) == 0)
{
return (targetRangeMinimum + targetRangeMaximum) / 2;
}
return targetRangeMinimum + (value - sourceRangeMinimum) * (targetRangeMaximum - targetRangeMinimum) / (sourceRangeMaximum - sourceRangeMinimum);
}
public class PerlinNoise
{
/* coherent noise function over 1, 2 or 3 dimensions */
/* (copyright Ken Perlin) */
const int B = 0x100; // 256
const int BM = 0xff;
const int N = 0x1000;
const int NP = 12; /* 2^N */
const int NM = 0xfff;
int[] p = new int[B + B + 2];
double[][] g3 = new double[B + B + 2][]; // each child needs 3
double[][] g2 = new double[B + B + 2][]; // each child needs 2
double[] g1 = new double[B + B + 2];
private Random rnd = new Random();
public PerlinNoise()
{
int i, j, k;
SizeArray(g2, 2);
SizeArray(g3, 3);
for (i = 0 ; i < B ; i++) {
p[i] = i;
g1[i] = (double)((rnd.Next() % (B + B)) - B) / B;
// Size the array.
for (j = 0 ; j < 2 ; j++)
g2[i][j] = (float)((rnd.Next() % (B + B)) - B) / B;
Normalize(g2[i]);
g3[i] = new double[3];
for (j = 0 ; j < 3 ; j++)
g3[i][j] = (float)((rnd.Next() % (B + B)) - B) / B;
Normalize(g3[i]);
}
while (--i > 0) {
k = p[i];
p[i] = p[j = rnd.Next() % B];
p[j] = k;
}
for (i = 0 ; i < B + 2 ; i++) {
p[B + i] = p[i];
g1[B + i] = g1[i];
for (j = 0 ; j < 2 ; j++)
g2[B + i][j] = g2[i][j];
for (j = 0 ; j < 3 ; j++)
g3[B + i][j] = g3[i][j];
}
}
private static double s_curve(double t)
{
return t * t * (3.0d - 2.0d * t);
}
private static double lerp(double t, double a, double b)
{
return a + t * (b - a);
}
public double Noise(double x)
{
double t = x + N;
int bx0 = ((int)t) & BM;
int bx1 = (bx0+1) & BM;
double rx0 = t - (int)t;
double rx1 = rx0 - 1.0d;
double sx = s_curve(rx0);
double u = rx0 * g1[ p[ bx0 ] ];
double v = rx1 * g1[ p[ bx1 ] ];
return lerp(sx, u, v);
}
private static double at2(double[] q, double rx, double ry)
{
return rx * q[0] + ry * q[1];
}
public double Noise(double x, double y)
{
// setup(0, bx0,bx1, rx0,rx1);
double t = x + N;
int bx0 = ((int)t) & BM;
int bx1 = (bx0+1) & BM;
double rx0 = t - (int)t;
double rx1 = rx0 - 1.0d;
//setup(1, by0,by1, ry0,ry1);
t = y + N;
int by0 = ((int)t) & BM;
int by1 = (by0+1) & BM;
double ry0 = t - (int)t;
double ry1 = ry0 - 1.0d;
int i = p[ bx0 ];
int j = p[ bx1 ];
int b00 = p[ i + by0 ];
int b10 = p[ j + by0 ];
int b01 = p[ i + by1 ];
int b11 = p[ j + by1 ];
double sx = s_curve(rx0);
double sy = s_curve(ry0);
double[] q;
q = g2[b00];
double u = at2(q, rx0,ry0);
q = g2[ b10 ] ;
double v = at2(q, rx1,ry0);
double a = lerp(sx, u, v);
q = g2[ b01 ] ;
u = at2(q, rx0,ry1);
q = g2[ b11 ] ;
v = at2(q, rx1,ry1);
double b = lerp(sx, u, v);
return lerp(sy, a, b);
}
private static double at3(double[] q, double rx, double ry, double rz)
{
return rx * q[0] + ry * q[1] + rz * q[2];
}
public double Noise(double x, double y, double z)
{
int bx0, bx1, by0, by1, bz0, bz1, b00, b10, b01, b11;
double rx0, rx1, ry0, ry1, rz0, rz1, sy, sz, a, b, c, d, t, u, v;
int i, j;
// setup(0, bx0,bx1, rx0,rx1);
t = x + N;
bx0 = ((int)t) & BM;
bx1 = (bx0+1) & BM;
rx0 = t - (int)t;
rx1 = rx0 - 1.0d;
//setup(1, by0,by1, ry0,ry1);
t = y + N;
by0 = ((int)t) & BM;
by1 = (by0+1) & BM;
ry0 = t - (int)t;
ry1 = ry0 - 1.0d;
// setup(2, bz0,bz1, rz0,rz1);
t = z + N;
bz0 = ((int)t) & BM;
bz1 = (bz0+1) & BM;
rz0 = t - (int)t;
rz1 = rz0 - 1.0d;
i = p[ bx0 ];
j = p[ bx1 ];
b00 = p[ i + by0 ];
b10 = p[ j + by0 ];
b01 = p[ i + by1 ];
b11 = p[ j + by1 ];
t = s_curve(rx0);
sy = s_curve(ry0);
sz = s_curve(rz0);
double[] q;
q = g3[ b00 + bz0 ] ; u = at3(q, rx0,ry0,rz0);
q = g3[ b10 + bz0 ] ; v = at3(q, rx1,ry0,rz0);
a = lerp(t, u, v);
q = g3[ b01 + bz0 ] ; u = at3(q, rx0,ry1,rz0);
q = g3[ b11 + bz0 ] ; v = at3(q, rx1,ry1,rz0);
b = lerp(t, u, v);
c = lerp(sy, a, b);
q = g3[ b00 + bz1 ] ; u = at3(q, rx0,ry0,rz1);
q = g3[ b10 + bz1 ] ; v = at3(q, rx1,ry0,rz1);
a = lerp(t, u, v);
q = g3[ b01 + bz1 ] ; u = at3(q, rx0,ry1,rz1);
q = g3[ b11 + bz1 ] ; v = at3(q, rx1,ry1,rz1);
b = lerp(t, u, v);
d = lerp(sy, a, b);
return lerp(sz, c, d);
}
private static void Normalize(double[] vec)
{
var sumOfSquares = vec.Select(v => v * v).Sum();
var squareRootOfSumOfSquares = Math.Sqrt(sumOfSquares);
for(int i = 0; i < vec.Length; i ++)
{
vec[i] = vec[i] / squareRootOfSumOfSquares;
}
}
private static void SizeArray(double[][] array, int childDimensions)
{
for(int i = 0; i < array.Length; i++)
{
array[i] = new double[childDimensions];
}
}
}
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