Complex Explorer
ComplexExplorer.exe
Meta.Numerics.dll
ComplexExplorer
ComplexExplorer
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Properties

using System;
using Meta.Numerics;
namespace ComplexExplorer {
// functions for mapping between color values
public static class ColorMap {
private const double TwoPI = 2.0 * Math.PI;
// Claudio Rocchini used this color mapping
// in his image at http://en.wikipedia.org/wiki/File:Color_complex_plot.jpg
// for the Wikipedia article on "Complex Analysis"
public static ColorTriplet ComplexToHsv (Complex z) {
// extract a phase 0 <= t < 2 pi
double t = ComplexMath.Arg(z);
while (t < 0.0) t += TwoPI;
while (t >= TwoPI) t = TwoPI;
// the hue is determined by the phase
double h = t / TwoPI;
// extract a magnitude m >= 0
double m = ComplexMath.Abs(z);
// map the magnitude logrithmicly into the repeating interval 0 < r < 1
// this is essentially where we are between countour lines
double r0 = 0.0;
double r1 = 1.0;
while (m > r1) {
r0 = r1;
r1 = r1 * Math.E;
}
double r = (m  r0) / (r1  r0);
// this puts contour lines at 0, 1, e, e^2, e^3, ...
// determine saturation and value based on r
// p and q are complementary distances from a countour line
double p = r < 0.5 ? 2.0 * r : 2.0 * (1.0  r);
double q = 1.0  p;
// only let p and q go to zero very close to zero; otherwise they should stay nearly 1
// this keep the countour lines from getting thick
double p1 = 1  q * q * q;
double q1 = 1  p * p * p;
// fix s and v from p1 and q1
double s = 0.4 + 0.6 * p1;
double v = 0.6 + 0.4 * q1;
return (new ColorTriplet() {X = h, Y = s, Z = v} );
}
// convert HSV to RGB
public static ColorTriplet HsvToRgb (ColorTriplet hsv) {
double h = hsv.X;
double s = hsv.Y;
double v = hsv.Z;
double r, g, b;
if (s == 0) {
r = g = b = v;
} else {
if (h == 1.0) h = 0.0;
double z = Math.Truncate(6 * h); int i = (int) z;
double f = h * 6  z;
double p = v * (1  s);
double q = v * (1  s * f);
double t = v * (1  s * (1  f));
switch (i) {
case 0: r = v; g = t; b = p; break;
case 1: r = q; g = v; b = p; break;
case 2: r = p; g = v; b = t; break;
case 3: r = p; g = q; b = v; break;
case 4: r = t; g = p; b = v; break;
case 5: r = v; g = p; b = q; break;
default: throw new InvalidOperationException();
}
}
return (new ColorTriplet() { X = r, Y = g, Z = b });
}
}
}

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I am a .NET developer who works daily on enterprisescale applications using C#, SQL, XML, ASP.NET, and myriad other technologies. My academic background is in physics and economics.
I am the original architect of
Sandcastle managed reference documentation engine and of the
Meta.Numerics library for scientific computation.