public Cplx Eval(Cplx x)
{
Cplx s = Cplx.Zero;
for (int i = 0; i < Coe.Count; i++)
{
Cplx coef = Coe[i];
Cplx bx = x;
int power = i;
if (i > 0)
{
for (int j = 0; j < power - 1; j++)
{
bx = bx.Multiply(x);
}
coef = coef.Multiply(bx);
}
s = s.Add(coef);
}
return(s);
}
public Cplx Subtract(Cplx b)
{
Cplx a = this;
return(new Cplx()
{
Re = a.Re - b.Re,
Im = a.Im - b.Im
});
}
public Cplx Add(Cplx b)
{
Cplx a = this;
return(new Cplx()
{
Re = a.Re + b.Re,
Im = a.Im + b.Im
});
}
public Cplx Multiply(Cplx b)
{
Cplx a = this;
// aRe*bRe + aRe*bIm*i + aIm*bRe*i + aIm*bIm*i*i
return(new Cplx()
{
Re = a.Re * b.Re - a.Im * b.Im,
Im = (float)(a.Re * b.Im + a.Im * b.Re)
});
}
internal Cplx Divide(Cplx b)
{
// (aRe + aIm*i) / (bRe + bIm*i)
// ((aRe + aIm*i) * (bRe - bIm*i)) / ((bRe + bIm*i) * (bRe - bIm*i))
// bRe*bRe - bIm*bIm*i*i
var tmp = this.Multiply(new Cplx()
{
Re = b.Re, Im = -b.Im
});
var tmp2 = b.Re * b.Re + b.Im * b.Im;
return(new Cplx()
{
Re = tmp.Re / tmp2,
Im = (float)(tmp.Im / tmp2)
});
}
static void Main(string[] args)
{
// TODO: add parameters from args?
// No to fakt ne
Bitmap bmp = new Bitmap(300, 300);
double xmin = -1.5;
double xmax = 1.5;
double ymin = -1.5;
double ymax = 1.5;
double xstep = (xmax - xmin) / 300;
double ystep = (ymax - ymin) / 300;
List <Cplx> koreny = new List <Cplx>();
// TODO: poly should be parameterised?
Poly p = new Poly();
p.Coe.Add(new Cplx()
{
Re = 1
});
p.Coe.Add(Cplx.Zero);
p.Coe.Add(Cplx.Zero);
//p.Coe.Add(Cplx.Zero);
p.Coe.Add(new Cplx()
{
Re = 1
});
Poly pd = p.Derive();
Console.WriteLine(p);
Console.WriteLine(pd);
var clrs = new Color[]
{
Color.Red, Color.Blue, Color.Green, Color.Yellow, Color.Orange, Color.Fuchsia, Color.Gold, Color.Cyan, Color.Magenta
};
var maxid = 0;
// TODO: cleanup!!!
// for every pixel in image...
for (int i = 0; i < 300; i++)
{
for (int j = 0; j < 300; j++)
{
// find "world" coordinates of pixel
double x = xmin + j * xstep;
double y = ymin + i * ystep;
Cplx ox = new Cplx()
{
Re = x,
Im = (float)(y)
};
if (ox.Re == 0)
{
ox.Re = 0.0001;
}
if (ox.Im == 0)
{
ox.Im = 0.0001f;
}
//Console.WriteLine(ox);
// find solution of equation using newton's iteration
float it = 0;
for (int q = 0; q < 30; q++)
{
var diff = p.Eval(ox).Divide(pd.Eval(ox));
ox = ox.Subtract(diff);
//Console.WriteLine($"{q} {ox} -({diff})");
if (Math.Pow(diff.Re, 2) + Math.Pow(diff.Im, 2) >= 0.5)
{
q--;
}
it++;
}
//Console.ReadKey();
// find solution root number
var known = false;
var id = 0;
for (int w = 0; w < koreny.Count; w++)
{
if (Math.Pow(ox.Re - koreny[w].Re, 2) + Math.Pow(ox.Im - koreny[w].Im, 2) <= 0.01)
{
known = true;
id = w;
}
}
if (!known)
{
koreny.Add(ox);
id = koreny.Count;
maxid = id + 1;
}
// colorize pixel according to root number
//int vv = id;
//int vv = id * 50 + (int)it*5;
var vv = clrs[id % clrs.Length];
vv = Color.FromArgb(vv.R, vv.G, vv.B);
vv = Color.FromArgb(Math.Min(Math.Max(0, vv.R - (int)it * 2), 255), Math.Min(Math.Max(0, vv.G - (int)it * 2), 255), Math.Min(Math.Max(0, vv.B - (int)it * 2), 255));
//vv = Math.Min(Math.Max(0, vv), 255);
bmp.SetPixel(j, i, vv);
//bmp.SetPixel(j, i, Color.FromArgb(vv, vv, vv));
}
}
// TODO: delete I suppose...
//for (int i = 0; i < 300; i++)
//{
// for (int j = 0; j < 300; j++)
// {
// Color c = bmp.GetPixel(j, i);
// int nv = (int)Math.Floor(c.R * (255.0 / maxid));
// bmp.SetPixel(j, i, Color.FromArgb(nv, nv, nv));
// }
//}
bmp.Save("../../../out.png");
//Console.ReadKey();
}