public static FractalGraph CalcNewtonSmooth(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, SKColor[] Palette, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
N = Palette.Length;
if (Width <= 2 || Height <= 2)
{
throw new ScriptRuntimeException("Width and Height has to be greater than 2.", Node);
}
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int Size = Width * Height;
double Conv = 1e-10;
double Div = 1e10;
double[] ColorIndex = new double[Size];
int Index = 0;
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, c, x2;
IElement Obj, Obj2;
double Mod;
Complex z;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width, r = r0; x < Width; x++, r += dr, x2++)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 == null || Row3 == null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}
else if (Row2.Length != c || Row3.Length != c)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Length returned: " +
Row2.Length.ToString() + " and " + Row3.Length.ToString() +
". Expected: " + c.ToString(), Node);
}
for (x = x2 = 0; x < c; x++)
{
j = Offset[x];
z = R * Row2[x] / Row3[x];
Row[x] -= z;
Mod = z.Magnitude;
if (Mod > Conv && Mod < Div)
{
if (x != x2)
{
Offset[x2] = j;
}
x2++;
}
else
{
if (n >= N)
{
ColorIndex[Index++] = N;
}
else
{
ColorIndex[j++] = n;
}
}
}
if (x2 < x)
{
Array.Resize <Complex>(ref Row, x2);
Array.Resize <int>(ref Offset, x2);
c = x2;
}
}
}
Node.Expression.Preview(new GraphBitmap(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette)));
double[] Boundary = FractalGraph.FindBoundaries(ColorIndex, Width, Height);
FractalGraph.Smooth(ColorIndex, Boundary, Width, Height, N, Palette, Node, Variables);
return(new FractalGraph(FractalGraph.ToBitmap(ColorIndex, Width, Height, Palette),
r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, SKColor[] Palette,
int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
object State)
{
byte[] reds;
byte[] greens;
byte[] blues;
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
SKColor cl;
Complex z;
N = Palette.Length;
reds = new byte[N];
greens = new byte[N];
blues = new byte[N];
for (x = 0; x < N; x++)
{
cl = Palette[x];
reds[x] = cl.Red;
greens[x] = cl.Green;
blues[x] = cl.Blue;
}
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int size = Width * Height * 4;
double Conv = 1e-10;
double Div = 1e10;
byte[] rgb = new byte[size];
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, c, x2;
IElement Obj, Obj2;
double Mod;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 == null || Row3 == null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}
else if (Row2.Length != c || Row3.Length != c)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Length returned: " +
Row2.Length.ToString() + " and " + Row3.Length.ToString() +
". Expected: " + c.ToString(), Node);
}
for (x = x2 = 0; x < c; x++)
{
j = Offset[x];
z = R * Row2[x] / Row3[x];
Row[x] -= z;
Mod = z.Magnitude;
if (Mod > Conv && Mod < Div)
{
if (x != x2)
{
Offset[x2] = j;
}
x2++;
}
else
{
if (n >= N)
{
rgb[j++] = 0;
rgb[j++] = 0;
rgb[j++] = 0;
}
else
{
rgb[j++] = blues[n];
rgb[j++] = greens[n];
rgb[j++] = reds[n];
}
rgb[j++] = 255;
}
}
if (x2 < x)
{
Array.Resize <Complex>(ref Row, x2);
Array.Resize <int>(ref Offset, x2);
c = x2;
}
}
}
using (SKData Data = SKData.Create(new MemoryStream(rgb)))
{
SKImage Bitmap = SKImage.FromPixelData(new SKImageInfo(Width, Height, SKColorType.Bgra8888), Data, Width * 4);
return(new FractalGraph(Bitmap, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
}
public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, int N, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
List <double> AttractorsR = new List <double>();
List <double> AttractorsI = new List <double>();
List <int> AttractorColors = new List <int>();
double[] AttractorsR2 = new double[0];
double[] AttractorsI2 = new double[0];
int[] AttractorsColors2 = new int[0];
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi;
double aspect;
int x, y, b, c, d;
int NrAttractors = 0;
int n;
int index;
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int size = Width * Height * 4;
double Conv = 1e-10;
double Div = 1e10;
double Conv2 = Conv * 2;
byte[] rgb = new byte[size];
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, x2;
IElement Obj, Obj2;
double Mod;
Complex z;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 == null || Row3 == null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}
else if (Row2.Length != c || Row3.Length != c)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Length returned: " +
Row2.Length.ToString() + " and " + Row3.Length.ToString() +
". Expected: " + c.ToString(), Node);
}
for (x = x2 = 0; x < c; x++)
{
j = Offset[x];
z = R * Row2[x] / Row3[x];
Row[x] -= z;
Mod = z.Magnitude;
if (Mod > Conv && Mod < Div)
{
if (x != x2)
{
Offset[x2] = j;
}
x2++;
}
else
{
if (n >= N)
{
rgb[j++] = 0;
rgb[j++] = 0;
rgb[j++] = 0;
}
else
{
zr = z.Real;
zi = z.Imaginary;
for (b = 0; b < NrAttractors; b++)
{
if (Math.Abs(AttractorsR2[b] - zr) < Conv2 &&
Math.Abs(AttractorsI2[b] - zi) < Conv2)
{
break;
}
}
if (b == NrAttractors)
{
AttractorsR.Add(zr);
AttractorsI.Add(zi);
int p1 = ~((b % 6) + 1);
int p2 = ((b / 6) % 7);
int Red = (p1 & 1) != 0 ? 255 : 0;
int Green = (p1 & 2) != 0 ? 255 : 0;
int Blue = (p1 & 4) != 0 ? 255 : 0;
if ((p2 & 1) != 0)
{
Red >>= 1;
}
if ((p2 & 2) != 0)
{
Green >>= 1;
}
if ((p2 & 4) != 0)
{
Blue >>= 1;
}
Blue <<= 8;
Blue |= Green;
Blue <<= 8;
Blue |= Red;
AttractorColors.Add(Blue);
AttractorsR2 = AttractorsR.ToArray();
AttractorsI2 = AttractorsI.ToArray();
AttractorsColors2 = AttractorColors.ToArray();
NrAttractors++;
}
b = AttractorColors[b];
d = (byte)b;
rgb[index++] = (byte)((d * (N - n + 1)) / N);
b >>= 8;
d = (byte)b;
rgb[index++] = (byte)((d * (N - n + 1)) / N);
b >>= 8;
d = (byte)b;
rgb[index++] = (byte)((d * (N - n + 1)) / N);
}
rgb[j++] = 255;
}
}
if (x2 < x)
{
Array.Resize <Complex>(ref Row, x2);
Array.Resize <int>(ref Offset, x2);
c = x2;
}
}
}
using (SKData Data = SKData.Create(new MemoryStream(rgb)))
{
SKImage Bitmap = SKImage.FromPixelData(new SKImageInfo(Width, Height, SKColorType.Bgra8888), Data, Width * 4);
return(new FractalGraph(Bitmap, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State));
}
}
public static FractalGraph CalcHalley(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, SKColor[] Palette, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
byte[] reds;
byte[] greens;
byte[] blues;
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
SKColor cl;
N = Palette.Length;
reds = new byte[N];
greens = new byte[N];
blues = new byte[N];
for (x = 0; x < N; x++)
{
cl = Palette[x];
reds[x] = cl.Red;
greens[x] = cl.Green;
blues[x] = cl.Blue;
}
Variables v = new Variables();
Variables.CopyTo(v);
string ParameterName;
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(ParameterName = Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
if (!(fPrim is IDifferentiable Differentiable2) ||
!(Differentiable2.Differentiate(ParameterName, v) is ILambdaExpression fBis))
{
throw new ScriptRuntimeException("Lambda expression not twice differentiable.", Node);
}
int size = Width * Height * 4;
double Conv = 1e-10;
double Div = 1e10;
byte[] rgb = new byte[size];
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
Complex[] Row4;
int[] Offset;
IElement[] P = new IElement[1];
int j, c, x2;
IElement Obj, Obj2, Obj3;
double Mod;
Complex z, z2, z3;
Complex R2 = R * 2;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Obj3 = fBis.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
Row4 = Obj3.AssociatedObjectValue as Complex[];
if (Row2 is null || Row3 is null || Row4 is null)
{
throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + ", " + Obj2.GetType().FullName + " and " + Obj3.GetType().FullName,
Node);
}
public static FractalGraph CalcNewtonSmooth(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, SKColor[] Palette, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
double r0, i0, r1, i1;
double dr, di;
double r, i;
double aspect;
int x, y;
int n, N;
N = Palette.Length;
if (Width <= 2 || Height <= 2)
{
throw new ScriptRuntimeException("Width and Height has to be greater than 2.", Node);
}
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int Size = Width * Height;
double Conv = 1e-10;
double Div = 1e10;
double[] ColorIndex = new double[Size];
int Index = 0;
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, c, x2;
IElement Obj, Obj2;
double Mod;
Complex z;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width, r = r0; x < Width; x++, r += dr, x2++)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 is null || Row3 is null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}
public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
ILambdaExpression f, ScriptNode fDef, Variables Variables, int N, int Width, int Height,
ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
{
double RRe = R.Real;
double RIm = R.Imaginary;
List <double> AttractorsR = new List <double>();
List <double> AttractorsI = new List <double>();
List <int> AttractorColors = new List <int>();
double[] AttractorsR2 = new double[0];
double[] AttractorsI2 = new double[0];
int[] AttractorsColors2 = new int[0];
double r0, i0, r1, i1;
double dr, di;
double r, i;
double zr, zi;
double aspect;
int x, y, b, c, d;
int NrAttractors = 0;
int n;
int index;
Variables v = new Variables();
Variables.CopyTo(v);
if (!(f is IDifferentiable Differentiable) ||
!(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
{
throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
}
int size = Width * Height * 4;
double Conv = 1e-10;
double Div = 1e10;
double Conv2 = Conv * 2;
byte[] rgb = new byte[size];
Complex[] Row;
Complex[] Row2;
Complex[] Row3;
int[] Offset;
IElement[] P = new IElement[1];
int j, x2;
IElement Obj, Obj2;
double Mod;
Complex z;
rDelta *= 0.5;
r0 = rCenter - rDelta;
r1 = rCenter + rDelta;
aspect = ((double)Width) / Height;
i0 = iCenter - rDelta / aspect;
i1 = iCenter + rDelta / aspect;
dr = (r1 - r0) / Width;
di = (i1 - i0) / Height;
for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
{
Row = new Complex[Width];
Offset = new int[Width];
c = Width;
for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
{
Row[x] = new Complex(r, i);
Offset[x] = x2;
}
n = 0;
while (n < N && c > 0)
{
n++;
P[0] = Expression.Encapsulate(Row);
Obj = f.Evaluate(P, v);
Obj2 = fPrim.Evaluate(P, v);
Row2 = Obj.AssociatedObjectValue as Complex[];
Row3 = Obj2.AssociatedObjectValue as Complex[];
if (Row2 is null || Row3 is null)
{
throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
"and return complex vectors of equal length. Type returned: " +
Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
}