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NewtonFractal.cs
1using System;
2using System.Numerics;
3using System.Text;
4using SkiaSharp;
5using Waher.Script.Abstraction.Elements;
6using Waher.Script.Model;
7using Waher.Script.Exceptions;
8using Waher.Script.Graphs;
9using Waher.Script.Objects.VectorSpaces;
10using Waher.Script.Fractals.Exceptions;
11
12namespace Waher.Script.Fractals.ComplexFractals
13{
47 public class NewtonFractal : FunctionMultiVariate
48 {
52 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
53 ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
54 : base(new ScriptNode[] { z, dr, R, c, Palette, DimX, DimY },
55 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
56 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar, ArgumentType.Scalar},
57 Start, Length, Expression)
58 {
59 }
60
64 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
65 ScriptNode DimX, int Start, int Length, Expression Expression)
66 : base(new ScriptNode[] { z, dr, R, c, Palette, DimX },
67 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
68 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar},
69 Start, Length, Expression)
70 {
71 }
72
76 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette,
77 int Start, int Length, Expression Expression)
78 : base(new ScriptNode[] { z, dr, R, c, Palette },
79 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
80 ArgumentType.Normal, ArgumentType.Vector },
81 Start, Length, Expression)
82 {
83 }
84
88 public NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c,
89 int Start, int Length, Expression Expression)
90 : base(new ScriptNode[] { z, dr, R, c },
91 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
92 ArgumentType.Normal },
93 Start, Length, Expression)
94 {
95 }
96
100 public override string[] DefaultArgumentNames
101 {
102 get
103 {
104 return new string[] { "z", "dr", "R", "c", "Palette", "DimX", "DimY" };
105 }
106 }
107
111 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
112 {
113 string ColorExpression = null;
114 SKColor[] Palette;
115 double[] Coefficients = null;
116 Complex[] CoefficientsZ = null;
117 ILambdaExpression f = null;
118 ScriptNode fDef = null;
119 double rc, ic;
120 double dr;
121 Complex R;
122 int dimx, dimy;
123 int c = Arguments.Length;
124 int i = 0;
125 object Obj;
126
127 Obj = Arguments[i++].AssociatedObjectValue;
128 if (Obj is Complex z)
129 {
130 rc = z.Real;
131 ic = z.Imaginary;
132 }
133 else
134 {
135 rc = Expression.ToDouble(Obj);
136 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
137 }
138
139 if (i >= c)
140 throw new ScriptRuntimeException("Insufficient parameters in call to NewtonFractal().", this);
141
142 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
143
144 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
145 {
146 R = Expression.ToComplex(Obj);
147 i++;
148 }
149 else
150 {
151 R = Complex.One;
152
153 if (i < c && this.Arguments[i] is null)
154 i++;
155 }
156
157 if (i < c)
158 {
159 if (Arguments[i] is DoubleVector)
160 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
161 else if (Arguments[i] is ComplexVector)
162 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
163 /*else if (Parameters[i] is RealPolynomial)
164 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
165 else if (Parameters[i] is ComplexPolynomial)
166 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
167 else if (Arguments[i] is IVector)
168 {
169 IVector Vector = (IVector)Arguments[i++];
170 int j, d = Vector.Dimension;
171
172 CoefficientsZ = new Complex[d];
173 for (j = 0; j < d; j++)
174 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
175 }
176 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
177 {
178 f = (ILambdaExpression)Arguments[i];
179 if (f.NrArguments != 1)
180 throw new ScriptRuntimeException("Lambda expression in calls to NewtonFractal() must be of one variable.", this);
181
182 fDef = this.Arguments[i++];
183 }
184 else
185 {
186 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
187 " in call to NewtonFractal has to be a vector of numbers, containing coefficients " +
188 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
189 this);
190 }
191 }
192 else
193 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
194
195 if (i < c && !(this.Arguments[i] is null) && Arguments[i] is ObjectVector)
196 {
197 ColorExpression = this.Arguments[i].SubExpression;
198 Palette = FractalGraph.ToPalette((ObjectVector)Arguments[i++]);
199 }
200 else
201 {
202 Palette = ColorModels.RandomLinearAnalogousHSL.CreatePalette(128, 4, out int Seed, this, Variables);
203 ColorExpression = "RandomLinearAnalogousHSL(128,4," + Seed.ToString() + ")";
204
205 if (i < c && this.Arguments[i] is null)
206 i++;
207 }
208
209 if (i < c)
210 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
211 else
212 dimx = 320;
213
214 if (i < c)
215 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
216 else
217 dimy = 200;
218
219 if (i < c)
220 {
221 throw new ScriptRuntimeException("Parameter mismatch in call to NewtonFractal(r,c,dr,Coefficients[,Palette][,dimx[,dimy]]).",
222 this);
223 }
224
225 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
226 throw new FractalImageSizeScriptException(this);
227
228 if (!(f is null))
229 {
230 return CalcNewton(rc, ic, dr, R, f, fDef, Variables, Palette, dimx, dimy,
231 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, fDef, ColorExpression });
232 }
233 else if (!(CoefficientsZ is null))
234 {
235 return CalcNewton(Variables, rc, ic, dr, R, CoefficientsZ, Palette, dimx, dimy,
236 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, CoefficientsZ, ColorExpression });
237 }
238 else
239 {
240 return CalcNewton(Variables, rc, ic, dr, R, Coefficients, Palette, dimx, dimy,
241 this, this.FractalZoomScript, new object[] { Palette, dimx, dimy, R, Coefficients, ColorExpression });
242 }
243 }
244
245 private string FractalZoomScript(double r, double i, double Size, object State)
246 {
247 object[] Parameters = (object[])State;
248 int DimX = (int)Parameters[1];
249 int DimY = (int)Parameters[2];
250 Complex R = (Complex)Parameters[3];
251 double[] Coefficients = Parameters[4] as double[];
252 string ColorExpression = (string)Parameters[5];
253
254 StringBuilder sb = new StringBuilder();
255
256 sb.Append("NewtonFractal((");
257 sb.Append(Expression.ToString(r));
258 sb.Append(',');
259 sb.Append(Expression.ToString(i));
260 sb.Append("),");
261 sb.Append(Expression.ToString(Size / 4));
262 sb.Append(',');
263 sb.Append(Expression.ToString(R));
264 sb.Append(',');
265
266 if (Parameters[4] is ScriptNode fDef)
267 sb.Append(fDef.SubExpression);
268 else if (Parameters[4] is Complex[] CoefficientsZ)
269 sb.Append(Expression.ToString(CoefficientsZ));
270 else
271 sb.Append(Expression.ToString(Coefficients));
272
273 if (!string.IsNullOrEmpty(ColorExpression))
274 {
275 sb.Append(',');
276 sb.Append(ColorExpression);
277 }
278
279 sb.Append(',');
280 sb.Append(DimX.ToString());
281 sb.Append(',');
282 sb.Append(DimY.ToString());
283 sb.Append(')');
284
285 return sb.ToString();
286 }
287
291 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
292 double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
293 object State)
294 {
295 byte[] reds;
296 byte[] greens;
297 byte[] blues;
298 double r0, i0, r1, i1;
299 double dr, di;
300 double r, i;
301 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
302 double RRe = R.Real;
303 double RIm = R.Imaginary;
304 double aspect;
305 double Temp;
306 int x, y;
307 int n, N;
308 int index;
309 int Degree = Coefficients.Length - 1;
310 SKColor cl;
311
312 N = Palette.Length;
313 reds = new byte[N];
314 greens = new byte[N];
315 blues = new byte[N];
316
317 for (x = 0; x < N; x++)
318 {
319 cl = Palette[x];
320 reds[x] = cl.Red;
321 greens[x] = cl.Green;
322 blues[x] = cl.Blue;
323 }
324
325 if (Degree < 2)
326 {
327 Array.Resize(ref Coefficients, 3);
328 while (Degree < 2)
329 Coefficients[++Degree] = 0;
330 }
331
332 double[] Prim = new double[Degree];
333 for (x = 1; x <= Degree; x++)
334 Prim[x - 1] = x * Coefficients[x];
335
336 Array.Reverse(Prim);
337 Coefficients = (double[])Coefficients.Clone();
338 Array.Reverse(Coefficients);
339
340 int size = Width * Height * 4;
341 double Conv = 1e-10;
342 double Div = 1e10;
343 byte[] rgb = new byte[size];
344
345 rDelta *= 0.5;
346 r0 = rCenter - rDelta;
347 r1 = rCenter + rDelta;
348
349 aspect = ((double)Width) / Height;
350
351 i0 = iCenter - rDelta / aspect;
352 i1 = iCenter + rDelta / aspect;
353
354 dr = (r1 - r0) / Width;
355 di = (i1 - i0) / Height;
356
357 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
358 {
359 for (x = 0, r = r0; x < Width; x++, r += dr)
360 {
361 zr = r;
362 zi = i;
363
364 n = 0;
365 do
366 {
367 // f:
368 zr2 = zi2 = 0;
369 foreach (double C in Coefficients)
370 {
371 Temp = zr2 * zr - zi2 * zi + C;
372 zi2 = zr2 * zi + zi2 * zr;
373 zr2 = Temp;
374 }
375
376 // f':
377 zr3 = zi3 = 0;
378 foreach (double C in Prim)
379 {
380 Temp = zr3 * zr - zi3 * zi + C;
381 zi3 = zr3 * zi + zi3 * zr;
382 zr3 = Temp;
383 }
384
385 // f/f':
386
387 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
388 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
389 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
390
391 // R*f/f'
392 Temp = zr4 * RRe - zi4 * RIm;
393 zi4 = zr4 * RIm + zi4 * RRe;
394 zr4 = Temp;
395
396 zr -= zr4;
397 zi -= zi4;
398
399 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
400 }
401 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
402
403 if (Temp < Conv && n < N)
404 {
405 rgb[index++] = blues[n];
406 rgb[index++] = greens[n];
407 rgb[index++] = reds[n];
408 }
409 else
410 {
411 rgb[index++] = 0;
412 rgb[index++] = 0;
413 rgb[index++] = 0;
414 }
415
416 rgb[index++] = 255;
417 }
418 }
419
420 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
421 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
422 }
423
427 public static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
428 Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript,
429 object State)
430 {
431 byte[] reds;
432 byte[] greens;
433 byte[] blues;
434 double RRe = R.Real;
435 double RIm = R.Imaginary;
436 double r0, i0, r1, i1;
437 double dr, di;
438 double r, i;
439 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4;
440 double aspect;
441 double Temp;
442 int x, y;
443 int n, N;
444 int index;
445 int Degree = Coefficients.Length - 1;
446 SKColor cl;
447
448 N = Palette.Length;
449 reds = new byte[N];
450 greens = new byte[N];
451 blues = new byte[N];
452
453 for (x = 0; x < N; x++)
454 {
455 cl = Palette[x];
456 reds[x] = cl.Red;
457 greens[x] = cl.Green;
458 blues[x] = cl.Blue;
459 }
460
461 if (Degree < 2)
462 {
463 Array.Resize(ref Coefficients, 3);
464 while (Degree < 2)
465 Coefficients[++Degree] = Complex.Zero;
466 }
467
468 Complex[] Prim = new Complex[Degree];
469 for (x = 1; x <= Degree; x++)
470 Prim[x - 1] = x * Coefficients[x];
471
472 Array.Reverse(Prim);
473 Coefficients = (Complex[])Coefficients.Clone();
474 Array.Reverse(Coefficients);
475
476 int j, c = Prim.Length;
477 double[] ReC = new double[c + 1];
478 double[] ImC = new double[c + 1];
479 double[] RePrim = new double[c];
480 double[] ImPrim = new double[c];
481 Complex z;
482
483 for (j = 0; j < c; j++)
484 {
485 z = Coefficients[j];
486 ReC[j] = z.Real;
487 ImC[j] = z.Imaginary;
488
489 z = Prim[j];
490 RePrim[j] = z.Real;
491 ImPrim[j] = z.Imaginary;
492 }
493
494 z = Coefficients[j];
495 ReC[j] = z.Real;
496 ImC[j] = z.Imaginary;
497
498 int size = Width * Height * 4;
499 double Conv = 1e-10;
500 double Div = 1e10;
501 byte[] rgb = new byte[size];
502
503 rDelta *= 0.5;
504 r0 = rCenter - rDelta;
505 r1 = rCenter + rDelta;
506
507 aspect = ((double)Width) / Height;
508
509 i0 = iCenter - rDelta / aspect;
510 i1 = iCenter + rDelta / aspect;
511
512 dr = (r1 - r0) / Width;
513 di = (i1 - i0) / Height;
514
515 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
516 {
517 for (x = 0, r = r0; x < Width; x++, r += dr)
518 {
519 zr = r;
520 zi = i;
521
522 n = 0;
523 do
524 {
525 // f:
526 zr2 = zi2 = 0;
527 for (j = 0; j <= c; j++)
528 {
529 Temp = zr2 * zr - zi2 * zi + ReC[j];
530 zi2 = zr2 * zi + zi2 * zr + ImC[j];
531 zr2 = Temp;
532 }
533
534 // f':
535 zr3 = zi3 = 0;
536 for (j = 0; j < c; j++)
537 {
538 Temp = zr3 * zr - zi3 * zi + RePrim[j];
539 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
540 zr3 = Temp;
541 }
542
543 // f/f':
544
545 Temp = 1.0 / (zr3 * zr3 + zi3 * zi3);
546 zr4 = (zr2 * zr3 + zi2 * zi3) * Temp;
547 zi4 = (zi2 * zr3 - zr2 * zi3) * Temp;
548
549 // R*f/f'
550 Temp = zr4 * RRe - zi4 * RIm;
551 zi4 = zr4 * RIm + zi4 * RRe;
552 zr4 = Temp;
553
554 zr -= zr4;
555 zi -= zi4;
556
557 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
558 }
559 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
560
561 if (Temp < Conv && n < N)
562 {
563 rgb[index++] = blues[n];
564 rgb[index++] = greens[n];
565 rgb[index++] = reds[n];
566 }
567 else
568 {
569 rgb[index++] = 0;
570 rgb[index++] = 0;
571 rgb[index++] = 0;
572 }
573
574 rgb[index++] = 255;
575 }
576 }
577
578 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
579 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
580 }
581
585 public static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R,
586 ILambdaExpression f, ScriptNode _, Variables Variables, SKColor[] Palette, int Width, int Height,
587 ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
588 {
589 byte[] reds;
590 byte[] greens;
591 byte[] blues;
592 double RRe = R.Real;
593 double RIm = R.Imaginary;
594 double r0, i0, r1, i1;
595 double dr, di;
596 double r, i;
597 double aspect;
598 int x, y;
599 int n, N;
600 SKColor cl;
601 Complex z;
602
603 N = Palette.Length;
604 reds = new byte[N];
605 greens = new byte[N];
606 blues = new byte[N];
607
608 for (x = 0; x < N; x++)
609 {
610 cl = Palette[x];
611 reds[x] = cl.Red;
612 greens[x] = cl.Green;
613 blues[x] = cl.Blue;
614 }
615
616 Variables v = new Variables();
617 Variables.CopyTo(v);
618
619 if (!(f is IDifferentiable Differentiable) ||
620 !(Differentiable.Differentiate(Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
621 {
622 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
623 }
624
625 int size = Width * Height * 4;
626 double Conv = 1e-10;
627 double Div = 1e10;
628 byte[] rgb = new byte[size];
629
630 Complex[] Row;
631 Complex[] Row2;
632 Complex[] Row3;
633 int[] Offset;
634 IElement[] P = new IElement[1];
635 int j, c, x2;
636 IElement Obj, Obj2;
637 double Mod;
638
639 rDelta *= 0.5;
640 r0 = rCenter - rDelta;
641 r1 = rCenter + rDelta;
642
643 aspect = ((double)Width) / Height;
644
645 i0 = iCenter - rDelta / aspect;
646 i1 = iCenter + rDelta / aspect;
647
648 dr = (r1 - r0) / Width;
649 di = (i1 - i0) / Height;
650
651 for (y = 0, i = i0; y < Height; y++, i += di)
652 {
653 Row = new Complex[Width];
654 Offset = new int[Width];
655
656 c = Width;
657 for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
658 {
659 Row[x] = new Complex(r, i);
660 Offset[x] = x2;
661 }
662
663 n = 0;
664 while (n < N && c > 0)
665 {
666 n++;
667 P[0] = new ComplexVector(Row);
668 Obj = f.Evaluate(P, v);
669 Obj2 = fPrim.Evaluate(P, v);
670 Row2 = Obj.AssociatedObjectValue as Complex[];
671 Row3 = Obj2.AssociatedObjectValue as Complex[];
672
673 if (Row2 is null || Row3 is null)
674 {
675 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
676 "and return complex vectors of equal length. Type returned: " +
677 Obj.GetType().FullName + " and " + Obj2.GetType().FullName, Node);
678 }
679 else if (Row2.Length != c || Row3.Length != c)
680 {
681 throw new ScriptRuntimeException("Lambda expression (and its first derivative) must be able to accept complex vectors, " +
682 "and return complex vectors of equal length. Length returned: " +
683 Row2.Length.ToString() + " and " + Row3.Length.ToString() +
684 ". Expected: " + c.ToString(), Node);
685 }
686
687 for (x = x2 = 0; x < c; x++)
688 {
689 j = Offset[x];
690 z = R * Row2[x] / Row3[x];
691 Row[x] -= z;
692
693 Mod = z.Magnitude;
694
695 if (Mod > Conv && Mod < Div)
696 {
697 if (x != x2)
698 Offset[x2] = j;
699
700 x2++;
701 }
702 else
703 {
704 if (n >= N)
705 {
706 rgb[j++] = 0;
707 rgb[j++] = 0;
708 rgb[j++] = 0;
709 }
710 else
711 {
712 rgb[j++] = blues[n];
713 rgb[j++] = greens[n];
714 rgb[j++] = reds[n];
715 }
716
717 rgb[j++] = 255;
718 }
719 }
720
721 if (x2 < x)
722 {
723 Array.Resize(ref Row, x2);
724 Array.Resize(ref Offset, x2);
725 c = x2;
726 }
727 }
728 }
729
730 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
731 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
732 }
733
737 public override string FunctionName => nameof(NewtonFractal);
738 }
739}
Waher.Script.Expression
Class managing a script expression.
Definition: Expression.cs:41
Waher.Script.Expression.ToComplex
static Complex ToComplex(object Object)
Converts an object to a complex value.
Definition: Expression.cs:5228
Waher.Script.Expression.ToDouble
static double ToDouble(object Object)
Converts an object to a double value.
Definition: Expression.cs:5110
Waher.Script.Expression.ToString
static string ToString(double Value)
Converts a value to a string, that can be parsed as part of an expression.
Definition: Expression.cs:4760
Waher.Script.Fractals.ComplexFractals.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonFractal.cs:427
Waher.Script.Fractals.ComplexFractals.NewtonFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: NewtonFractal.cs:111
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:64
Waher.Script.Fractals.ComplexFractals.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, ScriptNode _, Variables Variables, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonFractal.cs:585
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:76
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:88
Waher.Script.Fractals.ComplexFractals.NewtonFractal.NewtonFractal
NewtonFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode c, ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: NewtonFractal.cs:52
Waher.Script.Fractals.ComplexFractals.NewtonFractal.CalcNewton
static FractalGraph CalcNewton(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: NewtonFractal.cs:291
Waher.Script.Fractals.Exceptions.FractalImageSizeScriptException
Exception thrown if an image with invalid size is requested.
Definition: OperandOutOfBoundsScriptException.cs:10
Waher.Script.Fractals.FractalGraph
Defines a clickable fractal graph in the complex plane.
Definition: FractalGraph.cs:23
Waher.Script.Fractals.FractalGraph.ToPalette
static SKColor[] ToPalette(ObjectVector Vector)
TODO
Definition: FractalGraph.cs:110
Waher.Script.Graphs.PixelInformation
Contains pixel information
Definition: PixelInformation.cs:9
Waher.Script.Graphs.PixelInformationRaw
Contains pixel information in a raw unencoded format.
Definition: PixelInformationRaw.cs:11
Waher.Script.Model.FunctionMultiVariate
Base class for multivariate funcions.
Definition: FunctionMultiVariate.cs:17
Waher.Script.Model.FunctionMultiVariate.Arguments
ScriptNode[] Arguments
Function arguments.
Definition: FunctionMultiVariate.cs:185
Waher.Script.Model.ScriptNode
Base class for all nodes in a parsed script tree.
Definition: ScriptNode.cs:69
Waher.Script.Model.ScriptNode.Length
int Length
Length of expression covered by node.
Definition: ScriptNode.cs:101
Waher.Script.Model.ScriptNode.ToString
override string ToString()
Definition: ScriptNode.cs:359
Waher.Script.Model.ScriptNode.Expression
Expression Expression
Expression of which the node is a part.
Definition: ScriptNode.cs:177
Waher.Script.Model.ScriptNode.Start
int Start
Start position in script expression.
Definition: ScriptNode.cs:92
Waher.Script.Variables
Collection of variables.
Definition: Variables.cs:25
Waher.Script.Variables.CopyTo
void CopyTo(Variables Variables)
Copies available variables to another variable collection.
Definition: Variables.cs:334
Waher.Script.Abstraction.Elements.IElement
Basic interface for all types of elements.
Definition: IElement.cs:21
Waher.Script.Abstraction.Elements.IElement.AssociatedObjectValue
object AssociatedObjectValue
Associated object value.
Definition: IElement.cs:34
Waher.Script.Abstraction.Elements.IVector
Basic interface for vectors.
Definition: IVector.cs:9
Waher.Script.Abstraction.Elements.IVector.Dimension
int Dimension
Dimension of vector.
Definition: IVector.cs:14
Waher.Script.Abstraction.Elements.IVector.GetElement
IElement GetElement(int Index)
Gets an element of the vector.
Waher.Script.Model.IDifferentiable
Base interface for lambda expressions.
Definition: IDifferentiable.cs:9
Waher.Script.Model.ILambdaExpression
Base interface for lambda expressions.
Definition: ILambdaExpression.cs:11
Waher.Script.Model.ILambdaExpression.Evaluate
IElement Evaluate(IElement[] Arguments, Variables Variables)
Evaluates the lambda expression.
_
Definition: ImplTypes.g.cs:58
Waher.Script.Fractals.FractalZoomScript
delegate string FractalZoomScript(double r, double i, double Size, object State)
Generates new script when zoomed.
Waher.Script.Model.ArgumentType
ArgumentType
Type of parameter used in a function definition or a lambda definition.
Definition: IFunction.cs:9