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HalleyFractal.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{
43 public class HalleyFractal : FunctionMultiVariate
44 {
48 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
49 ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
50 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX, DimY },
51 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
52 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar, ArgumentType.Scalar}, Start, Length, Expression)
53 {
54 }
55
59 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
60 ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
61 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette, DimX },
62 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
63 ArgumentType.Normal, ArgumentType.Vector, ArgumentType.Scalar}, Start, Length, Expression)
64 {
65 }
66
70 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
71 ScriptNode Palette, int Start, int Length, Expression Expression)
72 : base(new ScriptNode[] { z, dr, R, Coefficients, Palette },
73 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
74 ArgumentType.Normal, ArgumentType.Vector}, Start, Length, Expression)
75 {
76 }
77
81 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients,
82 int Start, int Length, Expression Expression)
83 : base(new ScriptNode[] { z, dr, R, Coefficients },
84 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar,
85 ArgumentType.Normal}, Start, Length, Expression)
86 {
87 }
88
92 public HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
93 : base(new ScriptNode[] { z, dr, R },
94 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
95 {
96 }
97
101 public HalleyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
102 : base(new ScriptNode[] { z, dr },
103 new ArgumentType[] { ArgumentType.Scalar, ArgumentType.Scalar }, Start, Length, Expression)
104 {
105 }
106
110 public override string[] DefaultArgumentNames
111 {
112 get
113 {
114 return new string[] { "z", "dr", "R", "Coefficients", "Palette", "DimX", "DimY" };
115 }
116 }
117
121 public override IElement Evaluate(IElement[] Arguments, Variables Variables)
122 {
123 string ColorExpression = null;
124 SKColor[] Palette;
125 double[] Coefficients = null;
126 Complex[] CoefficientsZ = null;
127 ILambdaExpression f = null;
128 ScriptNode fDef = null;
129 double rc, ic;
130 double dr;
131 Complex R;
132 int dimx, dimy;
133 int c = Arguments.Length;
134 int i = 0;
135 object Obj;
136
137 Obj = Arguments[i++].AssociatedObjectValue;
138 if (Obj is Complex z)
139 {
140 rc = z.Real;
141 ic = z.Imaginary;
142 }
143 else
144 {
145 rc = Expression.ToDouble(Obj);
146 ic = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
147 }
148
149 if (i >= c)
150 throw new ScriptRuntimeException("Insufficient parameters in call to HalleyFractal().", this);
151
152 dr = Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
153
154 if (i < c && ((Obj = Arguments[i].AssociatedObjectValue) is double || Obj is Complex))
155 {
156 R = Expression.ToComplex(Obj);
157 i++;
158 }
159 else
160 {
161 R = Complex.One;
162
163 if (i < c && this.Arguments[i] is null)
164 i++;
165 }
166
167 if (i < c)
168 {
169 if (Arguments[i] is DoubleVector)
170 Coefficients = (double[])Arguments[i++].AssociatedObjectValue;
171 else if (Arguments[i] is ComplexVector)
172 CoefficientsZ = (Complex[])Arguments[i++].AssociatedObjectValue;
173 /*else if (Parameters[i] is RealPolynomial)
174 Coefficients = ((RealPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;
175 else if (Parameters[i] is ComplexPolynomial)
176 CoefficientsZ = ((ComplexPolynomial)Arguments[i++].AssociatedObjectValue).Coefficients;*/
177 else if (Arguments[i] is IVector)
178 {
179 IVector Vector = (IVector)Arguments[i++];
180 int j, d = Vector.Dimension;
181
182 CoefficientsZ = new Complex[d];
183 for (j = 0; j < d; j++)
184 CoefficientsZ[j] = Expression.ToComplex(Vector.GetElement(j).AssociatedObjectValue);
185 }
186 else if (Arguments[i].AssociatedObjectValue is ILambdaExpression)
187 {
188 f = (ILambdaExpression)Arguments[i];
189 if (f.NrArguments != 1)
190 throw new ScriptRuntimeException("Lambda expression in calls to HalleyFractal() must be of one variable.", this);
191
192 fDef = this.Arguments[i++];
193 }
194 else
195 {
196 throw new ScriptRuntimeException("Parameter " + (i + 1).ToString() +
197 " in call to HalleyFractal has to be a vector of numbers, containing coefficients " +
198 "of the polynomial to use. Now it was of type " + Arguments[i].GetType().FullName,
199 this);
200 }
201 }
202 else
203 throw new ScriptRuntimeException("Missing coefficients or lambda expression.", this);
204
205 if (i < c && !(this.Arguments[i] is null) && Arguments[i] is ObjectVector)
206 {
207 ColorExpression = this.Arguments[i].SubExpression;
208 Palette = FractalGraph.ToPalette((ObjectVector)Arguments[i++]);
209 }
210 else
211 {
212 Palette = ColorModels.RandomLinearAnalogousHSL.CreatePalette(128, 4, out int Seed, this, Variables);
213 ColorExpression = "RandomLinearAnalogousHSL(128,4," + Seed.ToString() + ")";
214
215 if (i < c && this.Arguments[i] is null)
216 i++;
217 }
218
219 if (i < c)
220 dimx = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
221 else
222 dimx = 320;
223
224 if (i < c)
225 dimy = (int)Expression.ToDouble(Arguments[i++].AssociatedObjectValue);
226 else
227 dimy = 200;
228
229 if (i < c)
230 {
231 throw new ScriptRuntimeException("Parameter mismatch in call to HalleyFractal(z,dr[,R][,Coefficients][,Palette][,dimx[,dimy]]).",
232 this);
233 }
234
235 if (dimx <= 0 || dimx > 5000 || dimy <= 0 || dimy > 5000)
236 throw new FractalImageSizeScriptException(this);
237
238 if (!(f is null))
239 {
240 return CalcHalley(Variables, rc, ic, dr, R, f, fDef, Palette, dimx, dimy,
241 this, this.FractalZoomScript,
242 new object[] { Palette, dimx, dimy, R, fDef, ColorExpression });
243 }
244 else if (!(CoefficientsZ is null))
245 {
246 return CalcHalley(Variables, rc, ic, dr, R, CoefficientsZ, Palette, dimx, dimy,
247 this, this.FractalZoomScript,
248 new object[] { Palette, dimx, dimy, R, CoefficientsZ, ColorExpression });
249 }
250 else
251 {
252 return CalcHalley(Variables, rc, ic, dr, R, Coefficients, Palette, dimx, dimy,
253 this, this.FractalZoomScript,
254 new object[] { Palette, dimx, dimy, R, Coefficients, ColorExpression });
255 }
256 }
257
258 private string FractalZoomScript(double r, double i, double Size, object State)
259 {
260 object[] Parameters = (object[])State;
261 int DimX = (int)Parameters[1];
262 int DimY = (int)Parameters[2];
263 Complex R = (Complex)Parameters[3];
264 double[] Coefficients = Parameters[4] as double[];
265 string ColorExpression = (string)Parameters[5];
266
267 StringBuilder sb = new StringBuilder();
268
269 sb.Append("HalleyFractal((");
270 sb.Append(Expression.ToString(r));
271 sb.Append(',');
272 sb.Append(Expression.ToString(i));
273 sb.Append("),");
274 sb.Append(Expression.ToString(Size / 4));
275 sb.Append(',');
276 sb.Append(Expression.ToString(R));
277 sb.Append(',');
278
279 if (Parameters[4] is ScriptNode fDef)
280 sb.Append(fDef.SubExpression);
281 else if (Parameters[4] is Complex[] CoefficientsZ)
282 sb.Append(Expression.ToString(CoefficientsZ));
283 else
284 sb.Append(Expression.ToString(Coefficients));
285
286 if (!string.IsNullOrEmpty(ColorExpression))
287 {
288 sb.Append(',');
289 sb.Append(ColorExpression);
290 }
291
292 sb.Append(',');
293 sb.Append(DimX.ToString());
294 sb.Append(',');
295 sb.Append(DimY.ToString());
296 sb.Append(')');
297
298 return sb.ToString();
299 }
300
316 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
317 double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node,
318 FractalZoomScript FractalZoomScript, object State)
319 {
320 byte[] reds;
321 byte[] greens;
322 byte[] blues;
323 double RRe = R.Real;
324 double RIm = R.Imaginary;
325 double r0, i0, r1, i1;
326 double dr, di;
327 double r, i;
328 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
329 double aspect;
330 double Temp;
331 int x, y;
332 int n, N;
333 int index;
334 int Degree = Coefficients.Length - 1;
335 SKColor cl;
336
337 N = Palette.Length;
338 reds = new byte[N];
339 greens = new byte[N];
340 blues = new byte[N];
341
342 for (x = 0; x < N; x++)
343 {
344 cl = Palette[x];
345 reds[x] = cl.Red;
346 greens[x] = cl.Green;
347 blues[x] = cl.Blue;
348 }
349
350 if (Degree < 3)
351 {
352 Array.Resize(ref Coefficients, 4);
353 while (Degree < 3)
354 Coefficients[++Degree] = 0;
355 }
356
357 double[] Prim = new double[Degree];
358 for (x = 1; x <= Degree; x++)
359 Prim[x - 1] = x * Coefficients[x];
360
361 double[] Bis = new double[Degree - 1];
362 for (x = 1; x < Degree; x++)
363 Bis[x - 1] = x * Prim[x];
364
365 Array.Reverse(Bis);
366 Array.Reverse(Prim);
367 Coefficients = (double[])Coefficients.Clone();
368 Array.Reverse(Coefficients);
369
370 int size = Width * Height * 4;
371 double Conv = 1e-10;
372 double Div = 1e10;
373 byte[] rgb = new byte[size];
374
375 rDelta *= 0.5;
376 r0 = rCenter - rDelta;
377 r1 = rCenter + rDelta;
378
379 aspect = ((double)Width) / Height;
380
381 i0 = iCenter - rDelta / aspect;
382 i1 = iCenter + rDelta / aspect;
383
384 dr = (r1 - r0) / Width;
385 di = (i1 - i0) / Height;
386
387 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
388 {
389 for (x = 0, r = r0; x < Width; x++, r += dr)
390 {
391 zr = r;
392 zi = i;
393
394 n = 0;
395 do
396 {
397 // f:
398 zr2 = zi2 = 0;
399 foreach (double C in Coefficients)
400 {
401 Temp = zr2 * zr - zi2 * zi + C;
402 zi2 = zr2 * zi + zi2 * zr;
403 zr2 = Temp;
404 }
405
406 // f':
407 zr3 = zi3 = 0;
408 foreach (double C in Prim)
409 {
410 Temp = zr3 * zr - zi3 * zi + C;
411 zi3 = zr3 * zi + zi3 * zr;
412 zr3 = Temp;
413 }
414
415 // f":
416 zr4 = zi4 = 0;
417 foreach (double C in Bis)
418 {
419 Temp = zr4 * zr - zi4 * zi + C;
420 zi4 = zr4 * zi + zi4 * zr;
421 zr4 = Temp;
422 }
423
424 // 2*f*f'
425
426 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
427 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
428
429 // 2f'^2-f*f"
430
431 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
432 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
433
434 // R*2*f*f'/2f'^2-f*f"
435
436 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
437 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
438 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
439
440 // R*2*f*f'/(2f'^2-f*f")
441 Temp = zr4 * RRe - zi4 * RIm;
442 zi4 = zr4 * RIm + zi4 * RRe;
443 zr4 = Temp;
444
445 zr -= zr4;
446 zi -= zi4;
447
448 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
449 }
450 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
451
452 if (Temp < Conv && n < N)
453 {
454 rgb[index++] = blues[n];
455 rgb[index++] = greens[n];
456 rgb[index++] = reds[n];
457 }
458 else
459 {
460 rgb[index++] = 0;
461 rgb[index++] = 0;
462 rgb[index++] = 0;
463 }
464
465 rgb[index++] = 255;
466 }
467 }
468
469 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
470 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
471 }
472
476 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
477 Complex[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node,
478 FractalZoomScript FractalZoomScript, object State)
479 {
480 byte[] reds;
481 byte[] greens;
482 byte[] blues;
483 double RRe = R.Real;
484 double RIm = R.Imaginary;
485 double r0, i0, r1, i1;
486 double dr, di;
487 double r, i;
488 double zr, zi, zr2, zi2, zr3, zi3, zr4, zi4, zr5, zi5, zr6, zi6;
489 double aspect;
490 double Temp;
491 int x, y;
492 int n, N;
493 int index;
494 int Degree = Coefficients.Length - 1;
495 SKColor cl;
496
497 N = Palette.Length;
498 reds = new byte[N];
499 greens = new byte[N];
500 blues = new byte[N];
501
502 for (x = 0; x < N; x++)
503 {
504 cl = Palette[x];
505 reds[x] = cl.Red;
506 greens[x] = cl.Green;
507 blues[x] = cl.Blue;
508 }
509
510 if (Degree < 3)
511 {
512 Array.Resize(ref Coefficients, 4);
513 while (Degree < 3)
514 Coefficients[++Degree] = Complex.Zero;
515 }
516
517 Complex[] Prim = new Complex[Degree];
518 for (x = 1; x <= Degree; x++)
519 Prim[x - 1] = x * Coefficients[x];
520
521 Complex[] Bis = new Complex[Degree - 1];
522 for (x = 1; x < Degree; x++)
523 Bis[x - 1] = x * Prim[x];
524
525 Array.Reverse(Bis);
526 Array.Reverse(Prim);
527 Coefficients = (Complex[])Coefficients.Clone();
528 Array.Reverse(Coefficients);
529
530 int j, c = Prim.Length;
531 int c2 = c - 1;
532 double[] ReC = new double[c + 1];
533 double[] ImC = new double[c + 1];
534 double[] RePrim = new double[c];
535 double[] ImPrim = new double[c];
536 double[] ReBis = new double[c2];
537 double[] ImBis = new double[c2];
538 Complex z;
539
540 for (j = 0; j < c; j++)
541 {
542 z = Coefficients[j];
543 ReC[j] = z.Real;
544 ImC[j] = z.Imaginary;
545
546 z = Prim[j];
547 RePrim[j] = z.Real;
548 ImPrim[j] = z.Imaginary;
549
550 if (j < c2)
551 {
552 z = Bis[j];
553 ReBis[j] = z.Real;
554 ImBis[j] = z.Imaginary;
555 }
556 }
557
558 z = Coefficients[j];
559 ReC[j] = z.Real;
560 ImC[j] = z.Imaginary;
561
562 int size = Width * Height * 4;
563 double Conv = 1e-10;
564 double Div = 1e10;
565 byte[] rgb = new byte[size];
566
567 rDelta *= 0.5;
568 r0 = rCenter - rDelta;
569 r1 = rCenter + rDelta;
570
571 aspect = ((double)Width) / Height;
572
573 i0 = iCenter - rDelta / aspect;
574 i1 = iCenter + rDelta / aspect;
575
576 dr = (r1 - r0) / Width;
577 di = (i1 - i0) / Height;
578
579 for (y = 0, i = i0, index = 0; y < Height; y++, i += di)
580 {
581 for (x = 0, r = r0; x < Width; x++, r += dr)
582 {
583 zr = r;
584 zi = i;
585
586 n = 0;
587 do
588 {
589 // f:
590 zr2 = zi2 = 0;
591 for (j = 0; j <= c; j++)
592 {
593 Temp = zr2 * zr - zi2 * zi + ReC[j];
594 zi2 = zr2 * zi + zi2 * zr + ImC[j];
595 zr2 = Temp;
596 }
597
598 // f':
599 zr3 = zi3 = 0;
600 for (j = 0; j < c; j++)
601 {
602 Temp = zr3 * zr - zi3 * zi + RePrim[j];
603 zi3 = zr3 * zi + zi3 * zr + ImPrim[j];
604 zr3 = Temp;
605 }
606
607 // f":
608 zr4 = zi4 = 0;
609 for (j = 0; j < c2; j++)
610 {
611 Temp = zr4 * zr - zi4 * zi + ReBis[j];
612 zi4 = zr4 * zi + zi4 * zr + ImBis[j];
613 zr4 = Temp;
614 }
615
616 // 2*f*f'
617
618 zr5 = 2 * (zr2 * zr3 - zi2 * zi3);
619 zi5 = 2 * (zr2 * zi3 + zi2 * zr3);
620
621 // 2f'^2-f*f"
622
623 zr6 = 2 * (zr3 * zr3 - zi3 * zi3) - (zr2 * zr4 - zi2 * zi4);
624 zi6 = 4 * zr3 * zi3 - (zr2 * zi4 + zr4 * zi2);
625
626 // R*2*f*f'/2f'^2-f*f"
627
628 Temp = 1.0 / (zr6 * zr6 + zi6 * zi6);
629 zr4 = (zr5 * zr6 + zi5 * zi6) * Temp;
630 zi4 = (zi5 * zr6 - zr5 * zi6) * Temp;
631
632 // R*2*f*f'/(2f'^2-f*f")
633 Temp = zr4 * RRe - zi4 * RIm;
634 zi4 = zr4 * RIm + zi4 * RRe;
635 zr4 = Temp;
636
637 zr -= zr4;
638 zi -= zi4;
639
640 Temp = Math.Sqrt(zr4 * zr4 + zi4 * zi4);
641 }
642 while ((Temp > Conv) && (Temp < Div) && (n++ < N));
643
644 if (Temp < Conv && n < N)
645 {
646 rgb[index++] = blues[n];
647 rgb[index++] = greens[n];
648 rgb[index++] = reds[n];
649 }
650 else
651 {
652 rgb[index++] = 0;
653 rgb[index++] = 0;
654 rgb[index++] = 0;
655 }
656
657 rgb[index++] = 255;
658 }
659 }
660
661 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
662 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
663 }
664
668 public static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R,
669 ILambdaExpression f, ScriptNode _, SKColor[] Palette, int Width, int Height, ScriptNode Node,
670 FractalZoomScript FractalZoomScript, object State)
671 {
672 byte[] reds;
673 byte[] greens;
674 byte[] blues;
675 double RRe = R.Real;
676 double RIm = R.Imaginary;
677 double r0, i0, r1, i1;
678 double dr, di;
679 double r, i;
680 double aspect;
681 int x, y;
682 int n, N;
683 SKColor cl;
684
685 N = Palette.Length;
686 reds = new byte[N];
687 greens = new byte[N];
688 blues = new byte[N];
689
690 for (x = 0; x < N; x++)
691 {
692 cl = Palette[x];
693 reds[x] = cl.Red;
694 greens[x] = cl.Green;
695 blues[x] = cl.Blue;
696 }
697
698 Variables v = new Variables();
699 Variables.CopyTo(v);
700
701 string ParameterName;
702 if (!(f is IDifferentiable Differentiable) ||
703 !(Differentiable.Differentiate(ParameterName = Differentiable.DefaultVariableName, v) is ILambdaExpression fPrim))
704 {
705 throw new ScriptRuntimeException("Lambda expression not differentiable.", Node);
706 }
707
708 if (!(fPrim is IDifferentiable Differentiable2) ||
709 !(Differentiable2.Differentiate(ParameterName, v) is ILambdaExpression fBis))
710 {
711 throw new ScriptRuntimeException("Lambda expression not twice differentiable.", Node);
712 }
713
714 int size = Width * Height * 4;
715 double Conv = 1e-10;
716 double Div = 1e10;
717 byte[] rgb = new byte[size];
718
719 Complex[] Row;
720 Complex[] Row2;
721 Complex[] Row3;
722 Complex[] Row4;
723 int[] Offset;
724 IElement[] P = new IElement[1];
725 int j, c, x2;
726 IElement Obj, Obj2, Obj3;
727 double Mod;
728 Complex z, z2, z3;
729 Complex R2 = R * 2;
730
731 rDelta *= 0.5;
732 r0 = rCenter - rDelta;
733 r1 = rCenter + rDelta;
734
735 aspect = ((double)Width) / Height;
736
737 i0 = iCenter - rDelta / aspect;
738 i1 = iCenter + rDelta / aspect;
739
740 dr = (r1 - r0) / Width;
741 di = (i1 - i0) / Height;
742
743 for (y = 0, i = i0; y < Height; y++, i += di)
744 {
745 Row = new Complex[Width];
746 Offset = new int[Width];
747
748 c = Width;
749 for (x = 0, x2 = y * Width * 4, r = r0; x < Width; x++, r += dr, x2 += 4)
750 {
751 Row[x] = new Complex(r, i);
752 Offset[x] = x2;
753 }
754
755 n = 0;
756 while (n < N && c > 0)
757 {
758 n++;
759 P[0] = new ComplexVector(Row);
760 Obj = f.Evaluate(P, v);
761 Obj2 = fPrim.Evaluate(P, v);
762 Obj3 = fBis.Evaluate(P, v);
763 Row2 = Obj.AssociatedObjectValue as Complex[];
764 Row3 = Obj2.AssociatedObjectValue as Complex[];
765 Row4 = Obj3.AssociatedObjectValue as Complex[];
766
767 if (Row2 is null || Row3 is null || Row4 is null)
768 {
769 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
770 "and return complex vectors of equal length. Type returned: " +
771 Obj.GetType().FullName + ", " + Obj2.GetType().FullName + " and " + Obj3.GetType().FullName,
772 Node);
773 }
774 else if (Row2.Length != c || Row3.Length != c)
775 {
776 throw new ScriptRuntimeException("Lambda expression (and its first and second derivative) must be able to accept complex vectors, " +
777 "and return complex vectors of equal length. Length returned: " +
778 Row2.Length.ToString() + ", " + Row3.Length.ToString() + " and " + Row4.Length.ToString() +
779 ". Expected: " + c.ToString(), Node);
780 }
781
782 for (x = x2 = 0; x < c; x++)
783 {
784 j = Offset[x];
785 z = Row2[x];
786 z2 = Row3[x];
787 z3 = Row4[x];
788
789 z = R2 * z * z2 / (2 * z2 * z2 - z * z3);
790 Row[x] -= z;
791
792 Mod = z.Magnitude;
793
794 if (Mod > Conv && Mod < Div)
795 {
796 if (x != x2)
797 Offset[x2] = j;
798
799 x2++;
800 }
801 else
802 {
803 if (n >= N)
804 {
805 rgb[j++] = 0;
806 rgb[j++] = 0;
807 rgb[j++] = 0;
808 }
809 else
810 {
811 rgb[j++] = blues[n];
812 rgb[j++] = greens[n];
813 rgb[j++] = reds[n];
814 }
815
816 rgb[j++] = 255;
817 }
818 }
819
820 if (x2 < x)
821 {
822 Array.Resize(ref Row, x2);
823 Array.Resize(ref Offset, x2);
824 c = x2;
825 }
826 }
827 }
828
829 PixelInformation Pixels = new PixelInformationRaw(SKColorType.Bgra8888, rgb, Width, Height, Width << 2);
830 return new FractalGraph(Variables, Pixels, r0, i0, r1, i1, rDelta * 2, true, Node, FractalZoomScript, State);
831 }
832
836 public override string FunctionName => nameof(HalleyFractal);
837 }
838}
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.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:70
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:101
Waher.Script.Fractals.ComplexFractals.HalleyFractal.CalcHalley
static FractalGraph CalcHalley(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: HalleyFractal.cs:476
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:59
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:92
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, ScriptNode Palette, ScriptNode DimX, ScriptNode DimY, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:48
Waher.Script.Fractals.ComplexFractals.HalleyFractal.HalleyFractal
HalleyFractal(ScriptNode z, ScriptNode dr, ScriptNode R, ScriptNode Coefficients, int Start, int Length, Expression Expression)
TODO
Definition: HalleyFractal.cs:81
Waher.Script.Fractals.ComplexFractals.HalleyFractal.CalcHalley
static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, double[] Coefficients, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
Calculates a Halley Fractal
Definition: HalleyFractal.cs:316
Waher.Script.Fractals.ComplexFractals.HalleyFractal.Evaluate
override IElement Evaluate(IElement[] Arguments, Variables Variables)
TODO
Definition: HalleyFractal.cs:121
Waher.Script.Fractals.ComplexFractals.HalleyFractal.CalcHalley
static FractalGraph CalcHalley(Variables Variables, double rCenter, double iCenter, double rDelta, Complex R, ILambdaExpression f, ScriptNode _, SKColor[] Palette, int Width, int Height, ScriptNode Node, FractalZoomScript FractalZoomScript, object State)
TODO
Definition: HalleyFractal.cs:668
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