// --------------------------------------------------------------------------------------------------------------------
//
// Copyright (c) 2014 OxyPlot contributors
//
//
// Appends the specified target.
//
// --------------------------------------------------------------------------------------------------------------------
namespace ExampleLibrary
{
using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Reflection;
using System.Threading;
using System.Threading.Tasks;
using System.Xml.Serialization;
using OxyPlot;
using OxyPlot.Annotations;
using OxyPlot.Axes;
using OxyPlot.Series;
using OxyPlot.Legends;
using System.Linq;
[Examples("Misc")]
public static class MiscExamples
{
[Example("Numeric ODE solvers (y'=y)")]
public static PlotModel NumericOdeSolvers1()
{
return NumericOdeSolvers("Numeric ODE solvers", "y'=y, y(0)=1", 0, 1, Math.Exp, (t, y) => y);
}
[Example("Numeric ODE solvers (y'=x)")]
public static PlotModel NumericOdeSolvers2()
{
return NumericOdeSolvers("Numeric ODE solvers", "y'=x, y(0)=0", 0, 0, t => 0.5 * t * t, (t, y) => t);
}
[Example("Numeric ODE solvers (y'=cos(x))")]
public static PlotModel NumericOdeSolvers3()
{
return NumericOdeSolvers("Numeric ODE solvers", "y'=cos(x), y(0)=0", 0, 0, Math.Sin, (t, y) => Math.Cos(t));
}
public static PlotModel NumericOdeSolvers(
string title,
string subtitle,
double t0,
double y0,
Func exact,
Func f)
{
var model = new PlotModel
{
Title = title,
Subtitle = subtitle,
};
var l = new Legend
{
LegendPosition = LegendPosition.BottomCenter,
LegendPlacement = LegendPlacement.Outside,
LegendOrientation = LegendOrientation.Horizontal
};
model.Legends.Add(l);
model.Series.Add(new FunctionSeries(exact, 0, 4, 100) { Title = "Exact solution", StrokeThickness = 5 });
var eulerSeries = new LineSeries
{
Title = "Euler, h=0.25",
MarkerType = MarkerType.Circle,
MarkerFill = OxyColors.Black,
};
eulerSeries.Points.AddRange(Euler(f, t0, y0, 4, 0.25));
model.Series.Add(eulerSeries);
//model.Series.Add(new LineSeries("Euler, h=1")
// {
// MarkerType = MarkerType.Circle,
// MarkerFill = OxyColors.Black,
// Points = Euler(f, t0, y0, 4, 1)
// });
var heunSeries = new LineSeries
{
Title = "Heun, h=0.25",
MarkerType = MarkerType.Circle,
MarkerFill = OxyColors.Black,
};
heunSeries.Points.AddRange(Heun(f, t0, y0, 4, 0.25));
model.Series.Add(heunSeries);
var midpointSeries = new LineSeries
{
Title = "Midpoint, h=0.25",
MarkerType = MarkerType.Circle,
MarkerFill = OxyColors.Black,
};
midpointSeries.Points.AddRange(Midpoint(f, t0, y0, 4, 0.25));
model.Series.Add(midpointSeries);
var rkSeries = new LineSeries
{
Title = "RK4, h=0.25",
MarkerType = MarkerType.Circle,
MarkerFill = OxyColors.Black,
};
rkSeries.Points.AddRange(RungeKutta4(f, t0, y0, 4, 0.25));
model.Series.Add(rkSeries);
//model.Series.Add(new LineSeries("RK4, h=1")
//{
// MarkerType = MarkerType.Circle,
// MarkerFill = OxyColors.Black,
// Points = RungeKutta4(f, t0, y0, 4, 1)
//});
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left });
return model;
}
private static List Euler(
Func f, double t0, double y0, double t1, double h)
{
var points = new List();
double y = y0;
for (double t = t0; t < t1 + h / 2; t += h)
{
points.Add(new DataPoint(t, y));
y += h * f(t, y);
}
return points;
}
private static IList Heun(Func f, double t0, double y0, double t1, double h)
{
var points = new List();
double y = y0;
for (double t = t0; t < t1 + h / 2; t += h)
{
points.Add(new DataPoint(t, y));
double ytilde = y + h * f(t, y);
y = y + h / 2 * (f(t, y) + f(t + h, ytilde));
}
return points;
}
private static List Midpoint(
Func f, double t0, double y0, double t1, double h)
{
var points = new List();
double y = y0;
for (double t = t0; t < t1 + h / 2; t += h)
{
points.Add(new DataPoint(t, y));
y += h * f(t + h / 2, y + h / 2 * f(t, y));
}
return points;
}
private static List RungeKutta4(
Func f, double t0, double y0, double t1, double h)
{
var points = new List();
double y = y0;
for (double t = t0; t < t1 + h / 2; t += h)
{
points.Add(new DataPoint(t, y));
double k1 = h * f(t, y);
double k2 = h * f(t + h / 2, y + k1 / 2);
double k3 = h * f(t + h / 2, y + k2 / 2);
double k4 = h * f(t + h, y + k3);
y += (k1 + 2 * k2 + 2 * k3 + k4) / 6;
}
return points;
}
[Example("MatrixSeries (chemical process simulation problem)")]
public static PlotModel MatrixSeriesWest0479()
{
// http://www.cise.ufl.edu/research/sparse/matrices/HB/west0479
var model = new PlotModel();
double[,] matrix = null;
using (var reader = new StreamReader(typeof(MiscExamples).GetTypeInfo().Assembly.GetManifestResourceStream("ExampleLibrary.Resources.west0479.mtx")))
{
while (!reader.EndOfStream)
{
var line = reader.ReadLine();
if (line.StartsWith("%"))
{
continue;
}
var v = line.Split(' ');
if (matrix == null)
{
int m = int.Parse(v[0]);
int n = int.Parse(v[1]);
matrix = new double[m, n];
continue;
}
int i = int.Parse(v[0]) - 1;
int j = int.Parse(v[1]) - 1;
matrix[i, j] = double.Parse(v[2], CultureInfo.InvariantCulture);
}
}
// Reverse the vertical axis
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, StartPosition = 1, EndPosition = 0 });
model.Axes.Add(new LinearAxis { Position = AxisPosition.Bottom });
model.Series.Add(new MatrixSeries { Matrix = matrix, ShowDiagonal = true });
return model;
}
[Example("Train schedule")]
public static PlotModel TrainSchedule()
{
//// http://www.edwardtufte.com/tufte/books_vdqi
//// http://marlenacompton.com/?p=103
//// http://mbostock.github.com/protovis/ex/caltrain.html
//// http://en.wikipedia.org/wiki/%C3%89tienne-Jules_Marey
//// http://mbostock.github.com/protovis/ex/marey-train-schedule.jpg
//// http://c82.net/posts.php?id=66
var model = new PlotModel
{
Title = "Train schedule",
Subtitle = "Bergensbanen (Oslo-Bergen, Norway)",
IsLegendVisible = false,
PlotAreaBorderColor = OxyColors.LightGray,
};
var distanceAxis = new LinearAxis
{
Position = AxisPosition.Left,
Minimum = -20,
Maximum = 540,
Title = "Distance from Oslo S",
IsAxisVisible = true,
StringFormat = "0",
};
model.Axes.Add(distanceAxis);
var stationAxis = new CustomAxis
{
MajorGridlineStyle = LineStyle.Solid,
MajorGridlineColor = OxyColors.LightGray,
Minimum = distanceAxis.Minimum,
Maximum = distanceAxis.Maximum,
Position = AxisPosition.Right,
IsPanEnabled = false,
IsZoomEnabled = false,
MajorTickSize = 0,
};
distanceAxis.AxisChanged += (sender, e) =>
{
stationAxis.Minimum = distanceAxis.ActualMinimum;
stationAxis.Maximum = distanceAxis.ActualMaximum;
};
model.Axes.Add(stationAxis);
model.Axes.Add(
new TimeSpanAxis
{
Position = AxisPosition.Bottom,
Minimum = 0,
Maximum = TimeSpanAxis.ToDouble(TimeSpan.FromHours(24)),
StringFormat = "hh",
Title = "Time",
MajorStep = TimeSpanAxis.ToDouble(TimeSpan.FromHours(1)),
MinorStep = TimeSpanAxis.ToDouble(TimeSpan.FromMinutes(10)),
TickStyle = TickStyle.None,
MajorGridlineStyle = LineStyle.Solid,
MajorGridlineColor = OxyColors.LightGray,
MinorGridlineStyle = LineStyle.Solid,
MinorGridlineColor = OxyColor.FromArgb(255, 240, 240, 240)
});
// Read the train schedule from a .csv resource
using (var reader = new StreamReader(GetResourceStream("Bergensbanen.csv")))
{
string header = reader.ReadLine();
var headerFields = header.Split(';');
int lines = headerFields.Length - 3;
var stations = new LineSeries()
{
StrokeThickness = 0,
MarkerType = MarkerType.Circle,
MarkerFill = OxyColor.FromAColor(200, OxyColors.Black),
MarkerSize = 4,
};
// Add the line series for each train line
var series = new LineSeries[lines];
for (int i = 0; i < series.Length; i++)
{
series[i] = new LineSeries
{
Title = headerFields[3 + i],
Color =
OxyColor.FromAColor(
180, OxyColors.Black),
StrokeThickness = 2,
TrackerFormatString =
"Train {0}\nTime: {2}\nDistance from Oslo S: {4:0.0} km",
};
model.Series.Add(series[i]);
}
// Parse the train schedule
while (!reader.EndOfStream)
{
var line = reader.ReadLine();
// skip comments
if (line == null || line.StartsWith("//"))
{
continue;
}
var fields = line.Split(';');
double x = double.Parse(fields[1], CultureInfo.InvariantCulture);
if (!string.IsNullOrEmpty(fields[0]))
{
stationAxis.MajorTicks.Add(x);
stationAxis.Labels.Add(fields[0]);
}
for (int i = 0; i < series.Length; i++)
{
if (string.IsNullOrEmpty(fields[i + 3]))
{
continue;
}
// Convert time from hhmm to a time span
int hhmm = int.Parse(fields[i + 3]);
var span = new TimeSpan(0, hhmm / 100, (hhmm % 100), 0);
double t = TimeSpanAxis.ToDouble(span);
// Add the point to the line
series[i].Points.Add(new DataPoint(t, x));
// Add the point for the station
stations.Points.Add(new DataPoint(t, x));
}
}
// add points and NaN (to make a line break) when passing midnight
double tmidnight = TimeSpanAxis.ToDouble(TimeSpan.FromHours(24));
foreach (LineSeries s in model.Series)
{
for (int i = 0; i + 1 < s.Points.Count; i++)
{
if (Math.Abs(s.Points[i].X - s.Points[i + 1].X) > tmidnight / 2)
{
double x0 = s.Points[i].X;
if (x0 > tmidnight / 2)
{
x0 -= tmidnight;
}
double x1 = s.Points[i + 1].X;
if (x1 > tmidnight / 2)
{
x1 -= tmidnight;
}
double y = s.Points[i].Y + (s.Points[i + 1].Y - s.Points[i].Y) / (x1 - x0) * (0 - x0);
s.Points.Insert(i + 1, new DataPoint(x0 < x1 ? 0 : tmidnight, y));
s.Points.Insert(i + 1, new DataPoint(double.NaN, y));
s.Points.Insert(i + 1, new DataPoint(x0 < x1 ? tmidnight : 0, y));
i += 3;
}
}
}
model.Series.Add(stations);
}
return model;
}
[Example("La Linea (AreaSeries)")]
public static PlotModel LaLineaAreaSeries()
{
// http://en.wikipedia.org/wiki/La_Linea_(TV_series)
var model = new PlotModel
{
Title = "La Linea",
PlotType = PlotType.Cartesian,
Background = OxyColor.FromRgb(84, 98, 207)
};
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -500, Maximum = 1000 });
var series1 = new AreaSeries { Fill = OxyColors.White, StrokeThickness = 0 };
series1.Points.Append(GetLineaPoints());
model.Series.Add(series1);
return model;
}
[Example("La Linea (LineSeries)")]
public static PlotModel LaLinea()
{
// http://en.wikipedia.org/wiki/La_Linea_(TV_series)
var model = new PlotModel
{
Title = "La Linea",
PlotType = PlotType.Cartesian,
Background = OxyColor.FromRgb(84, 98, 207)
};
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -500, Maximum = 1000 });
var series1 = new LineSeries { Color = OxyColors.White, StrokeThickness = 1.5 };
series1.Points.Append(GetLineaPoints());
model.Series.Add(series1);
return model;
}
///
/// Appends the specified target.
///
///
/// The target.
/// The source.
public static void Append(this IList target, IEnumerable source)
{
foreach (var item in source)
{
target.Add(item);
}
}
private static IEnumerable GetLineaPoints()
{
var points = new List();
// The original image was vectorized by http://www.autotracer.org/
// Then inkscape was used to convert from svg to xaml http://inkscape.org/
// The xaml geometry was imported by Geometry.Parse and converted to a polyline
// by Geometry.GetFlattenedPathGeometry();
// The resulting points were output to the following code:
points.Add(new DataPoint(589.3649979, 16.10595703));
points.Add(new DataPoint(437.9979935, 16.10595703));
points.Add(new DataPoint(400.4249954, 16.10595703));
points.Add(new DataPoint(399.1255264, 16.05047607));
points.Add(new DataPoint(397.463356, 15.92333984));
points.Add(new DataPoint(393.5852432, 15.69073486));
points.Add(new DataPoint(389.8589859, 15.88067627));
points.Add(new DataPoint(388.3866653, 16.28186035));
points.Add(new DataPoint(387.3529739, 16.96594238));
points.Add(new DataPoint(386.8373489, 18.53930664));
points.Add(new DataPoint(387.2163773, 20.51794434));
points.Add(new DataPoint(387.9814529, 22.51843262));
points.Add(new DataPoint(388.6240005, 24.15698242));
points.Add(new DataPoint(395.958992, 45.09094238));
points.Add(new DataPoint(399.2686234, 54.89562988));
points.Add(new DataPoint(402.1330338, 64.90338135));
points.Add(new DataPoint(404.5822525, 75.06884766));
points.Add(new DataPoint(406.6462479, 85.34680176));
points.Add(new DataPoint(409.7385635, 106.0593262));
points.Add(new DataPoint(411.6500015, 126.6789551));
points.Add(new DataPoint(412.0961685, 137.0930786));
points.Add(new DataPoint(412.0253677, 147.4713135));
points.Add(new DataPoint(411.4655228, 157.8103638));
points.Add(new DataPoint(410.4446182, 168.1069336));
points.Add(new DataPoint(408.9906387, 178.3577881));
points.Add(new DataPoint(407.1315689, 188.5595703));
points.Add(new DataPoint(404.8953629, 198.7091064));
points.Add(new DataPoint(402.3099747, 208.8029785));
points.Add(new DataPoint(392.9860001, 237.2509766));
points.Add(new DataPoint(392.1175613, 240.0527954));
points.Add(new DataPoint(391.2060013, 243.0959473));
points.Add(new DataPoint(390.5509415, 246.1691284));
points.Add(new DataPoint(390.4520035, 249.0609741));
points.Add(new DataPoint(391.406044, 252.6694336));
points.Add(new DataPoint(393.1980057, 256.0982056));
points.Add(new DataPoint(395.3566971, 259.3631287));
points.Add(new DataPoint(397.4109879, 262.47995));
points.Add(new DataPoint(411.7649918, 287.7079468));
points.Add(new DataPoint(426.5997696, 312.9102173));
points.Add(new DataPoint(441.8913651, 337.8200684));
points.Add(new DataPoint(457.3402786, 362.6333923));
points.Add(new DataPoint(472.6469803, 387.5459595));
points.Add(new DataPoint(478.0007401, 395.7557983));
points.Add(new DataPoint(483.6958694, 403.8400879));
points.Add(new DataPoint(489.2894974, 411.9628296));
points.Add(new DataPoint(494.3389969, 420.2879639));
points.Add(new DataPoint(494.9800491, 421.8480225));
points.Add(new DataPoint(495.4455032, 423.6903687));
points.Add(new DataPoint(496.1577225, 427.7724609));
points.Add(new DataPoint(497.0915604, 431.6355591));
points.Add(new DataPoint(497.8341141, 433.2041321));
points.Add(new DataPoint(498.8629837, 434.3809509));
points.Add(new DataPoint(500.0935135, 434.9877625));
points.Add(new DataPoint(501.7391434, 435.3059082));
points.Add(new DataPoint(505.7623367, 435.3148193));
points.Add(new DataPoint(509.9061356, 434.8848267));
points.Add(new DataPoint(511.7024612, 434.6542969));
points.Add(new DataPoint(513.1439896, 434.4929504));
points.Add(new DataPoint(520.0768509, 434.1251831));
points.Add(new DataPoint(527.3961258, 434.1952209));
points.Add(new DataPoint(534.6892776, 434.728363));
points.Add(new DataPoint(541.544014, 435.7499695));
points.Add(new DataPoint(544.2357864, 436.3025513));
points.Add(new DataPoint(547.021492, 437.0792236));
points.Add(new DataPoint(549.6099319, 438.2590027));
points.Add(new DataPoint(551.7099686, 440.0209656));
points.Add(new DataPoint(552.7028275, 441.4446106));
points.Add(new DataPoint(553.2691116, 442.791626));
points.Add(new DataPoint(553.4498978, 444.0619202));
points.Add(new DataPoint(553.2864456, 445.2554626));
points.Add(new DataPoint(552.0910721, 447.4119873));
points.Add(new DataPoint(550.0122147, 449.2607117));
points.Add(new DataPoint(547.3790359, 450.8010864));
points.Add(new DataPoint(544.5206985, 452.0325928));
points.Add(new DataPoint(541.766304, 452.9547119));
points.Add(new DataPoint(539.445015, 453.5669556));
points.Add(new DataPoint(539.445015, 454.6409607));
points.Add(new DataPoint(542.6554031, 455.4246521));
points.Add(new DataPoint(546.0063553, 455.8735962));
points.Add(new DataPoint(549.2799149, 456.4869385));
points.Add(new DataPoint(552.2580032, 457.7639465));
points.Add(new DataPoint(554.3335648, 459.5966797));
points.Add(new DataPoint(555.6600418, 461.8208313));
points.Add(new DataPoint(556.278389, 464.282959));
points.Add(new DataPoint(556.2294998, 466.8295898));
points.Add(new DataPoint(555.55439, 469.307251));
points.Add(new DataPoint(554.2939529, 471.5625));
points.Add(new DataPoint(552.4892044, 473.4418945));
points.Add(new DataPoint(550.1809769, 474.7919617));
points.Add(new DataPoint(547.1414261, 475.8059387));
points.Add(new DataPoint(543.8482132, 476.5288391));
points.Add(new DataPoint(537.2979813, 477.0559692));
points.Add(new DataPoint(535.5239944, 476.8666077));
points.Add(new DataPoint(533.5114822, 476.5535889));
points.Add(new DataPoint(531.5334549, 476.4162598));
points.Add(new DataPoint(529.8629837, 476.7539673));
points.Add(new DataPoint(529.0471268, 477.3421631));
points.Add(new DataPoint(528.5394363, 478.1289673));
points.Add(new DataPoint(528.1448441, 480.0927124));
points.Add(new DataPoint(528.071846, 482.2338257));
points.Add(new DataPoint(527.7129593, 484.1409607));
points.Add(new DataPoint(526.901741, 485.4877014));
points.Add(new DataPoint(525.8139114, 486.4950867));
points.Add(new DataPoint(523.0528641, 487.6643372));
points.Add(new DataPoint(519.9188919, 487.9933777));
points.Add(new DataPoint(516.9010086, 487.8269653));
points.Add(new DataPoint(511.7325516, 486.9451599));
points.Add(new DataPoint(506.4563065, 485.4539185));
points.Add(new DataPoint(501.155159, 483.4500427));
points.Add(new DataPoint(495.912117, 481.0302124));
points.Add(new DataPoint(485.9321365, 475.3295898));
points.Add(new DataPoint(481.3610916, 472.2423096));
points.Add(new DataPoint(477.1800003, 469.125946));
points.Add(new DataPoint(465.3709793, 459.3179626));
points.Add(new DataPoint(464.3509598, 458.3116455));
points.Add(new DataPoint(463.1867142, 457.1624451));
points.Add(new DataPoint(461.9141312, 456.2180176));
points.Add(new DataPoint(460.5689774, 455.8259583));
points.Add(new DataPoint(459.6923904, 456.0762939));
points.Add(new DataPoint(458.8656693, 456.7503662));
points.Add(new DataPoint(457.3631058, 458.907959));
points.Add(new DataPoint(456.063179, 461.3753052));
points.Add(new DataPoint(455.4898758, 462.436554));
points.Add(new DataPoint(454.9679642, 463.2289734));
points.Add(new DataPoint(453.0795364, 465.3183289));
points.Add(new DataPoint(450.8528519, 467.2734985));
points.Add(new DataPoint(448.3575516, 468.9848328));
points.Add(new DataPoint(445.6630936, 470.3425903));
points.Add(new DataPoint(442.83918, 471.2370605));
points.Add(new DataPoint(439.9552689, 471.5585938));
points.Add(new DataPoint(437.0810318, 471.1974487));
points.Add(new DataPoint(434.2859879, 470.0439453));
points.Add(new DataPoint(432.4744034, 468.6621399));
points.Add(new DataPoint(431.3244705, 467.0726013));
points.Add(new DataPoint(430.7551956, 465.3302612));
points.Add(new DataPoint(430.6856155, 463.4900818));
points.Add(new DataPoint(431.0347672, 461.6070251));
points.Add(new DataPoint(431.7216873, 459.7360229));
points.Add(new DataPoint(433.7849808, 456.2499695));
points.Add(new DataPoint(438.1093216, 450.118988));
points.Add(new DataPoint(441.4749832, 444.3893433));
points.Add(new DataPoint(444.0351639, 438.28302));
points.Add(new DataPoint(445.0610428, 434.845459));
points.Add(new DataPoint(445.9430008, 431.0219727));
points.Add(new DataPoint(446.6270218, 428.7687378));
points.Add(new DataPoint(447.4476395, 426.4767151));
points.Add(new DataPoint(447.9032059, 424.1760559));
points.Add(new DataPoint(447.492012, 421.8969727));
points.Add(new DataPoint(445.6156082, 418.2295837));
points.Add(new DataPoint(443.3608475, 414.6139832));
points.Add(new DataPoint(438.1008682, 407.5364685));
points.Add(new DataPoint(432.48069, 400.6614685));
points.Add(new DataPoint(427.2689896, 393.9859619));
points.Add(new DataPoint(389.1699905, 339.2359619));
points.Add(new DataPoint(374.5550003, 318.3009644));
points.Add(new DataPoint(372.5515823, 314.8404541));
points.Add(new DataPoint(370.2787552, 310.9485779));
points.Add(new DataPoint(367.7467728, 307.2946777));
points.Add(new DataPoint(366.3868484, 305.7660828));
points.Add(new DataPoint(364.9659805, 304.5479736));
points.Add(new DataPoint(363.9477615, 304.0406799));
points.Add(new DataPoint(363.082222, 304.0159912));
points.Add(new DataPoint(361.6236038, 304.9024658));
points.Add(new DataPoint(360.2191849, 306.1834412));
points.Add(new DataPoint(359.4213638, 306.651886));
points.Add(new DataPoint(358.4979935, 306.8349609));
points.Add(new DataPoint(356.6694107, 306.4464722));
points.Add(new DataPoint(354.9371109, 305.5308228));
points.Add(new DataPoint(353.2544937, 304.4515076));
points.Add(new DataPoint(351.5749893, 303.5719604));
points.Add(new DataPoint(343.4895706, 301.1234131));
points.Add(new DataPoint(335.0169449, 299.8048401));
points.Add(new DataPoint(326.3076553, 299.5128174));
points.Add(new DataPoint(317.5122147, 300.1439514));
points.Add(new DataPoint(308.7811966, 301.5948486));
points.Add(new DataPoint(300.2651443, 303.762085));
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points.Add(new DataPoint(131.9611282, 351.0648499));
points.Add(new DataPoint(139.1423569, 346.2359619));
points.Add(new DataPoint(146.0040054, 341.5639648));
points.Add(new DataPoint(153.3126602, 336.4172363));
points.Add(new DataPoint(160.8510056, 331.6148376));
points.Add(new DataPoint(176.060997, 322.2139587));
points.Add(new DataPoint(223.2120132, 292.0619507));
points.Add(new DataPoint(241.0090103, 281.0089722));
points.Add(new DataPoint(244.4554214, 278.2832642));
points.Add(new DataPoint(248.0213699, 275.5827026));
points.Add(new DataPoint(251.8383865, 273.5125122));
points.Add(new DataPoint(253.8821487, 272.9029541));
points.Add(new DataPoint(256.038002, 272.677948));
points.Add(new DataPoint(255.5765762, 275.73526));
points.Add(new DataPoint(254.4421158, 278.3285828));
points.Add(new DataPoint(252.9171219, 280.7803345));
points.Add(new DataPoint(251.2840042, 283.4129639));
points.Add(new DataPoint(249.1513138, 287.4288635));
points.Add(new DataPoint(247.2273636, 291.7029724));
points.Add(new DataPoint(245.725502, 296.1263123));
points.Add(new DataPoint(244.8589859, 300.5899658));
points.Add(new DataPoint(244.4298477, 307.2876587));
points.Add(new DataPoint(244.5635757, 313.9535828));
points.Add(new DataPoint(245.2291336, 320.570282));
points.Add(new DataPoint(246.3955154, 327.1204224));
points.Add(new DataPoint(248.0315933, 333.5866089));
points.Add(new DataPoint(250.1063919, 339.951416));
points.Add(new DataPoint(252.5888138, 346.1975098));
points.Add(new DataPoint(255.4478531, 352.3074646));
points.Add(new DataPoint(262.1715469, 364.0494385));
points.Add(new DataPoint(270.0290298, 375.0382385));
points.Add(new DataPoint(278.7719803, 385.1347656));
points.Add(new DataPoint(288.1519852, 394.1999512));
points.Add(new DataPoint(294.92173, 399.6752014));
points.Add(new DataPoint(302.1428604, 404.5257263));
points.Add(new DataPoint(309.7718277, 408.7135925));
points.Add(new DataPoint(317.7649918, 412.2009583));
points.Add(new DataPoint(322.0982132, 413.5901184));
points.Add(new DataPoint(326.4935989, 414.2129517));
points.Add(new DataPoint(328.6687698, 414.1019592));
points.Add(new DataPoint(330.8044205, 413.6372986));
points.Add(new DataPoint(332.8823013, 412.7649841));
points.Add(new DataPoint(334.8839798, 411.4309692));
points.Add(new DataPoint(336.700325, 409.4726868));
points.Add(new DataPoint(337.756813, 407.2593689));
points.Add(new DataPoint(338.1652908, 404.8675537));
points.Add(new DataPoint(338.0374832, 402.3738403));
points.Add(new DataPoint(337.4851761, 399.8547668));
points.Add(new DataPoint(336.6201553, 397.3868713));
points.Add(new DataPoint(334.3989944, 392.9109497));
points.Add(new DataPoint(331.2719803, 388.0760193));
points.Add(new DataPoint(327.7468643, 383.5949097));
points.Add(new DataPoint(319.7087479, 375.5498352));
points.Add(new DataPoint(310.6974869, 368.4870605));
points.Add(new DataPoint(301.1259842, 362.1179504));
points.Add(new DataPoint(289.341011, 355.3789673));
points.Add(new DataPoint(288.3749161, 354.5166321));
points.Add(new DataPoint(287.4871292, 353.3829651));
points.Add(new DataPoint(287.1665115, 352.1690369));
points.Add(new DataPoint(287.3716812, 351.5917053));
points.Add(new DataPoint(287.9019852, 351.0659485));
points.Add(new DataPoint(290.0786819, 350.5000305));
points.Add(new DataPoint(292.8593826, 350.8098145));
points.Add(new DataPoint(295.6623917, 351.5259399));
points.Add(new DataPoint(297.9060135, 352.1789551));
points.Add(new DataPoint(300.6676102, 353.0059814));
points.Add(new DataPoint(303.7700882, 354.0613708));
points.Add(new DataPoint(310.5398636, 356.3453369));
points.Add(new DataPoint(313.9782486, 357.3178101));
points.Add(new DataPoint(317.2997208, 358.0065918));
points.Add(new DataPoint(320.3897781, 358.2836609));
points.Add(new DataPoint(323.1339798, 358.0209656));
points.Add(new DataPoint(311.4509048, 349.4853516));
points.Add(new DataPoint(299.2507401, 341.6953125));
points.Add(new DataPoint(286.5124283, 334.8171387));
points.Add(new DataPoint(273.215004, 329.0169678));
points.Add(new DataPoint(258.7229996, 323.8179626));
points.Add(new DataPoint(257.2878494, 323.337738));
points.Add(new DataPoint(255.7744827, 322.6670837));
points.Add(new DataPoint(254.4943924, 321.7168884));
points.Add(new DataPoint(253.7590103, 320.3979492));
points.Add(new DataPoint(253.827034, 319.0723267));
points.Add(new DataPoint(254.5322647, 317.7234802));
points.Add(new DataPoint(255.711647, 316.3885193));
points.Add(new DataPoint(257.2022476, 315.1045837));
points.Add(new DataPoint(260.465126, 312.8383789));
points.Add(new DataPoint(261.9114456, 311.9303589));
points.Add(new DataPoint(263.0170059, 311.2219543));
points.Add(new DataPoint(271.8112259, 305.8678284));
points.Add(new DataPoint(281.198616, 301.1617126));
points.Add(new DataPoint(290.8884659, 297.0829773));
points.Add(new DataPoint(300.590004, 293.6109619));
points.Add(new DataPoint(310.0823746, 291.1308289));
points.Add(new DataPoint(319.4608536, 289.9150696));
points.Add(new DataPoint(328.9314041, 289.7652893));
points.Add(new DataPoint(338.6999893, 290.4829712));
points.Add(new DataPoint(354.2659988, 293.3499451));
points.Add(new DataPoint(355.8602982, 293.1119995));
points.Add(new DataPoint(357.197731, 292.2803345));
points.Add(new DataPoint(358.3595047, 291.0731506));
points.Add(new DataPoint(359.4267349, 289.7085876));
points.Add(new DataPoint(360.4805679, 288.4048157));
points.Add(new DataPoint(361.6021194, 287.3800049));
points.Add(new DataPoint(362.8725357, 286.8523254));
points.Add(new DataPoint(364.3729935, 287.0399475));
points.Add(new DataPoint(365.9158707, 287.8427734));
points.Add(new DataPoint(367.3995438, 289.0066833));
points.Add(new DataPoint(370.1699905, 292.0510864));
points.Add(new DataPoint(372.6456985, 295.4399109));
points.Add(new DataPoint(374.788002, 298.4399719));
points.Add(new DataPoint(394.8579788, 325.8149719));
points.Add(new DataPoint(397.3873978, 329.0663757));
points.Add(new DataPoint(399.9987259, 332.6233521));
points.Add(new DataPoint(402.1026993, 336.3991089));
points.Add(new DataPoint(402.7802811, 338.3419189));
points.Add(new DataPoint(403.109993, 340.3069458));
points.Add(new DataPoint(403.7992325, 340.2913818));
points.Add(new DataPoint(404.1172256, 340.3743286));
points.Add(new DataPoint(404.2001114, 340.691864));
points.Add(new DataPoint(404.1839981, 341.3799744));
points.Add(new DataPoint(405.9170609, 342.5977478));
points.Add(new DataPoint(407.5672379, 344.3135681));
points.Add(new DataPoint(410.6323624, 348.6974487));
points.Add(new DataPoint(413.4063187, 353.4481201));
points.Add(new DataPoint(414.6925125, 355.6223755));
points.Add(new DataPoint(415.9159927, 357.4819641));
points.Add(new DataPoint(446.1409988, 402.5239563));
points.Add(new DataPoint(447.8941116, 404.6854248));
points.Add(new DataPoint(449.9755325, 406.9086609));
points.Add(new DataPoint(454.483345, 411.5653381));
points.Add(new DataPoint(456.5896683, 414.0111694));
points.Add(new DataPoint(458.3842239, 416.5435791));
points.Add(new DataPoint(459.7070389, 419.1687927));
points.Add(new DataPoint(460.3980179, 421.8929749));
points.Add(new DataPoint(460.330513, 423.2209473));
points.Add(new DataPoint(459.8673782, 424.4043274));
points.Add(new DataPoint(458.1563797, 426.4813232));
points.Add(new DataPoint(456.0694046, 428.4118958));
points.Add(new DataPoint(454.4110184, 430.4839478));
points.Add(new DataPoint(453.6341629, 432.6287231));
points.Add(new DataPoint(453.2503738, 434.9552002));
points.Add(new DataPoint(452.6709671, 439.6079712));
points.Add(new DataPoint(451.6133499, 443.3995361));
points.Add(new DataPoint(450.0984573, 447.2178345));
points.Add(new DataPoint(448.1988602, 450.8544312));
points.Add(new DataPoint(445.9870071, 454.1009521));
points.Add(new DataPoint(445.2327957, 454.9499512));
points.Add(new DataPoint(444.120369, 456.1347046));
points.Add(new DataPoint(441.6337357, 459.0782166));
points.Add(new DataPoint(440.6658401, 460.6203003));
points.Add(new DataPoint(440.1524734, 462.0648193));
points.Add(new DataPoint(440.2967911, 463.3034973));
points.Add(new DataPoint(441.3020096, 464.2279663));
points.Add(new DataPoint(443.0089798, 464.4325867));
points.Add(new DataPoint(444.7705154, 463.7559509));
points.Add(new DataPoint(446.3872757, 462.6180725));
points.Add(new DataPoint(447.6599808, 461.4389648));
points.Add(new DataPoint(449.96418, 458.7336426));
points.Add(new DataPoint(451.896492, 455.7789612));
points.Add(new DataPoint(454.7979813, 449.3179626));
points.Add(new DataPoint(455.2873001, 447.6248474));
points.Add(new DataPoint(455.8775101, 445.8508301));
points.Add(new DataPoint(456.8382034, 444.3796387));
points.Add(new DataPoint(458.4389725, 443.5949707));
points.Add(new DataPoint(460.0345535, 443.7620239));
points.Add(new DataPoint(461.7698441, 444.6128235));
points.Add(new DataPoint(463.5780106, 445.9676208));
points.Add(new DataPoint(465.3921585, 447.6465759));
points.Add(new DataPoint(468.7708817, 451.2580566));
points.Add(new DataPoint(470.2016678, 452.8309631));
points.Add(new DataPoint(471.3709793, 454.0089722));
points.Add(new DataPoint(478.8518143, 460.0104675));
points.Add(new DataPoint(486.9943924, 465.3340759));
points.Add(new DataPoint(495.4878006, 470.1171265));
points.Add(new DataPoint(504.0210037, 474.4969482));
points.Add(new DataPoint(509.5540848, 477.1457214));
points.Add(new DataPoint(515.2860184, 479.3189697));
points.Add(new DataPoint(516.4008255, 479.6032104));
points.Add(new DataPoint(517.6022415, 479.6870728));
points.Add(new DataPoint(518.5872879, 479.3061523));
points.Add(new DataPoint(519.0529861, 478.1959534));
points.Add(new DataPoint(518.8626175, 476.8864441));
points.Add(new DataPoint(518.1857986, 475.7019958));
points.Add(new DataPoint(515.84095, 473.7122192));
points.Add(new DataPoint(512.9545975, 472.234314));
points.Add(new DataPoint(510.4629593, 471.2759705));
points.Add(new DataPoint(507.6074905, 470.256958));
points.Add(new DataPoint(504.0599442, 468.8930969));
points.Add(new DataPoint(496.255867, 465.2143555));
points.Add(new DataPoint(492.682869, 462.9411621));
points.Add(new DataPoint(489.7850418, 460.4066467));
points.Add(new DataPoint(487.9041214, 457.6316223));
points.Add(new DataPoint(487.4518509, 456.1604309));
points.Add(new DataPoint(487.3819656, 454.6369629));
points.Add(new DataPoint(491.1286697, 455.6597595));
points.Add(new DataPoint(494.7612381, 457.2131958));
points.Add(new DataPoint(498.3274002, 458.9732666));
points.Add(new DataPoint(501.8750076, 460.6159668));
points.Add(new DataPoint(508.6896439, 463.2619934));
points.Add(new DataPoint(515.7986526, 465.5415649));
points.Add(new DataPoint(523.0577469, 467.2131042));
points.Add(new DataPoint(530.3230057, 468.0349731));
points.Add(new DataPoint(536.5177689, 468.0764465));
points.Add(new DataPoint(542.669014, 467.3979492));
points.Add(new DataPoint(543.9200516, 466.9833069));
points.Add(new DataPoint(545.0242386, 466.2348328));
points.Add(new DataPoint(545.5588455, 465.2004089));
points.Add(new DataPoint(545.1009598, 463.927948));
points.Add(new DataPoint(544.175972, 463.0953064));
points.Add(new DataPoint(542.9511795, 462.4622803));
points.Add(new DataPoint(539.9430008, 461.6712036));
points.Add(new DataPoint(536.7585526, 461.3072815));
points.Add(new DataPoint(534.0799637, 461.1229553));
points.Add(new DataPoint(520.8706131, 459.9545898));
points.Add(new DataPoint(514.2815628, 459.0859985));
points.Add(new DataPoint(507.7789993, 457.8509521));
points.Add(new DataPoint(506.4525833, 457.5542603));
points.Add(new DataPoint(504.8121414, 457.1582336));
points.Add(new DataPoint(501.1944656, 455.9819641));
points.Add(new DataPoint(499.5198441, 455.1585083));
points.Add(new DataPoint(498.1362991, 454.1494141));
points.Add(new DataPoint(497.1952591, 452.9331055));
points.Add(new DataPoint(496.8479691, 451.4879456));
points.Add(new DataPoint(497.117012, 450.6549377));
points.Add(new DataPoint(497.8393021, 450.1732788));
points.Add(new DataPoint(500.1341019, 449.9840698));
points.Add(new DataPoint(502.7133255, 450.3605652));
points.Add(new DataPoint(503.7911453, 450.5859985));
points.Add(new DataPoint(504.557991, 450.7429504));
points.Add(new DataPoint(511.3823318, 451.3563843));
points.Add(new DataPoint(518.3227615, 451.0169373));
points.Add(new DataPoint(525.2244949, 449.9740295));
points.Add(new DataPoint(531.932991, 448.4769592));
points.Add(new DataPoint(532.8128738, 448.2760315));
points.Add(new DataPoint(534.1250076, 447.9761353));
points.Add(new DataPoint(537.3393631, 447.0833435));
points.Add(new DataPoint(538.8882523, 446.4923706));
points.Add(new DataPoint(540.1627884, 445.8063354));
points.Add(new DataPoint(540.9862747, 445.0262146));
points.Add(new DataPoint(541.1820145, 444.1529541));
points.Add(new DataPoint(540.6489334, 443.4705505));
points.Add(new DataPoint(539.4853592, 443.0022888));
points.Add(new DataPoint(537.8792191, 442.7068176));
points.Add(new DataPoint(536.0183792, 442.5428467));
points.Add(new DataPoint(532.2842484, 442.4439392));
points.Add(new DataPoint(530.7866898, 442.4263916));
points.Add(new DataPoint(529.7860184, 442.3749695));
points.Add(new DataPoint(522.7177811, 441.8120117));
points.Add(new DataPoint(515.5401077, 441.6993408));
points.Add(new DataPoint(501.2470169, 442.2559509));
points.Add(new DataPoint(498.6232986, 442.5908508));
points.Add(new DataPoint(495.6024857, 442.9595947));
points.Add(new DataPoint(492.7076492, 442.7930298));
points.Add(new DataPoint(491.4709549, 442.3311157));
points.Add(new DataPoint(490.4619827, 441.5219727));
points.Add(new DataPoint(489.3800125, 439.9010925));
points.Add(new DataPoint(488.6179276, 438.0290833));
points.Add(new DataPoint(487.6418533, 433.8266907));
points.Add(new DataPoint(486.7113724, 429.5046997));
points.Add(new DataPoint(486.0061722, 427.4831848));
points.Add(new DataPoint(485.0039749, 425.6529541));
points.Add(new DataPoint(464.5570145, 397.51297));
points.Add(new DataPoint(441.859993, 359.0939636));
points.Add(new DataPoint(419.5407486, 322.4837036));
points.Add(new DataPoint(397.7539749, 285.5569458));
points.Add(new DataPoint(392.6534195, 277.3995361));
points.Add(new DataPoint(387.2727432, 269.1647034));
points.Add(new DataPoint(382.4174271, 260.6722412));
points.Add(new DataPoint(380.4385147, 256.2730713));
points.Add(new DataPoint(378.8929825, 251.7419434));
points.Add(new DataPoint(378.4342422, 247.8017578));
points.Add(new DataPoint(378.8919754, 243.618103));
points.Add(new DataPoint(379.8762283, 239.4705811));
points.Add(new DataPoint(380.9969864, 235.6389771));
points.Add(new DataPoint(388.6119766, 208.7999878));
points.Add(new DataPoint(391.0815811, 198.9997559));
points.Add(new DataPoint(393.3593521, 188.8963623));
points.Add(new DataPoint(395.3594131, 178.5748901));
points.Add(new DataPoint(396.9958572, 168.1204834));
points.Add(new DataPoint(398.1828384, 157.6182251));
points.Add(new DataPoint(398.8344498, 147.1533203));
points.Add(new DataPoint(398.8647842, 136.8108521));
points.Add(new DataPoint(398.1879959, 126.6759644));
points.Add(new DataPoint(395.2633438, 103.3844604));
points.Add(new DataPoint(393.3301468, 91.60638428));
points.Add(new DataPoint(390.9952469, 79.85656738));
points.Add(new DataPoint(388.1928177, 68.22253418));
points.Add(new DataPoint(384.8570328, 56.79168701));
points.Add(new DataPoint(380.9220352, 45.65136719));
points.Add(new DataPoint(376.3219986, 34.88897705));
points.Add(new DataPoint(371.1558609, 23.22259521));
points.Add(new DataPoint(366.6760025, 11.27197266));
points.Add(new DataPoint(365.8827591, 9.214355469));
points.Add(new DataPoint(365.0445023, 6.805603027));
points.Add(new DataPoint(364.7049942, 4.406799316));
points.Add(new DataPoint(364.892189, 3.323974609));
points.Add(new DataPoint(365.4079971, 2.378967285));
points.Add(new DataPoint(366.5955276, 1.439331055));
points.Add(new DataPoint(368.2348099, 0.826660156));
points.Add(new DataPoint(372.3311234, 0.333557129));
points.Add(new DataPoint(376.6218643, 0.40246582));
points.Add(new DataPoint(378.5041885, 0.4921875));
points.Add(new DataPoint(380.0319901, 0.535949707));
points.Add(new DataPoint(420.2889786, 0));
points.Add(new DataPoint(527.1040115, 0));
points.Add(new DataPoint(558.0751419, 0.09362793));
points.Add(new DataPoint(573.5140457, 0.204589844));
points.Add(new DataPoint(588.6629715, 0.352966309));
points.Add(new DataPoint(588.6629715, 0.352966309));
return points;
}
[Example("Conway's Game of Life")]
public static PlotModel ConwayLife()
{
// http://en.wikipedia.org/wiki/Conway's_Game_of_Life
var model = new PlotModel { Title = "Conway's Game of Life", Subtitle = "Click the mouse to step to the next generation." };
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, StartPosition = 1, EndPosition = 0 });
model.Axes.Add(new LinearAxis { Position = AxisPosition.Bottom });
int m = 40;
int n = 40;
var matrix = new double[m, n];
var ms = new MatrixSeries { Matrix = matrix };
Action blinker = (i, j) => { matrix[i, j] = matrix[i, j + 1] = matrix[i, j + 2] = 1; };
Action glider = (i, j) => { matrix[i, j] = matrix[i + 1, j + 1] = matrix[i + 1, j + 2] = matrix[i + 2, j] = matrix[i + 2, j + 1] = 1; };
Action rpentomino = (i, j) => { matrix[i, j + 1] = matrix[i, j + 2] = matrix[i + 1, j] = matrix[i + 1, j + 1] = matrix[i + 2, j + 1] = 1; };
blinker(2, 10);
glider(2, 2);
rpentomino(20, 20);
model.Series.Add(ms);
int g = 0;
Action stepToNextGeneration = () =>
{
var next = new double[m, n];
for (int i = 1; i < m - 1; i++)
{
for (int j = 1; j < n - 1; j++)
{
int k = (int)(matrix[i - 1, j - 1] + matrix[i - 1, j] + matrix[i - 1, j + 1] + matrix[i, j - 1]
+ matrix[i, j + 1] + matrix[i + 1, j - 1] + matrix[i + 1, j]
+ matrix[i + 1, j + 1]);
if (matrix[i, j].Equals(0) && k == 3)
{
// Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
next[i, j] = 1;
continue;
}
if (matrix[i, j].Equals(1) && (k == 2 || k == 3))
{
// Any live cell with two or three live neighbours lives on to the next generation.
next[i, j] = 1;
}
// Any live cell with fewer than two live neighbours dies, as if caused by under-population.
// Any live cell with more than three live neighbours dies, as if by overcrowding.
}
}
g++;
ms.Title = "Generation " + g;
ms.Matrix = matrix = next;
model.InvalidatePlot(true);
};
model.MouseDown += (s, e) =>
{
if (e.ChangedButton == OxyMouseButton.Left)
{
stepToNextGeneration();
e.Handled = true;
}
};
return model;
}
[Example("Mandelbrot custom series")]
public static PlotModel Mandelbrot()
{
// http://en.wikipedia.org/wiki/Mandelbrot_set
var model = new PlotModel { Title = "The Mandelbrot set" };
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -1.4, Maximum = 1.4 });
model.Axes.Add(new LinearAxis { Position = AxisPosition.Bottom, Minimum = -2, Maximum = 1 });
model.Axes.Add(
new LinearColorAxis
{
Position = AxisPosition.Right,
Minimum = 0,
Maximum = 64,
Palette = OxyPalettes.Jet(64),
HighColor = OxyColors.Black
});
model.Series.Add(new MandelbrotSetSeries());
return model;
}
[Example("Julia set custom series")]
public static PlotModel JuliaSet()
{
// http://en.wikipedia.org/wiki/Julia_set
var model = new PlotModel { Subtitle = "Click and move the mouse" };
model.Axes.Add(new LinearAxis { Position = AxisPosition.Left, Minimum = -2, Maximum = 2 });
model.Axes.Add(new LinearAxis { Position = AxisPosition.Bottom, Minimum = -2.5, Maximum = 2.5 });
model.Axes.Add(
new LinearColorAxis
{
Position = AxisPosition.Right,
Minimum = 0,
Maximum = 64,
Palette = OxyPalettes.Jet(64),
HighColor = OxyColors.Black
});
var jss = new JuliaSetSeries();
// Delegate to set the c and title
Action setConstant = (c1, c2) =>
{
jss.C1 = c1;
jss.C2 = c2;
model.Title = string.Format("The Julia set, c={0:0.00000}+{1:0.00000}i", jss.C1, jss.C2);
};
// Update the c by the position where the mouse was clicked/moved
Action handleMouseEvent = e =>
{
var c = jss.InverseTransform(e.Position);
setConstant(c.X, c.Y);
model.InvalidatePlot(true);
e.Handled = true;
};
jss.MouseDown += (s, e) => handleMouseEvent(e);
jss.MouseMove += (s, e) => handleMouseEvent(e);
// set the initial c
setConstant(-0.726895347709114071439, 0.188887129043845954792);
model.Series.Add(jss);
return model;
}
[Example("Elephant curve")]
public static PlotModel ElephantCurve()
{
// http://www.wolframalpha.com/input/?i=elephant+curve
// See also https://gist.github.com/purem/4687549/raw/8dda1f16cc70469aedecec19af1530534eadbae3/Wolfram+alpha+named+parametric+curves
Func sin = Math.Sin;
Func x =
t =>
-27d / 5 * sin(3d / 2 - 30 * t) - 16d / 3 * sin(9d / 8 - 29 * t) - 29d / 5 * sin(5d / 4 - 27 * t)
- 8d / 3 * sin(1d / 4 - 26 * t) - 25d / 7 * sin(1d / 3 - 25 * t) - 31d / 4 * sin(4d / 7 - 22 * t)
- 25d / 4 * sin(4d / 3 - 20 * t) - 33d / 2 * sin(2d / 3 - 19 * t) - 67d / 4 * sin(6d / 5 - 16 * t)
- 100d / 11 * sin(1d / 4 - 10 * t) - 425d / 7 * sin(1 - 4 * t) + 149d / 4 * sin(8 * t)
+ 1172d / 3 * sin(t + 21d / 5) + 661d / 11 * sin(2 * t + 3) + 471d / 8 * sin(3 * t + 10d / 7)
+ 211d / 7 * sin(5 * t + 13d / 4) + 39d / 4 * sin(6 * t + 10d / 7) + 139d / 10 * sin(7 * t + 7d / 6)
+ 77d / 3 * sin(9 * t + 18d / 7) + 135d / 8 * sin(11 * t + 1d / 2) + 23d / 4 * sin(12 * t + 8d / 5)
+ 95d / 4 * sin(13 * t + 4) + 31d / 4 * sin(14 * t + 3d / 5) + 67d / 11 * sin(15 * t + 7d / 3)
+ 127d / 21 * sin(17 * t + 17d / 4) + 95d / 8 * sin(18 * t + 7d / 8)
+ 32d / 11 * sin(21 * t + 8d / 3) + 81d / 10 * sin(23 * t + 45d / 11)
+ 13d / 3 * sin(24 * t + 13d / 4) + 7d / 4 * sin(28 * t + 3d / 2) + 11d / 5 * sin(31 * t + 5d / 2)
+ 1d / 3 * sin(32 * t + 12d / 5) + 13d / 4 * sin(33 * t + 22d / 5) + 14d / 3 * sin(34 * t + 9d / 4)
+ 9d / 5 * sin(35 * t + 8d / 5) + 17d / 9 * sin(36 * t + 22d / 5) + 1d / 3 * sin(37 * t + 15d / 7)
+ 3d / 2 * sin(38 * t + 39d / 10) + 4d / 3 * sin(39 * t + 7d / 2) + 5d / 3 * sin(40 * t + 17d / 6);
Func y =
t =>
-13d / 7 * sin(1d / 2 - 40 * t) - 31d / 8 * sin(1d / 11 - 34 * t) - 12d / 5 * sin(1d / 4 - 31 * t)
- 9d / 4 * sin(4d / 3 - 29 * t) - 5d / 3 * sin(4d / 3 - 28 * t) - 11d / 2 * sin(6d / 5 - 26 * t)
- 17d / 7 * sin(3d / 2 - 25 * t) - 5d / 2 * sin(1 - 24 * t) - 39d / 7 * sin(1 - 19 * t)
- 59d / 5 * sin(2d / 3 - 18 * t) - 179d / 9 * sin(13d / 12 - 12 * t)
- 103d / 2 * sin(1d / 10 - 9 * t) - 356d / 5 * sin(1 - 5 * t) - 429d / 2 * sin(20d / 19 - t)
+ 288d / 5 * sin(2 * t + 10d / 3) + 53d / 6 * sin(3 * t + 5d / 2) + 351d / 7 * sin(4 * t + 5d / 2)
+ 201d / 4 * sin(6 * t + 17d / 7) + 167d / 3 * sin(7 * t + 19d / 5) + 323d / 5 * sin(8 * t + 1d / 4)
+ 153d / 7 * sin(10 * t + 2d / 3) + 71d / 5 * sin(11 * t + 6d / 5)
+ 47d / 12 * sin(13 * t + 11d / 5) + 391d / 26 * sin(14 * t + 2) + 164d / 11 * sin(15 * t + 1d / 7)
+ 11d / 2 * sin(16 * t + 2d / 3) + 31d / 3 * sin(17 * t + 1d / 7) + 54d / 11 * sin(20 * t + 1d / 4)
+ 43d / 5 * sin(21 * t + 13d / 3) + 13d / 5 * sin(22 * t + 3d / 2) + 17d / 5 * sin(23 * t + 11d / 5)
+ 19d / 10 * sin(27 * t + 4) + 15d / 2 * sin(30 * t + 55d / 18) + 4d / 3 * sin(32 * t + 3d / 5)
+ 5d / 3 * sin(33 * t + 4) + 27d / 7 * sin(35 * t + 13d / 6) + 1d / 4 * sin(36 * t + 43d / 11)
+ 16d / 5 * sin(37 * t + 9d / 2) + 20d / 19 * sin(38 * t + 23d / 6) + 8d / 3 * sin(39 * t + 4d / 7);
var model = new PlotModel { Title = "Elephant curve", PlotType = PlotType.Cartesian };
model.Series.Add(new FunctionSeries(x, y, 0, Math.PI * 2, 1000));
return model;
}
[Example("PI curve")]
public static PlotModel PiCurve()
{
// http://www.wolframalpha.com/input/?i=pi+curve
Func sin = Math.Sin;
Func x =
t => 17d / 31 * sin(235d / 57 - 32 * t) + 19d / 17 * sin(192d / 55 - 30 * t) + 47d / 32 * sin(69d / 25 - 29 * t) + 35d / 26 * sin(75d / 34 - 27 * t) + 6d / 31 * sin(23d / 10 - 26 * t) + 35d / 43 * sin(10d / 33 - 25 * t) + 126d / 43 * sin(421d / 158 - 24 * t) + 143d / 57 * sin(35d / 22 - 22 * t) + 106d / 27 * sin(84d / 29 - 21 * t) + 88d / 25 * sin(23d / 27 - 20 * t) + 74d / 27 * sin(53d / 22 - 19 * t) + 44d / 53 * sin(117d / 25 - 18 * t) + 126d / 25 * sin(88d / 49 - 17 * t) + 79d / 11 * sin(43d / 26 - 16 * t) + 43d / 12 * sin(41d / 17 - 15 * t) + 47d / 27 * sin(244d / 81 - 14 * t) + 8d / 5 * sin(79d / 19 - 13 * t) + 373d / 46 * sin(109d / 38 - 12 * t) + 1200d / 31 * sin(133d / 74 - 11 * t) + 67d / 24 * sin(157d / 61 - 10 * t) + 583d / 28 * sin(13d / 8 - 8 * t) + 772d / 35 * sin(59d / 16 - 7 * t) + 3705d / 46 * sin(117d / 50 - 6 * t) + 862d / 13 * sin(19d / 8 - 5 * t) + 6555d / 34 * sin(157d / 78 - 3 * t) + 6949d / 13 * sin(83d / 27 - t) - 6805d / 54 * sin(2 * t + 1d / 145) - 5207d / 37 * sin(4 * t + 49d / 74) - 1811d / 58 * sin(9 * t + 55d / 43) - 63d / 20 * sin(23 * t + 2d / 23) - 266d / 177 * sin(28 * t + 13d / 18) - 2d / 21 * sin(31 * t + 7d / 16);
Func y =
t => 70d / 37 * sin(65d / 32 - 32 * t) + 11d / 12 * sin(98d / 41 - 31 * t) + 26d / 29 * sin(35d / 12 - 30 * t) + 54d / 41 * sin(18d / 7 - 29 * t) + 177d / 71 * sin(51d / 19 - 27 * t) + 59d / 34 * sin(125d / 33 - 26 * t) + 49d / 29 * sin(18d / 11 - 25 * t) + 151d / 75 * sin(59d / 22 - 24 * t) + 52d / 9 * sin(118d / 45 - 22 * t) + 52d / 33 * sin(133d / 52 - 21 * t) + 37d / 45 * sin(61d / 14 - 20 * t) + 143d / 46 * sin(144d / 41 - 19 * t) + 254d / 47 * sin(19d / 52 - 18 * t) + 246d / 35 * sin(92d / 25 - 17 * t) + 722d / 111 * sin(176d / 67 - 16 * t) + 136d / 23 * sin(3d / 19 - 15 * t) + 273d / 25 * sin(32d / 21 - 13 * t) + 229d / 33 * sin(117d / 28 - 12 * t) + 19d / 4 * sin(43d / 11 - 11 * t) + 135d / 8 * sin(23d / 10 - 10 * t) + 205d / 6 * sin(33d / 23 - 8 * t) + 679d / 45 * sin(55d / 12 - 7 * t) + 101d / 8 * sin(11d / 12 - 6 * t) + 2760d / 59 * sin(40d / 11 - 5 * t) + 1207d / 18 * sin(21d / 23 - 4 * t) + 8566d / 27 * sin(39d / 28 - 3 * t) + 12334d / 29 * sin(47d / 37 - 2 * t) + 15410d / 39 * sin(185d / 41 - t) - 596d / 17 * sin(9 * t + 3d / 26) - 247d / 28 * sin(14 * t + 25d / 21) - 458d / 131 * sin(23 * t + 21d / 37) - 41d / 36 * sin(28 * t + 7d / 8);
var model = new PlotModel { Title = "PI curve", PlotType = PlotType.Cartesian };
model.Series.Add(new FunctionSeries(x, y, 0, Math.PI * 2, 1000));
return model;
}
[Example("Angelina Jolie curve")]
public static PlotModel AngelinaJolieCurve()
{
// http://www.wolframalpha.com/input/?i=Angelina+Jolie+curve
// Heaviside step function
Func theta = x => x < 0 ? 0 : 1;
Func sin = Math.Sin;
double pi = Math.PI;
Func xt =
t =>
((-23d / 4 * sin(29d / 20 - 41 * t) - 47d / 15 * sin(47d / 34 - 38 * t)
- 979d / 196 * sin(45d / 31 - 36 * t) - 59d / 6 * sin(25d / 17 - 33 * t)
- 259d / 26 * sin(104d / 69 - 32 * t) - 49d / 24 * sin(57d / 37 - 31 * t)
- 37d / 21 * sin(32d / 23 - 30 * t) - 324d / 31 * sin(85d / 57 - 27 * t)
- 47d / 26 * sin(24d / 17 - 25 * t) - 247d / 29 * sin(39d / 25 - 24 * t)
- 834d / 71 * sin(63d / 41 - 23 * t) - 475d / 49 * sin(62d / 41 - 22 * t)
- 20d / 7 * sin(29d / 20 - 17 * t) - 1286d / 61 * sin(98d / 65 - 16 * t)
- 2312d / 25 * sin(20d / 13 - 14 * t) - 2662d / 41 * sin(23d / 15 - 13 * t)
- 2292d / 131 * sin(92d / 61 - 11 * t) - 1690d / 37 * sin(48d / 31 - 8 * t)
+ 993d / 23 * sin(t + 52d / 33) + 407d / 31 * sin(2 * t + 25d / 16)
+ 1049d / 57 * sin(3 * t + 49d / 31) + 1385d / 42 * sin(4 * t + 80d / 17)
+ 2929d / 40 * sin(5 * t + 49d / 31) + 500d / 39 * sin(6 * t + 164d / 35)
+ 116d / 25 * sin(7 * t + 155d / 33) + 2593d / 26 * sin(9 * t + 43d / 27)
+ 200d / 37 * sin(10 * t + 65d / 42) + 2866d / 39 * sin(12 * t + 133d / 83)
+ 703d / 234 * sin(15 * t + 46d / 27) + 133d / 8 * sin(18 * t + 13d / 8)
+ 716d / 33 * sin(19 * t + 27d / 17) + 180d / 53 * sin(20 * t + 47d / 30)
+ 476d / 31 * sin(21 * t + 57d / 35) + 73d / 22 * sin(26 * t + 77d / 48)
+ 549d / 49 * sin(28 * t + 44d / 27) + 657d / 68 * sin(29 * t + 27d / 17)
+ 29d / 22 * sin(34 * t + 140d / 31) + 180d / 49 * sin(35 * t + 14d / 9)
+ 43d / 4 * sin(37 * t + 77d / 46) + 68d / 23 * sin(39 * t + 39d / 25)
+ 80d / 47 * sin(40 * t + 49d / 27) + 16829d / 29) * theta(119 * pi - t)
* theta(t - 115 * pi)
+ (-43d / 40 * sin(39d / 29 - 62 * t) - 44d / 17 * sin(56d / 37 - 58 * t)
- 23d / 39 * sin(14d / 11 - 57 * t) - 59d / 10 * sin(49d / 32 - 51 * t)
- 215d / 31 * sin(20d / 13 - 46 * t) - 447d / 22 * sin(110d / 73 - 34 * t)
- 407d / 39 * sin(54d / 35 - 33 * t) - 432d / 35 * sin(14d / 9 - 29 * t)
- 175d / 33 * sin(35d / 24 - 28 * t) - 102d / 5 * sin(64d / 41 - 22 * t)
+ 833d / 46 * sin(t + 131d / 28) + 1360d / 9 * sin(2 * t + 52d / 33)
+ 139d / 3 * sin(3 * t + 43d / 27) + 108d / 29 * sin(4 * t + 244d / 53)
+ 4269d / 41 * sin(5 * t + 113d / 24) + 7407d / 31 * sin(6 * t + 65d / 41)
+ 2159d / 32 * sin(7 * t + 103d / 22) + 5476d / 51 * sin(8 * t + 37d / 23)
+ 3855d / 37 * sin(9 * t + 60d / 37) + 2247d / 46 * sin(10 * t + 18d / 11)
+ 216d / 31 * sin(11 * t + 81d / 40) + 3364d / 35 * sin(12 * t + 69d / 43)
+ 1492d / 21 * sin(13 * t + 47d / 10) + 1981d / 29 * sin(14 * t + 21d / 13)
+ 1852d / 35 * sin(15 * t + 18d / 11) + 255d / 23 * sin(16 * t + 72d / 41)
+ 499d / 25 * sin(17 * t + 134d / 29) + 754d / 17 * sin(18 * t + 57d / 35)
+ 203d / 31 * sin(19 * t + 35d / 19) + 1289d / 32 * sin(20 * t + 41d / 25)
+ 65d / 21 * sin(21 * t + 55d / 13) + 731d / 31 * sin(23 * t + 34d / 21)
+ 816d / 83 * sin(24 * t + 23d / 14) + 467d / 29 * sin(25 * t + 197d / 42)
+ 496d / 37 * sin(26 * t + 64d / 39) + 34d / 9 * sin(27 * t + 40d / 27)
+ 204d / 23 * sin(30 * t + 76d / 43) + 34d / 3 * sin(31 * t + 50d / 29)
+ 1579d / 57 * sin(32 * t + 51d / 31) + 37d / 6 * sin(35 * t + 69d / 44)
+ 128d / 21 * sin(36 * t + 21d / 13) + 194d / 83 * sin(37 * t + 52d / 27)
+ 35d / 37 * sin(38 * t + 46d / 19) + 39d / 38 * sin(39 * t + 234d / 55)
+ 113d / 16 * sin(40 * t + 71d / 43) + 126d / 101 * sin(41 * t + 145d / 83)
+ 13d / 6 * sin(42 * t + 184d / 41) + 100d / 31 * sin(43 * t + 117d / 25)
+ 355d / 36 * sin(44 * t + 48d / 29) + 148d / 57 * sin(45 * t + 30d / 17)
+ 3d / 2 * sin(47 * t + 51d / 28) + 107d / 61 * sin(48 * t + 27d / 16)
+ 72d / 13 * sin(49 * t + 93d / 56) + 55d / 37 * sin(50 * t + 144d / 31)
+ 53d / 24 * sin(52 * t + 59d / 34) + 182d / 47 * sin(53 * t + 41d / 24)
+ 481d / 103 * sin(54 * t + 110d / 61) + 97d / 29 * sin(55 * t + 89d / 19)
+ 7d / 4 * sin(56 * t + 49d / 30) + 82d / 37 * sin(59 * t + 55d / 28)
+ 20d / 13 * sin(60 * t + 45d / 23) + 147d / 34 * sin(61 * t + 77d / 45) - 27563d / 35)
* theta(115 * pi - t) * theta(t - 111 * pi)
+ (-11d / 13 * sin(37d / 33 - 98 * t) - 13d / 32 * sin(69d / 44 - 97 * t)
- 33d / 19 * sin(38d / 29 - 88 * t) - 124d / 45 * sin(44d / 29 - 87 * t)
- 72d / 37 * sin(56d / 43 - 77 * t) - 78d / 77 * sin(197d / 131 - 72 * t)
- 39d / 58 * sin(7d / 33 - 54 * t) - 31d / 20 * sin(26d / 25 - 37 * t)
- 265d / 58 * sin(122d / 81 - 35 * t) - 4901d / 196 * sin(49d / 32 - 12 * t)
- 7950d / 49 * sin(91d / 58 - 8 * t) - 515d / 12 * sin(25d / 16 - 5 * t)
+ 21289d / 23 * sin(t + 80d / 51) + 4245d / 8 * sin(2 * t + 36d / 23)
+ 394321d / 930 * sin(3 * t + 113d / 24) + 4699d / 17 * sin(4 * t + 113d / 24)
+ 1931d / 41 * sin(6 * t + 43d / 28) + 745d / 24 * sin(7 * t + 40d / 27)
+ 861d / 8 * sin(9 * t + 113d / 24) + 1348d / 15 * sin(10 * t + 146d / 31)
+ 1015d / 39 * sin(11 * t + 43d / 28) + 590d / 39 * sin(13 * t + 53d / 34)
+ 271d / 37 * sin(14 * t + 48d / 31) + 268d / 29 * sin(15 * t + 63d / 38)
+ 443d / 25 * sin(16 * t + 127d / 27) + 872d / 37 * sin(17 * t + 53d / 35)
+ 2329d / 82 * sin(18 * t + 145d / 31) + 11d / 4 * sin(19 * t + 832d / 185)
+ 1139d / 36 * sin(20 * t + 49d / 32) + 203d / 13 * sin(21 * t + 114d / 25)
+ 2807d / 72 * sin(22 * t + 48d / 31) + 639d / 26 * sin(23 * t + 19d / 12)
+ 163d / 23 * sin(24 * t + 43d / 26) + 517d / 36 * sin(25 * t + 75d / 47)
+ 359d / 30 * sin(26 * t + 159d / 34) + 603d / 32 * sin(27 * t + 46d / 31)
+ 1679d / 34 * sin(28 * t + 387d / 83) + 269d / 22 * sin(29 * t + 41d / 28)
+ 94d / 39 * sin(30 * t + 56d / 51) + 1219d / 54 * sin(31 * t + 51d / 11)
+ 535d / 29 * sin(32 * t + 61d / 41) + 17d / 52 * sin(33 * t + 54d / 49)
+ 133d / 33 * sin(34 * t + 308d / 67) + 73d / 18 * sin(36 * t + 262d / 57)
+ 131d / 20 * sin(38 * t + 134d / 29) + 391d / 72 * sin(39 * t + 428d / 93)
+ 505d / 26 * sin(40 * t + 3d / 2) + 39d / 10 * sin(41 * t + 256d / 57)
+ 76d / 21 * sin(42 * t + 22d / 13) + 341d / 37 * sin(43 * t + 16d / 11)
+ 67d / 39 * sin(44 * t + 93d / 22) + 211d / 26 * sin(45 * t + 167d / 36)
+ 161d / 20 * sin(46 * t + 19d / 13) + 175d / 23 * sin(47 * t + 124d / 27)
+ 229d / 35 * sin(48 * t + 59d / 39) + 23d / 19 * sin(49 * t + 36d / 23)
+ 59d / 34 * sin(50 * t + 40d / 9) + 399d / 46 * sin(51 * t + 75d / 52)
+ 351d / 49 * sin(52 * t + 119d / 26) + 23d / 17 * sin(53 * t + 49d / 44)
+ 179d / 17 * sin(55 * t + 308d / 67) + 74d / 25 * sin(56 * t + 84d / 61)
+ 7d / 10 * sin(57 * t + 21d / 17) + 58d / 39 * sin(58 * t + 94d / 21)
+ 44d / 23 * sin(59 * t + 97d / 54) + 265d / 36 * sin(60 * t + 47d / 32)
+ 44d / 87 * sin(61 * t + 49d / 26) + 899d / 142 * sin(62 * t + 143d / 31)
+ 109d / 29 * sin(63 * t + 93d / 70) + 391d / 55 * sin(64 * t + 51d / 11)
+ 24d / 37 * sin(65 * t + 29d / 38) + 151d / 30 * sin(66 * t + 78d / 17)
+ 291d / 50 * sin(67 * t + 44d / 29) + 124d / 29 * sin(68 * t + 82d / 55)
+ 83d / 52 * sin(69 * t + 95d / 47) + 22d / 21 * sin(70 * t + 81d / 38)
+ 301d / 47 * sin(71 * t + 13d / 9) + 341d / 28 * sin(73 * t + 239d / 52)
+ 133d / 22 * sin(74 * t + 14d / 11) + 245d / 39 * sin(75 * t + 47d / 10)
+ 136d / 29 * sin(76 * t + 537d / 115) + 250d / 43 * sin(78 * t + 25d / 17)
+ 30d / 41 * sin(79 * t + 83d / 23) + 5d / 2 * sin(80 * t + 198d / 113)
+ 129d / 29 * sin(81 * t + 21d / 13) + 169d / 32 * sin(82 * t + 73d / 47)
+ 28d / 29 * sin(83 * t + 133d / 33) + 129d / 40 * sin(84 * t + 86d / 19)
+ 34d / 11 * sin(85 * t + 56d / 43) + 143d / 32 * sin(86 * t + 163d / 35)
+ 77d / 25 * sin(89 * t + 27d / 20) + 418d / 93 * sin(90 * t + 166d / 37)
+ 103d / 37 * sin(91 * t + 55d / 39) + 16d / 13 * sin(92 * t + 45d / 26)
+ 87d / 40 * sin(93 * t + 55d / 32) + 53d / 25 * sin(94 * t + 67d / 41)
+ 58d / 43 * sin(95 * t + 26d / 15) + 67d / 30 * sin(96 * t + 149d / 99)
+ 155d / 41 * sin(99 * t + 124d / 27) - 6637d / 21) * theta(111 * pi - t)
* theta(t - 107 * pi)
+ (-27d / 23 * sin(5d / 12 - 35 * t) - 94d / 23 * sin(32d / 31 - 34 * t)
- 26d / 9 * sin(17d / 27 - 33 * t) - 226d / 31 * sin(43d / 33 - 32 * t)
- 211d / 50 * sin(38d / 25 - 29 * t) - 11d / 18 * sin(18d / 23 - 28 * t)
- 23d / 18 * sin(32d / 31 - 27 * t) - 255d / 94 * sin(27d / 20 - 25 * t)
- 41d / 31 * sin(65d / 47 - 21 * t) - 59d / 12 * sin(33d / 28 - 19 * t)
- 160d / 31 * sin(31d / 29 - 18 * t) - 859d / 78 * sin(165d / 124 - 17 * t)
- 137d / 13 * sin(37d / 26 - 16 * t) - 25d / 23 * sin(175d / 117 - 9 * t)
+ 937d / 6 * sin(t + 41d / 26) + 41d / 9 * sin(2 * t + 163d / 36)
+ 563d / 33 * sin(3 * t + 21d / 13) + 19d / 8 * sin(4 * t + 181d / 40)
+ 53d / 15 * sin(5 * t + 77d / 46) + 10d / 31 * sin(6 * t + 73d / 23)
+ 133d / 39 * sin(7 * t + 67d / 42) + 5d / 9 * sin(8 * t + 30d / 19)
+ 22d / 13 * sin(10 * t + 47d / 27) + 108d / 37 * sin(11 * t + 90d / 53)
+ 37d / 40 * sin(12 * t + 47d / 23) + 18d / 13 * sin(13 * t + 49d / 11)
+ 63d / 40 * sin(14 * t + 139d / 31) + 453d / 34 * sin(15 * t + 65d / 41)
+ 27d / 32 * sin(20 * t + 13d / 46) + 8d / 19 * sin(22 * t + 58d / 35)
+ 19d / 30 * sin(23 * t + 157d / 34) + 10d / 23 * sin(24 * t + 7d / 27)
+ 51d / 31 * sin(26 * t + 29d / 24) + 83d / 26 * sin(30 * t + 52d / 31)
+ 179d / 45 * sin(31 * t + 56d / 37) + 14d / 23 * sin(36 * t + 45d / 29)
+ 56d / 33 * sin(37 * t + 69d / 37) + 62d / 61 * sin(38 * t + 192d / 47)
+ 4d / 5 * sin(39 * t + 102d / 47) + 7d / 43 * sin(40 * t + 67d / 18)
+ 3d / 13 * sin(41 * t + 39d / 38) + 15d / 32 * sin(42 * t + 75d / 16)
+ 34d / 31 * sin(43 * t + 53d / 29) + 31d / 32 * sin(44 * t + 52d / 25)
+ 11d / 29 * sin(45 * t + 23d / 6) + 19d / 11 * sin(46 * t + 134d / 29)
+ 55d / 27 * sin(47 * t + 30d / 17) + 8d / 25 * sin(48 * t + 185d / 44)
+ 12d / 31 * sin(49 * t + 61d / 41) - 803d / 16) * theta(107 * pi - t)
* theta(t - 103 * pi)
+ (-183d / 137 * sin(41d / 31 - 53 * t) - 3d / 2 * sin(45d / 32 - 51 * t)
- 21d / 37 * sin(17d / 24 - 50 * t) - 109d / 73 * sin(21d / 16 - 49 * t)
- 28d / 23 * sin(26d / 19 - 46 * t) - 499d / 95 * sin(49d / 38 - 44 * t)
- 79d / 37 * sin(37d / 28 - 41 * t) - 28d / 25 * sin(35d / 33 - 35 * t)
- 39d / 10 * sin(23d / 17 - 34 * t) - 17d / 6 * sin(27d / 22 - 33 * t)
- 40d / 29 * sin(4d / 3 - 32 * t) - 159d / 65 * sin(23d / 16 - 30 * t)
- 130d / 31 * sin(43d / 34 - 29 * t) - 182d / 27 * sin(37d / 26 - 28 * t)
- 19d / 13 * sin(35d / 23 - 26 * t) - 67d / 39 * sin(58d / 49 - 25 * t)
- 131d / 37 * sin(81d / 59 - 24 * t) - 29d / 18 * sin(53d / 40 - 23 * t)
- 77d / 51 * sin(14d / 11 - 22 * t) - 457d / 61 * sin(68d / 47 - 21 * t)
- 293d / 27 * sin(53d / 36 - 15 * t) - 80d / 39 * sin(23d / 15 - 14 * t)
- 65d / 17 * sin(31d / 21 - 11 * t) - 21d / 17 * sin(26d / 17 - 10 * t)
- 41d / 13 * sin(57d / 37 - 8 * t) + 17496d / 85 * sin(t + 41d / 26)
+ 26d / 17 * sin(2 * t + 418d / 93) + 449d / 24 * sin(3 * t + 27d / 17)
+ 221d / 63 * sin(4 * t + 51d / 11) + 283d / 43 * sin(5 * t + 69d / 43)
+ 16d / 15 * sin(6 * t + 64d / 37) + 29d / 11 * sin(7 * t + 59d / 36)
+ 201d / 44 * sin(9 * t + 59d / 37) + 97d / 83 * sin(12 * t + 35d / 22)
+ 77d / 10 * sin(13 * t + 173d / 104) + 23d / 22 * sin(16 * t + 61d / 32)
+ 349d / 32 * sin(17 * t + 61d / 36) + 60d / 17 * sin(18 * t + 79d / 46)
+ 11d / 23 * sin(19 * t + 61d / 29) + 373d / 86 * sin(20 * t + 48d / 29)
+ 99d / 16 * sin(27 * t + 67d / 40) + 217d / 38 * sin(31 * t + 46d / 27)
+ 25d / 29 * sin(36 * t + 189d / 41) + 423d / 106 * sin(37 * t + 49d / 27)
+ 11d / 12 * sin(38 * t + 59d / 29) + 184d / 105 * sin(39 * t + 65d / 34)
+ 93d / 50 * sin(40 * t + 93d / 49) + 8d / 25 * sin(42 * t + 45d / 22)
+ 13d / 11 * sin(43 * t + 46d / 29) + 19d / 28 * sin(45 * t + 27d / 28)
+ 14d / 23 * sin(47 * t + 37d / 31) + 9d / 31 * sin(48 * t + 25d / 16)
+ 52d / 31 * sin(52 * t + 56d / 31) - 20749d / 273) * theta(103 * pi - t)
* theta(t - 99 * pi)
+ (-2d / 27 * sin(47d / 30 - 3 * t) + 321d / 16 * sin(t + 63d / 40)
+ 219d / 31 * sin(2 * t + 41d / 26) + 69d / 47 * sin(4 * t + 30d / 19)
+ 36d / 23 * sin(5 * t + 27d / 17) + 888d / 11) * theta(99 * pi - t)
* theta(t - 95 * pi)
+ (-93d / 25 * sin(25d / 16 - 8 * t) - 85d / 33 * sin(25d / 16 - 7 * t)
- 217d / 38 * sin(47d / 30 - 6 * t) - 989d / 49 * sin(25d / 16 - 5 * t)
+ 6925d / 39 * sin(t + 11d / 7) + 3173d / 138 * sin(2 * t + 52d / 33)
+ 289d / 9 * sin(3 * t + 146d / 31) + 187d / 23 * sin(4 * t + 41d / 26)
+ 16d / 7 * sin(9 * t + 164d / 35) + 19d / 22 * sin(10 * t + 429d / 92)
+ 4d / 27 * sin(11 * t + 47d / 32) + 23d / 40 * sin(12 * t + 29d / 19) - 1249d / 41)
* theta(95 * pi - t) * theta(t - 91 * pi)
+ (-14d / 51 * sin(65d / 43 - 4 * t) + 2519d / 13 * sin(t + 74d / 47)
+ 14d / 11 * sin(2 * t + 151d / 33) + 601d / 28 * sin(3 * t + 30d / 19) - 5627d / 23)
* theta(91 * pi - t) * theta(t - 87 * pi)
+ (-268d / 37 * sin(91d / 58 - t) + 1d / 47 * sin(2 * t + 31d / 22)
+ 68d / 41 * sin(3 * t + 113d / 24) + 185d / 19 * sin(4 * t + 52d / 33)
+ 133d / 53 * sin(5 * t + 65d / 41) + 3d / 35 * sin(6 * t + 122d / 65) - 14306d / 33)
* theta(87 * pi - t) * theta(t - 83 * pi)
+ (-64d / 15 * sin(66d / 43 - 12 * t) - 244d / 63 * sin(38d / 25 - 10 * t)
- 6d / 5 * sin(17d / 12 - 9 * t) - 632d / 39 * sin(20d / 13 - 8 * t)
- 986d / 33 * sin(20d / 13 - 7 * t) - 123d / 23 * sin(31d / 20 - 6 * t)
- 923d / 32 * sin(36d / 23 - 4 * t) + 1270d / 19 * sin(t + 74d / 47)
+ 70d / 19 * sin(2 * t + 53d / 32) + 1359d / 43 * sin(3 * t + 41d / 26)
+ 854d / 27 * sin(5 * t + 30d / 19) + 32d / 13 * sin(11 * t + 19d / 12) + 15881d / 49)
* theta(83 * pi - t) * theta(t - 79 * pi)
+ (-1009d / 28 * sin(36d / 23 - 6 * t) + 1362d / 19 * sin(t + 11d / 7)
+ 113d / 11 * sin(2 * t + 174d / 37) + 2128d / 45 * sin(3 * t + 30d / 19)
+ 3805d / 58 * sin(4 * t + 30d / 19) + 1316d / 51 * sin(5 * t + 41d / 26)
+ 500d / 33 * sin(7 * t + 85d / 54) + 69d / 8 * sin(8 * t + 179d / 38)
+ 337d / 37 * sin(9 * t + 19d / 12) + 59d / 18 * sin(10 * t + 53d / 33)
+ 5d / 24 * sin(11 * t + 87d / 46) + 335d / 44 * sin(12 * t + 46d / 29) - 9149d / 24)
* theta(79 * pi - t) * theta(t - 75 * pi)
+ (-3d / 32 * sin(37d / 27 - 14 * t) - 31d / 25 * sin(54d / 35 - 11 * t)
- 101d / 51 * sin(39d / 25 - 6 * t) + 4553d / 33 * sin(t + 63d / 40)
+ 771d / 43 * sin(2 * t + 65d / 41) + 679d / 45 * sin(3 * t + 49d / 31)
+ 79d / 19 * sin(4 * t + 65d / 41) + 468d / 67 * sin(5 * t + 68d / 43)
+ 127d / 52 * sin(7 * t + 59d / 37) + 30d / 29 * sin(8 * t + 155d / 33)
+ 89d / 49 * sin(9 * t + 35d / 22) + 50d / 99 * sin(10 * t + 19d / 12)
+ 35d / 52 * sin(12 * t + 49d / 30) + 80d / 39 * sin(13 * t + 21d / 13)
+ 25d / 23 * sin(15 * t + 34d / 21) + 13d / 38 * sin(16 * t + 96d / 61)
+ 17d / 31 * sin(17 * t + 17d / 10) + 55d / 39 * sin(18 * t + 61d / 38)
+ 17d / 32 * sin(19 * t + 179d / 38) + 16d / 13 * sin(20 * t + 55d / 34) + 10772d / 39)
* theta(75 * pi - t) * theta(t - 71 * pi)
+ (-sin(54d / 35 - 16 * t) - 17d / 29 * sin(86d / 57 - 12 * t)
- 43d / 19 * sin(47d / 30 - 2 * t) + 4197d / 25 * sin(t + 11d / 7)
+ 904d / 39 * sin(3 * t + 36d / 23) + 6d / 11 * sin(4 * t + 127d / 27)
+ 209d / 31 * sin(5 * t + 85d / 54) + 12d / 61 * sin(6 * t + 41d / 34)
+ 143d / 46 * sin(7 * t + 14d / 9) + 28d / 29 * sin(8 * t + 30d / 19)
+ 63d / 32 * sin(9 * t + 36d / 23) + 17d / 43 * sin(10 * t + 149d / 32)
+ 29d / 19 * sin(11 * t + 25d / 16) + 5d / 8 * sin(13 * t + 36d / 23)
+ 21d / 17 * sin(14 * t + 61d / 39) + 28d / 57 * sin(15 * t + 39d / 25)
+ 19d / 31 * sin(17 * t + 49d / 31) + 25d / 42 * sin(18 * t + 127d / 27)
+ 17d / 25 * sin(19 * t + 74d / 47) + 5d / 19 * sin(20 * t + 32d / 21)
+ 62d / 55 * sin(21 * t + 47d / 30) - 14987d / 44) * theta(71 * pi - t)
* theta(t - 67 * pi)
+ (-82d / 31 * sin(35d / 23 - 23 * t) - 165d / 82 * sin(31d / 20 - 22 * t)
- 109d / 20 * sin(36d / 23 - 12 * t) - 74d / 11 * sin(14d / 9 - 11 * t)
- 12d / 29 * sin(89d / 59 - 10 * t) - 8d / 17 * sin(19d / 13 - 7 * t)
- 211d / 35 * sin(14d / 9 - 6 * t) - 59d / 23 * sin(25d / 16 - 5 * t)
- 148d / 13 * sin(80d / 51 - 4 * t) - 465d / 13 * sin(36d / 23 - 2 * t)
+ 2488d / 25 * sin(t + 11d / 7) + 95d / 26 * sin(3 * t + 49d / 31)
+ 12d / 29 * sin(8 * t + 69d / 44) + 197d / 58 * sin(9 * t + 49d / 31)
+ 26d / 33 * sin(13 * t + 79d / 17) + 67d / 9 * sin(14 * t + 62d / 39)
+ 400d / 37 * sin(15 * t + 35d / 22) + 355d / 43 * sin(16 * t + 59d / 37)
+ 19d / 20 * sin(17 * t + 70d / 43) + 5d / 16 * sin(18 * t + 55d / 32)
+ 31d / 18 * sin(19 * t + 34d / 21) + 26d / 19 * sin(20 * t + 76d / 47)
+ 6d / 19 * sin(21 * t + 119d / 26) + 6093d / 19) * theta(67 * pi - t)
* theta(t - 63 * pi)
+ (-73d / 52 * sin(54d / 35 - 23 * t) - 54d / 25 * sin(58d / 37 - 19 * t)
- 73d / 20 * sin(14d / 9 - 17 * t) - 5d / 33 * sin(43d / 28 - 14 * t)
- 52d / 21 * sin(25d / 16 - 12 * t) + 4675d / 43 * sin(t + 96d / 61)
+ 353d / 28 * sin(2 * t + 30d / 19) + 3799d / 200 * sin(3 * t + 41d / 26)
+ 28d / 5 * sin(4 * t + 41d / 26) + 200d / 31 * sin(5 * t + 11d / 7)
+ 41d / 28 * sin(6 * t + 41d / 26) + 21d / 29 * sin(7 * t + 31d / 20)
+ 95d / 46 * sin(8 * t + 99d / 62) + 49d / 99 * sin(9 * t + 74d / 47)
+ 17d / 22 * sin(10 * t + 211d / 45) + 77d / 34 * sin(11 * t + 27d / 17)
+ 40d / 17 * sin(13 * t + 155d / 97) + 20d / 27 * sin(15 * t + 43d / 26)
+ 47d / 16 * sin(16 * t + 59d / 37) + 149d / 37 * sin(18 * t + 43d / 27)
+ 30d / 17 * sin(20 * t + 8d / 5) + 3d / 31 * sin(21 * t + 92d / 41)
+ 16d / 23 * sin(22 * t + 45d / 29) + 28d / 39 * sin(24 * t + 17d / 11) - 9671d / 24)
* theta(63 * pi - t) * theta(t - 59 * pi)
+ (-278d / 19 * sin(47d / 30 - 3 * t) - 181d / 29 * sin(58d / 37 - 2 * t)
- 2421d / 26 * sin(69d / 44 - t) + 9898d / 27) * theta(59 * pi - t)
* theta(t - 55 * pi)
+ (7671d / 67 * sin(t + 107d / 68) + 355d / 36 * sin(2 * t + 11d / 7)
+ 377d / 24 * sin(3 * t + 49d / 31) - 28766d / 63) * theta(55 * pi - t)
* theta(t - 51 * pi)
+ (-1345d / 28 * sin(80d / 51 - 2 * t) - 359d / 25 * sin(113d / 72 - t)
+ 259d / 15 * sin(3 * t + 11d / 7) + 5273d / 19) * theta(51 * pi - t)
* theta(t - 47 * pi)
+ (-10399d / 100 * sin(91d / 58 - t) + 1514d / 33 * sin(2 * t + 85d / 54) - 24712d / 67)
* theta(47 * pi - t) * theta(t - 43 * pi)
+ (-14d / 37 * sin(13d / 11 - 10 * t) + 300d / 41 * sin(t + 77d / 36)
+ 102d / 23 * sin(2 * t + 73d / 110) + 259d / 30 * sin(3 * t + 11d / 4)
+ 323d / 63 * sin(4 * t + 87d / 28) + 150d / 41 * sin(5 * t + 18d / 25)
+ 26d / 37 * sin(6 * t + 69d / 19) + 16d / 35 * sin(7 * t + 19d / 25)
+ 18d / 25 * sin(8 * t + 17d / 4) + 11d / 19 * sin(9 * t + 79d / 28)
+ 5d / 19 * sin(11 * t + 19d / 10) + 13d / 31 * sin(12 * t + 95d / 21) + 8431d / 36)
* theta(43 * pi - t) * theta(t - 39 * pi)
+ (-3d / 13 * sin(5d / 4 - 12 * t) - 21d / 29 * sin(59d / 38 - 6 * t)
- 70d / 11 * sin(26d / 19 - t) + 76d / 11 * sin(2 * t + 19d / 14)
+ 162d / 29 * sin(3 * t + 203d / 45) + 439d / 73 * sin(4 * t + 124d / 27)
+ 14d / 33 * sin(5 * t + 38d / 29) + 34d / 33 * sin(7 * t + 24d / 11)
+ 39d / 46 * sin(8 * t + 94d / 21) + 11d / 40 * sin(9 * t + 13d / 15)
+ 9d / 19 * sin(10 * t + 229d / 51) + 4d / 35 * sin(11 * t + 22d / 7) - 2147d / 6)
* theta(39 * pi - t) * theta(t - 35 * pi)
+ (769d / 16 * sin(t + 20d / 17) + 49d / 31 * sin(2 * t + 84d / 23)
+ 129d / 41 * sin(3 * t + 13d / 37) + 11433d / 47) * theta(35 * pi - t)
* theta(t - 31 * pi)
+ (-14d / 17 * sin(22d / 23 - 4 * t) - 21d / 25 * sin(37d / 56 - 2 * t)
+ 1493d / 31 * sin(t + 48d / 37) + 49d / 27 * sin(3 * t + 5d / 17) - 8077d / 23)
* theta(31 * pi - t) * theta(t - 27 * pi)
+ (2099d / 23 * sin(t + 112d / 67) + 25d / 32 * sin(2 * t + 68d / 23)
+ 129d / 16 * sin(3 * t + 50d / 27) + 31d / 34 * sin(4 * t + 373d / 112)
+ 38d / 17 * sin(5 * t + 21d / 11) + 38d / 53 * sin(6 * t + 32d / 9)
+ 25d / 28 * sin(7 * t + 83d / 46) + 10d / 19 * sin(8 * t + 134d / 35) + 10721d / 42)
* theta(27 * pi - t) * theta(t - 23 * pi)
+ (3072d / 29 * sin(t + 29d / 19) + 9d / 8 * sin(2 * t + 256d / 73)
+ 254d / 25 * sin(3 * t + 43d / 28) + 19d / 21 * sin(4 * t + 87d / 25)
+ 95d / 26 * sin(5 * t + 81d / 52) + 21d / 32 * sin(6 * t + 23d / 6)
+ 86d / 53 * sin(7 * t + 45d / 29) + 23d / 38 * sin(8 * t + 243d / 67) - 3827d / 11)
* theta(23 * pi - t) * theta(t - 19 * pi)
+ (-25d / 17 * sin(36d / 25 - 6 * t) - 99d / 46 * sin(18d / 29 - 4 * t)
+ 3796d / 29 * sin(t + 43d / 31) + 5d / 2 * sin(2 * t + 5d / 28)
+ 227d / 35 * sin(3 * t + 26d / 21) + 47d / 20 * sin(5 * t + 43d / 39)
+ 23d / 17 * sin(7 * t + 11d / 13) + 4572d / 17) * theta(19 * pi - t)
* theta(t - 15 * pi)
+ (6353d / 37 * sin(t + 37d / 21) + 430d / 59 * sin(2 * t + 165d / 37)
+ 537d / 43 * sin(3 * t + 78d / 31) + 133d / 25 * sin(4 * t + 143d / 32)
+ 128d / 25 * sin(5 * t + 78d / 23) + 218d / 61 * sin(6 * t + 174d / 37)
+ 51d / 22 * sin(7 * t + 34d / 9) - 12821d / 38) * theta(15 * pi - t)
* theta(t - 11 * pi)
+ (-36d / 23 * sin(13d / 18 - 12 * t) - 77d / 36 * sin(17d / 30 - 10 * t)
- 82d / 31 * sin(17d / 24 - 8 * t) - 255d / 62 * sin(26d / 37 - 6 * t)
- 192d / 37 * sin(9d / 16 - 4 * t) - 199d / 40 * sin(21d / 47 - 2 * t)
+ 5791d / 22 * sin(t + 63d / 41) + 1140d / 47 * sin(3 * t + 34d / 23)
+ 92d / 13 * sin(5 * t + 29d / 21) + 63d / 22 * sin(7 * t + 19d / 17)
+ 31d / 28 * sin(9 * t + 21d / 23) + 13d / 19 * sin(11 * t + 54d / 35) - 3874d / 61)
* theta(11 * pi - t) * theta(t - 7 * pi)
+ (-186d / 29 * sin(3d / 2 - 6 * t) - 452d / 43 * sin(81d / 65 - 4 * t)
- 487d / 39 * sin(31d / 34 - 2 * t) + 3854d / 13 * sin(t + 102d / 73)
+ 313d / 17 * sin(3 * t + 31d / 30) + 56d / 23 * sin(5 * t + 4d / 13)
+ 46d / 33 * sin(7 * t + 33d / 13) + 110d / 27 * sin(8 * t + 57d / 13)
+ 67d / 38 * sin(9 * t + 71d / 33) + 138d / 59 * sin(10 * t + 101d / 26)
+ 11d / 8 * sin(11 * t + 46d / 25) + 20d / 23 * sin(12 * t + 103d / 29) - 605d / 13)
* theta(7 * pi - t) * theta(t - 3 * pi)
+ (-320d / 43 * sin(21d / 34 - 6 * t) - 205d / 29 * sin(299d / 298 - 4 * t)
+ 47179d / 69 * sin(t + 6d / 13) + 307d / 32 * sin(2 * t + 46d / 51)
+ 1152d / 19 * sin(3 * t + 60d / 37) + 107d / 8 * sin(5 * t + 143d / 37)
+ 2626d / 175 * sin(7 * t + 45d / 26) + 131d / 22 * sin(8 * t + 143d / 40)
+ 296d / 47 * sin(9 * t + 500d / 499) + 16d / 7 * sin(10 * t + 93d / 25) - 4117d / 31)
* theta(3 * pi - t) * theta(t + pi)) * theta(Math.Sqrt(Math.Sign(sin(t / 2))));
Func yt =
t =>
((-52d / 5 * sin(54d / 37 - 34 * t) - 179d / 56 * sin(46d / 33 - 31 * t)
- 513d / 28 * sin(59d / 39 - 25 * t) - 316d / 105 * sin(43d / 28 - 22 * t)
- 259d / 16 * sin(102d / 65 - 17 * t) - 26239d / 64 * sin(36d / 23 - 3 * t)
- 18953d / 51 * sin(58d / 37 - t) + 11283d / 29 * sin(2 * t + 30d / 19)
+ 29123d / 35 * sin(4 * t + 49d / 31) + 6877d / 14 * sin(5 * t + 65d / 41)
+ 117d / 50 * sin(6 * t + 103d / 51) + 587d / 13 * sin(7 * t + 164d / 35)
+ 102d / 13 * sin(8 * t + 236d / 51) + 975d / 14 * sin(9 * t + 101d / 63)
+ 122d / 41 * sin(10 * t + 79d / 44) + 1900d / 139 * sin(11 * t + 117d / 25)
+ 597d / 22 * sin(12 * t + 31d / 19) + 1219d / 39 * sin(13 * t + 8d / 5)
+ 552d / 13 * sin(14 * t + 35d / 22) + 621d / 26 * sin(15 * t + 31d / 19)
+ 705d / 28 * sin(16 * t + 212d / 45) + 579d / 11 * sin(18 * t + 34d / 21)
+ 19d / 27 * sin(19 * t + 190d / 43) + 15d / 29 * sin(20 * t + 89d / 20)
+ 497d / 23 * sin(21 * t + 128d / 77) + 205d / 51 * sin(23 * t + 57d / 34)
+ 317d / 35 * sin(24 * t + 68d / 39) + 17d / 4 * sin(26 * t + 202d / 43)
+ 927d / 34 * sin(27 * t + 33d / 20) + 31d / 23 * sin(28 * t + 154d / 123)
+ 37d / 6 * sin(29 * t + 28d / 17) + 159d / 19 * sin(30 * t + 22d / 13)
+ 87d / 23 * sin(32 * t + 82d / 49) + 57d / 28 * sin(33 * t + 103d / 52)
+ 77d / 29 * sin(35 * t + 116d / 25) + 489d / 41 * sin(36 * t + 49d / 29)
+ 61d / 30 * sin(37 * t + 62d / 39) + 313d / 47 * sin(38 * t + 69d / 40)
+ 36d / 11 * sin(39 * t + 41d / 23) + 90d / 91 * sin(40 * t + 7d / 4)
+ 47d / 19 * sin(41 * t + 101d / 63) - 8810d / 27) * theta(119 * pi - t)
* theta(t - 115 * pi)
+ (-91d / 46 * sin(11d / 8 - 62 * t) - 59d / 28 * sin(39d / 34 - 61 * t)
- 11d / 2 * sin(89d / 67 - 60 * t) - 15d / 8 * sin(32d / 35 - 59 * t)
- 53d / 22 * sin(48d / 35 - 58 * t) - 175d / 176 * sin(13d / 12 - 54 * t)
- 71d / 15 * sin(30d / 23 - 53 * t) - 166d / 27 * sin(25d / 18 - 52 * t)
- 48d / 29 * sin(20d / 31 - 51 * t) - 547d / 114 * sin(43d / 31 - 50 * t)
- 271d / 41 * sin(51d / 37 - 46 * t) - 141d / 20 * sin(42d / 31 - 45 * t)
- 129d / 13 * sin(37d / 26 - 44 * t) - 164d / 23 * sin(37d / 26 - 41 * t)
- 451d / 52 * sin(31d / 21 - 40 * t) - 27d / 22 * sin(63d / 44 - 38 * t)
- 83d / 7 * sin(35d / 24 - 36 * t) - 874d / 93 * sin(7d / 5 - 35 * t)
- 117d / 22 * sin(22d / 17 - 34 * t) - 911d / 69 * sin(3d / 2 - 32 * t)
- 109d / 37 * sin(27d / 19 - 31 * t) - 31d / 13 * sin(16d / 19 - 27 * t)
- 383d / 10 * sin(64d / 43 - 26 * t) - 455d / 19 * sin(31d / 21 - 24 * t)
- 764d / 17 * sin(58d / 39 - 18 * t) - 5417d / 48 * sin(74d / 49 - 17 * t)
- 1557d / 35 * sin(80d / 53 - 16 * t) - 3366d / 25 * sin(71d / 46 - 12 * t)
- 2267d / 100 * sin(91d / 61 - 11 * t) - 1523d / 27 * sin(239d / 159 - 10 * t)
- 7929d / 44 * sin(36d / 23 - 7 * t) + 32716d / 55 * sin(t + 146d / 31)
+ 26497d / 40 * sin(2 * t + 30d / 19) + 28971d / 35 * sin(3 * t + 19d / 12)
+ 12399d / 44 * sin(4 * t + 117d / 73) + 3783d / 29 * sin(5 * t + 145d / 31)
+ 21737d / 40 * sin(6 * t + 46d / 29) + 132d / 7 * sin(8 * t + 23d / 14)
+ 887d / 32 * sin(9 * t + 25d / 16) + 963d / 14 * sin(13 * t + 67d / 41)
+ 972d / 11 * sin(14 * t + 47d / 29) + 5575d / 77 * sin(15 * t + 53d / 33)
+ 382d / 25 * sin(19 * t + 47d / 32) + 855d / 44 * sin(20 * t + 28d / 17)
+ 701d / 42 * sin(21 * t + 33d / 20) + 109d / 23 * sin(22 * t + 14d / 3)
+ 197d / 38 * sin(23 * t + 43d / 29) + 118d / 37 * sin(25 * t + 37d / 38)
+ 272d / 31 * sin(28 * t + 44d / 27) + 5d / 23 * sin(29 * t + 25d / 26)
+ 195d / 28 * sin(30 * t + 47d / 28) + 185d / 24 * sin(33 * t + 57d / 37)
+ 103d / 13 * sin(37 * t + 46d / 29) + 43d / 9 * sin(39 * t + 41d / 26)
+ 257d / 32 * sin(42 * t + 51d / 32) + 33d / 13 * sin(43 * t + 41d / 30)
+ 67d / 15 * sin(47 * t + 31d / 19) + 39d / 14 * sin(48 * t + 44d / 25)
+ 88d / 31 * sin(49 * t + 30d / 19) + 113d / 68 * sin(55 * t + 103d / 69)
+ 1d / 54 * sin(56 * t + 197d / 58) + 79d / 24 * sin(57 * t + 167d / 100) + 287d / 29)
* theta(115 * pi - t) * theta(t - 111 * pi)
+ (-8d / 25 * sin(17d / 31 - 90 * t) - 144d / 37 * sin(29d / 19 - 89 * t)
- 102d / 47 * sin(37d / 24 - 88 * t) - 74d / 43 * sin(24d / 17 - 87 * t)
- 95d / 17 * sin(25d / 16 - 49 * t) - 137d / 27 * sin(16d / 11 - 27 * t)
+ 21445d / 52 * sin(t + 69d / 44) + 24223d / 27 * sin(2 * t + 113d / 24)
+ 23911d / 28 * sin(3 * t + 146d / 31) + 2675d / 8 * sin(4 * t + 64d / 41)
+ 5772d / 19 * sin(5 * t + 36d / 23) + 3258d / 17 * sin(6 * t + 11d / 7)
+ 5245d / 37 * sin(7 * t + 174d / 37) + 355d / 16 * sin(8 * t + 117d / 73)
+ 225d / 8 * sin(9 * t + 88d / 19) + 3255d / 26 * sin(10 * t + 11d / 7)
+ 1137d / 19 * sin(11 * t + 39d / 25) + 1310d / 21 * sin(12 * t + 8d / 5)
+ 943d / 21 * sin(13 * t + 29d / 18) + 9679d / 81 * sin(14 * t + 80d / 51)
+ 113d / 20 * sin(15 * t + 47d / 28) + 1342d / 47 * sin(16 * t + 86d / 53)
+ 3679d / 84 * sin(17 * t + 55d / 36) + 353d / 20 * sin(18 * t + 50d / 11)
+ 939d / 50 * sin(19 * t + 201d / 43) + 4789d / 82 * sin(20 * t + 48d / 31)
+ 2649d / 85 * sin(21 * t + 303d / 65) + 1753d / 59 * sin(22 * t + 36d / 23)
+ 268d / 29 * sin(23 * t + 58d / 39) + 55d / 16 * sin(24 * t + 82d / 43)
+ 228d / 37 * sin(25 * t + 353d / 235) + 8d / 25 * sin(26 * t + 49d / 31)
+ 422d / 25 * sin(28 * t + 93d / 20) + 211d / 21 * sin(29 * t + 38d / 27)
+ 60d / 41 * sin(30 * t + 131d / 29) + 162d / 11 * sin(31 * t + 65d / 14)
+ 2489d / 63 * sin(32 * t + 35d / 23) + 688d / 27 * sin(33 * t + 129d / 28)
+ 1447d / 62 * sin(34 * t + 55d / 36) + 233d / 26 * sin(35 * t + 85d / 57)
+ 259d / 26 * sin(36 * t + 95d / 21) + 149d / 10 * sin(37 * t + 25d / 17)
+ 235d / 57 * sin(38 * t + 50d / 11) + 185d / 38 * sin(39 * t + 183d / 41)
+ 125d / 13 * sin(40 * t + 68d / 45) + 223d / 31 * sin(41 * t + 39d / 25)
+ 61d / 12 * sin(42 * t + 355d / 79) + 1262d / 99 * sin(43 * t + 160d / 107)
+ 309d / 40 * sin(44 * t + 41d / 26) + 307d / 38 * sin(45 * t + 221d / 48)
+ 49d / 5 * sin(46 * t + 137d / 91) + 193d / 31 * sin(47 * t + 190d / 41)
+ 77d / 54 * sin(48 * t + 95d / 63) + 20d / 33 * sin(50 * t + 148d / 51)
+ 256d / 47 * sin(51 * t + 53d / 39) + 133d / 37 * sin(52 * t + 92d / 21)
+ 19d / 7 * sin(53 * t + 121d / 81) + 39d / 4 * sin(54 * t + 71d / 47)
+ 341d / 85 * sin(55 * t + 113d / 25) + 71d / 31 * sin(56 * t + 115d / 67)
+ 31d / 10 * sin(57 * t + 36d / 25) + 11d / 5 * sin(58 * t + 30d / 7)
+ 62d / 23 * sin(59 * t + 33d / 23) + 40d / 33 * sin(60 * t + 67d / 36)
+ 13d / 40 * sin(61 * t + 32d / 19) + 47d / 6 * sin(62 * t + 80d / 53)
+ 48d / 11 * sin(63 * t + 73d / 16) + 301d / 47 * sin(64 * t + 56d / 37)
+ 361d / 120 * sin(65 * t + 191d / 41) + 59d / 31 * sin(66 * t + 83d / 52)
+ 132d / 25 * sin(67 * t + 117d / 25) + 37d / 13 * sin(68 * t + 4d / 3)
+ 167d / 35 * sin(69 * t + 183d / 40) + 67d / 41 * sin(70 * t + 4d / 3)
+ 103d / 42 * sin(71 * t + 49d / 34) + 199d / 71 * sin(72 * t + 101d / 23)
+ 200d / 31 * sin(73 * t + 77d / 53) + 81d / 58 * sin(74 * t + 169d / 38)
+ 17d / 21 * sin(75 * t + 83d / 20) + 27d / 38 * sin(76 * t + 79d / 59)
+ 59d / 29 * sin(77 * t + 47d / 33) + 175d / 44 * sin(78 * t + 114d / 25)
+ 54d / 19 * sin(79 * t + 63d / 43) + 19d / 27 * sin(80 * t + 61d / 27)
+ 149d / 26 * sin(81 * t + 16d / 11) + 68d / 29 * sin(82 * t + 102d / 25)
+ 313d / 68 * sin(83 * t + 54d / 35) + 147d / 23 * sin(84 * t + 47d / 32)
+ 73d / 12 * sin(85 * t + 107d / 24) + 191d / 51 * sin(86 * t + 38d / 27)
+ 37d / 28 * sin(91 * t + 173d / 37) + 70d / 43 * sin(92 * t + 35d / 23)
+ 44d / 35 * sin(93 * t + 53d / 13) + 164d / 35 * sin(94 * t + 107d / 67)
+ 141d / 34 * sin(95 * t + 37d / 25) + 19d / 12 * sin(96 * t + 83d / 21)
+ 22d / 23 * sin(97 * t + 47d / 31) + 152d / 39 * sin(98 * t + 60d / 43)
+ 123d / 28 * sin(99 * t + 132d / 29) - 15137d / 22) * theta(111 * pi - t)
* theta(t - 107 * pi)
+ (-43d / 40 * sin(102d / 65 - 45 * t) - 74d / 41 * sin(25d / 27 - 35 * t)
- 47d / 19 * sin(15d / 16 - 34 * t) - 67d / 32 * sin(21d / 25 - 33 * t)
- 161d / 39 * sin(27d / 20 - 32 * t) - 12d / 23 * sin(17d / 12 - 29 * t)
- 29d / 57 * sin(45d / 37 - 27 * t) - 19d / 16 * sin(117d / 88 - 25 * t)
- 11d / 36 * sin(15d / 22 - 24 * t) - 11d / 30 * sin(33d / 82 - 23 * t)
- 43d / 57 * sin(14d / 17 - 22 * t) - 87d / 65 * sin(49d / 41 - 21 * t)
- 50d / 21 * sin(64d / 47 - 20 * t) - 17d / 59 * sin(56d / 55 - 6 * t)
- 56d / 61 * sin(77d / 58 - 5 * t) + 127d / 28 * sin(t + 149d / 32)
+ 15d / 2 * sin(2 * t + 21d / 13) + 35d / 29 * sin(3 * t + 49d / 29)
+ 1d / 9 * sin(4 * t + 51d / 43) + 37d / 38 * sin(7 * t + 19d / 12)
+ 18d / 31 * sin(8 * t + 57d / 13) + 38d / 31 * sin(9 * t + 55d / 12)
+ 7d / 10 * sin(10 * t + 74d / 45) + 9d / 34 * sin(11 * t + 69d / 34)
+ 39d / 19 * sin(12 * t + 41d / 26) + 89d / 26 * sin(13 * t + 67d / 42)
+ 63d / 26 * sin(14 * t + 107d / 23) + 119d / 16 * sin(15 * t + 23d / 5)
+ 311d / 18 * sin(16 * t + 56d / 33) + 1929d / 386 * sin(17 * t + 99d / 50)
+ 79d / 41 * sin(18 * t + 64d / 29) + 34d / 41 * sin(19 * t + 67d / 35)
+ 16d / 41 * sin(26 * t + 49d / 33) + 1d / 34 * sin(28 * t + 5d / 14)
+ 36d / 43 * sin(30 * t + 193d / 41) + 173d / 42 * sin(31 * t + 30d / 19)
+ 15d / 19 * sin(36 * t + 31d / 28) + 2d / 19 * sin(37 * t + 87d / 43)
+ 22d / 39 * sin(38 * t + 33d / 14) + 13d / 23 * sin(39 * t + 19d / 6)
+ 21d / 19 * sin(40 * t + 1641d / 820) + 29d / 28 * sin(41 * t + 172d / 39)
+ 39d / 34 * sin(42 * t + 58d / 31) + 16d / 29 * sin(43 * t + 50d / 23)
+ 24d / 25 * sin(44 * t + 41d / 23) + 17d / 23 * sin(46 * t + 289d / 62)
+ 37d / 25 * sin(47 * t + 30d / 17) + 17d / 29 * sin(48 * t + 239d / 52)
+ 29d / 73 * sin(49 * t + 41d / 26) - 8044d / 23) * theta(107 * pi - t)
* theta(t - 103 * pi)
+ (-33d / 29 * sin(7d / 6 - 53 * t) - 67d / 44 * sin(62d / 45 - 51 * t)
- 32d / 65 * sin(1d / 14 - 50 * t) - 151d / 49 * sin(54d / 41 - 49 * t)
- 63d / 38 * sin(29d / 23 - 47 * t) - 59d / 103 * sin(14d / 23 - 46 * t)
- 11d / 30 * sin(8d / 23 - 45 * t) - 151d / 32 * sin(99d / 79 - 44 * t)
- 53d / 26 * sin(45d / 38 - 43 * t) - 67d / 27 * sin(38d / 29 - 36 * t)
- 113d / 32 * sin(39d / 29 - 35 * t) - 182d / 51 * sin(81d / 58 - 33 * t)
- 391d / 65 * sin(33d / 23 - 29 * t) - 48d / 13 * sin(31d / 20 - 25 * t)
- 59d / 32 * sin(24d / 17 - 19 * t) - 90d / 91 * sin(41d / 33 - 18 * t)
- 863d / 54 * sin(35d / 24 - 17 * t) - 384d / 43 * sin(73d / 51 - 16 * t)
- 149d / 26 * sin(19d / 13 - 13 * t) - 90d / 19 * sin(65d / 43 - 12 * t)
+ 10d / 29 * sin(t + 47d / 32) + 15d / 17 * sin(2 * t + 77d / 45)
+ 300d / 37 * sin(3 * t + 62d / 39) + 4d / 13 * sin(4 * t + 8d / 5)
+ 7d / 29 * sin(5 * t + 109d / 25) + 46d / 27 * sin(6 * t + 49d / 30)
+ 39d / 23 * sin(7 * t + 30d / 19) + 64d / 47 * sin(8 * t + 72d / 43)
+ 19d / 20 * sin(9 * t + 63d / 37) + 14d / 5 * sin(10 * t + 41d / 25)
+ 37d / 14 * sin(11 * t + 27d / 16) + 207d / 28 * sin(14 * t + 248d / 149)
+ 288d / 25 * sin(15 * t + 58d / 35) + 123d / 52 * sin(20 * t + 85d / 46)
+ 194d / 13 * sin(21 * t + 17d / 10) + 64d / 13 * sin(22 * t + 103d / 22)
+ 335d / 27 * sin(23 * t + 31d / 18) + 103d / 18 * sin(24 * t + 13d / 7)
+ 83d / 20 * sin(26 * t + 117d / 67) + 243d / 52 * sin(27 * t + 36d / 19)
+ 1907d / 477 * sin(28 * t + 125d / 73) + 73d / 30 * sin(30 * t + 182d / 109)
+ 182d / 109 * sin(31 * t + 43d / 23) + 53d / 23 * sin(32 * t + 147d / 92)
+ 21d / 43 * sin(34 * t + 145d / 144) + 20d / 17 * sin(37 * t + 29d / 14)
+ 110d / 27 * sin(38 * t + 79d / 44) + 22d / 27 * sin(39 * t + 74d / 17)
+ 99d / 37 * sin(40 * t + 52d / 29) + 36d / 25 * sin(41 * t + 255d / 128)
+ 11d / 15 * sin(42 * t + 124d / 69) + 31d / 17 * sin(48 * t + 67d / 41)
+ 15d / 14 * sin(52 * t + 73d / 47) - 10105d / 36) * theta(103 * pi - t)
* theta(t - 99 * pi)
+ (3683d / 48 * sin(t + 74d / 47) + 41d / 26 * sin(2 * t + 103d / 22)
+ 149d / 17 * sin(3 * t + 85d / 54) + 6d / 13 * sin(4 * t + 51d / 11)
+ 112d / 43 * sin(5 * t + 11d / 7) + 17294d / 53) * theta(99 * pi - t)
* theta(t - 95 * pi)
+ (-19d / 40 * sin(29d / 20 - 11 * t) - 289d / 38 * sin(36d / 23 - 9 * t)
+ 802d / 33 * sin(t + 179d / 38) + 3002d / 35 * sin(2 * t + 85d / 54)
+ 159d / 41 * sin(3 * t + 61d / 39) + 1321d / 44 * sin(4 * t + 52d / 33)
+ 131d / 22 * sin(5 * t + 113d / 24) + 52d / 35 * sin(6 * t + 69d / 44)
+ 321d / 37 * sin(7 * t + 36d / 23) + 789d / 158 * sin(8 * t + 36d / 23)
+ 56d / 113 * sin(10 * t + 50d / 33) + 237d / 118 * sin(12 * t + 39d / 25) - 703d / 42)
* theta(95 * pi - t) * theta(t - 91 * pi)
+ (-121d / 68 * sin(25d / 16 - 4 * t) - 55d / 27 * sin(81d / 52 - 3 * t)
- 613d / 68 * sin(25d / 16 - 2 * t) - 505d / 19 * sin(47d / 30 - t) + 16067d / 23)
* theta(91 * pi - t) * theta(t - 87 * pi)
+ (-83d / 19 * sin(47d / 30 - 5 * t) + 56d / 25 * sin(t + 193d / 41)
+ 35d / 29 * sin(2 * t + 146d / 31) + 127d / 25 * sin(3 * t + 74d / 47)
+ 143d / 35 * sin(4 * t + 63d / 40) + 33d / 50 * sin(6 * t + 107d / 68) + 17679d / 28)
* theta(87 * pi - t) * theta(t - 83 * pi)
+ (-35d / 32 * sin(31d / 20 - 11 * t) - 55d / 48 * sin(61d / 39 - 9 * t)
- 30d / 17 * sin(50d / 33 - 6 * t) - 247d / 17 * sin(64d / 41 - 5 * t)
- 471d / 35 * sin(58d / 37 - 3 * t) + 405d / 23 * sin(t + 41d / 26)
+ 829d / 69 * sin(2 * t + 11d / 7) + 279d / 17 * sin(4 * t + 30d / 19)
+ 185d / 27 * sin(7 * t + 93d / 58) + 92d / 25 * sin(8 * t + 43d / 27)
+ 1d / 17 * sin(10 * t + 56d / 31) + 64d / 35 * sin(12 * t + 37d / 23) + 3306d / 17)
* theta(83 * pi - t) * theta(t - 79 * pi)
+ (-143d / 24 * sin(36d / 23 - t) + 9d / 22 * sin(2 * t + 47d / 10)
+ 31d / 42 * sin(3 * t + 28d / 17) + 1287d / 103 * sin(4 * t + 30d / 19)
+ 626d / 51 * sin(5 * t + 41d / 26) + 173d / 31 * sin(6 * t + 113d / 24)
+ 138d / 19 * sin(7 * t + 19d / 12) + 15d / 4 * sin(8 * t + 27d / 17)
+ 39d / 34 * sin(9 * t + 8d / 5) + 11d / 18 * sin(10 * t + 202d / 43)
+ 23d / 25 * sin(11 * t + 71d / 44) + 133d / 34 * sin(12 * t + 27d / 17) + 19064d / 89)
* theta(79 * pi - t) * theta(t - 75 * pi)
+ (-69d / 38 * sin(44d / 29 - 19 * t) - 49d / 17 * sin(119d / 79 - 16 * t)
- 65d / 23 * sin(83d / 55 - 11 * t) - 149d / 35 * sin(32d / 21 - 10 * t)
- 311d / 56 * sin(14d / 9 - 8 * t) - 83d / 40 * sin(20d / 13 - 7 * t)
- 35d / 6 * sin(57d / 37 - 6 * t) - 55d / 19 * sin(57d / 37 - 5 * t)
- 93d / 19 * sin(39d / 25 - 4 * t) - 87d / 8 * sin(39d / 25 - 3 * t)
- 517d / 30 * sin(25d / 16 - 2 * t) + 387d / 28 * sin(t + 91d / 58)
+ 68d / 33 * sin(9 * t + 27d / 17) + 67d / 34 * sin(12 * t + 76d / 47)
+ 13d / 20 * sin(13 * t + 45d / 26) + 2d / 25 * sin(14 * t + 127d / 28)
+ 131d / 56 * sin(15 * t + 61d / 38) + 62d / 29 * sin(17 * t + 188d / 113)
+ 26d / 37 * sin(18 * t + 77d / 46) + 8d / 33 * sin(20 * t + 43d / 38) + 5327d / 11)
* theta(75 * pi - t) * theta(t - 71 * pi)
+ (-21d / 23 * sin(98d / 65 - 16 * t) - 22d / 23 * sin(47d / 30 - 9 * t)
- 13d / 19 * sin(25d / 16 - 7 * t) + 28d / 57 * sin(t + 87d / 56)
+ 1265d / 47 * sin(2 * t + 179d / 38) + 223d / 20 * sin(3 * t + 11d / 7)
+ 227d / 19 * sin(4 * t + 179d / 38) + 45d / 22 * sin(5 * t + 11d / 7)
+ 188d / 53 * sin(6 * t + 127d / 27) + 116d / 35 * sin(8 * t + 179d / 38)
+ 19d / 12 * sin(10 * t + 27d / 17) + 8d / 11 * sin(11 * t + 19d / 12)
+ 29d / 13 * sin(12 * t + 179d / 38) + 69d / 43 * sin(13 * t + 25d / 16)
+ 277d / 278 * sin(14 * t + 107d / 23) + 31d / 27 * sin(15 * t + 127d / 27)
+ 63d / 22 * sin(17 * t + 155d / 33) + 13d / 19 * sin(18 * t + 43d / 27)
+ 107d / 89 * sin(19 * t + 103d / 22) + 13d / 12 * sin(20 * t + 61d / 13)
+ 22d / 17 * sin(21 * t + 39d / 25) + 8121d / 16) * theta(71 * pi - t)
* theta(t - 67 * pi)
+ (-89d / 18 * sin(68d / 45 - 23 * t) - 27d / 17 * sin(26d / 17 - 20 * t)
- 109d / 39 * sin(73d / 47 - 18 * t) - 142d / 57 * sin(26d / 17 - 17 * t)
- 146d / 27 * sin(45d / 29 - 14 * t) - 43d / 9 * sin(31d / 20 - 13 * t)
- 164d / 33 * sin(95d / 61 - 12 * t) - 91d / 34 * sin(43d / 28 - 11 * t)
- 30d / 19 * sin(29d / 19 - 9 * t) - 55d / 17 * sin(59d / 38 - 8 * t)
- 183d / 29 * sin(64d / 41 - 6 * t) - 137d / 25 * sin(53d / 34 - 5 * t)
- 124d / 19 * sin(36d / 23 - 4 * t) - 655d / 44 * sin(47d / 30 - 2 * t)
- 472d / 13 * sin(58d / 37 - t) + 43d / 57 * sin(3 * t + 70d / 43)
+ 41d / 12 * sin(7 * t + 85d / 54) + 29d / 115 * sin(10 * t + 38d / 23)
+ 27d / 7 * sin(15 * t + 19d / 12) + 21d / 20 * sin(16 * t + 36d / 23)
+ 26d / 51 * sin(19 * t + 36d / 23) + 2d / 31 * sin(21 * t + 67d / 42)
+ 59d / 26 * sin(22 * t + 31d / 19) + 8662d / 25) * theta(67 * pi - t)
* theta(t - 63 * pi)
+ (-40d / 27 * sin(86d / 57 - 24 * t) - 5d / 33 * sin(4d / 15 - 23 * t)
- 107d / 27 * sin(57d / 37 - 22 * t) - 163d / 12 * sin(37d / 24 - 18 * t)
- 80d / 43 * sin(73d / 47 - 15 * t) - 245d / 57 * sin(31d / 20 - 13 * t)
- 22d / 29 * sin(43d / 28 - 10 * t) - 99d / 20 * sin(59d / 38 - 8 * t)
- 18d / 11 * sin(59d / 38 - 7 * t) - 35d / 16 * sin(58d / 37 - 6 * t)
- 81d / 161 * sin(41d / 28 - 3 * t) - 271d / 13 * sin(58d / 37 - 2 * t)
+ 148d / 7 * sin(t + 85d / 54) + 98d / 25 * sin(4 * t + 146d / 31)
+ 67d / 24 * sin(5 * t + 30d / 19) + 8d / 25 * sin(9 * t + 179d / 38)
+ 5d / 9 * sin(11 * t + 131d / 28) + 46d / 51 * sin(12 * t + 32d / 21)
+ 108d / 31 * sin(14 * t + 69d / 43) + 149d / 29 * sin(16 * t + 45d / 28)
+ 59d / 15 * sin(17 * t + 46d / 29) + 134d / 21 * sin(19 * t + 125d / 78)
+ 158d / 27 * sin(20 * t + 44d / 27) + 35d / 29 * sin(21 * t + 31d / 19) + 9838d / 25)
* theta(63 * pi - t) * theta(t - 59 * pi)
+ (-385d / 16 * sin(47d / 30 - 3 * t) - 21082d / 91 * sin(69d / 44 - t)
+ 21d / 13 * sin(2 * t + 8d / 5) - 31214d / 91) * theta(59 * pi - t)
* theta(t - 55 * pi)
+ (-860d / 41 * sin(39d / 25 - 3 * t) - 5675d / 26 * sin(69d / 44 - t)
+ 265d / 43 * sin(2 * t + 46d / 29) - 33516d / 73) * theta(55 * pi - t)
* theta(t - 51 * pi)
+ (-621d / 28 * sin(36d / 23 - 3 * t) - 244d / 31 * sin(91d / 58 - 2 * t)
- 4739d / 19 * sin(102d / 65 - t) - 20129d / 76) * theta(51 * pi - t)
* theta(t - 47 * pi)
+ (-504d / 31 * sin(25d / 16 - 2 * t) - 6167d / 31 * sin(80d / 51 - t) - 4810d / 29)
* theta(47 * pi - t) * theta(t - 43 * pi)
+ (-1d / 14 * sin(9d / 11 - 12 * t) - 21d / 41 * sin(29d / 25 - 11 * t)
- 7d / 10 * sin(48d / 35 - 9 * t) + 157d / 25 * sin(t + 118d / 41)
+ 92d / 41 * sin(2 * t + 110d / 39) + 571d / 84 * sin(3 * t + 101d / 23)
+ 146d / 37 * sin(4 * t + 211d / 48) + 71d / 34 * sin(5 * t + 45d / 26)
+ 7d / 31 * sin(6 * t + 4d / 3) + 7d / 13 * sin(7 * t + 44d / 25)
+ 9d / 11 * sin(8 * t + 37d / 53) + 12d / 29 * sin(10 * t + 31d / 18) + 16173d / 50)
* theta(43 * pi - t) * theta(t - 39 * pi)
+ (-25d / 29 * sin(1d / 110 - 10 * t) - 81d / 71 * sin(11d / 29 - 6 * t)
- 101d / 19 * sin(16d / 49 - 4 * t) - 81d / 19 * sin(11d / 43 - 3 * t)
+ 167d / 43 * sin(t + 175d / 41) + 181d / 37 * sin(2 * t + 58d / 17)
+ 6d / 5 * sin(5 * t + 61d / 14) + 25d / 22 * sin(7 * t + 3)
+ 37d / 30 * sin(8 * t + 1d / 25) + 31d / 40 * sin(9 * t + 61d / 22)
+ 9d / 35 * sin(11 * t + 103d / 30) + 14d / 19 * sin(12 * t + 1d / 10) + 8453d / 25)
* theta(39 * pi - t) * theta(t - 35 * pi)
+ (-151d / 36 * sin(17d / 23 - 3 * t) - 331d / 12 * sin(8d / 31 - t)
+ 184d / 47 * sin(2 * t + 160d / 39) + 324) * theta(35 * pi - t) * theta(t - 31 * pi)
+ (-50d / 19 * sin(6d / 17 - 3 * t) - 1333d / 36 * sin(1d / 5 - t)
+ 23d / 19 * sin(2 * t + 23d / 9) + 29d / 36 * sin(4 * t + 67d / 24) + 13271d / 39)
* theta(31 * pi - t) * theta(t - 27 * pi)
+ (-119d / 22 * sin(27d / 19 - 2 * t) + 1265d / 36 * sin(t + 4d / 29)
+ 98d / 15 * sin(3 * t + 3d / 5) + 89d / 48 * sin(4 * t + 142d / 31)
+ 55d / 19 * sin(5 * t + 32d / 37) + 16d / 17 * sin(6 * t + 89d / 25)
+ 21d / 16 * sin(7 * t + 23d / 40) + 8d / 13 * sin(8 * t + 37d / 12) + 10562d / 33)
* theta(27 * pi - t) * theta(t - 23 * pi)
+ (-71d / 46 * sin(1d / 11 - 7 * t) - 115d / 64 * sin(5d / 19 - 5 * t)
- 11d / 28 * sin(16d / 25 - 4 * t) - 44d / 17 * sin(33d / 43 - 3 * t)
- 1265d / 29 * sin(2d / 13 - t) + 59d / 16 * sin(2 * t + 211d / 53)
+ 12d / 25 * sin(6 * t + 57d / 20) + 26d / 51 * sin(8 * t + 65d / 17) + 11467d / 34)
* theta(23 * pi - t) * theta(t - 19 * pi)
+ (-23d / 41 * sin(81d / 58 - 5 * t) + 4367d / 48 * sin(t + 111d / 38)
+ 49d / 16 * sin(2 * t + 173d / 39) + 134d / 45 * sin(3 * t + 70d / 29)
+ 64d / 37 * sin(4 * t + 41d / 17) + 21d / 46 * sin(6 * t + 29d / 13)
+ 10d / 19 * sin(7 * t + 53d / 37) + 10855d / 34) * theta(19 * pi - t)
* theta(t - 15 * pi)
+ (-127d / 13 * sin(7d / 18 - 3 * t) + 2713d / 29 * sin(t + 2d / 37)
+ 101d / 13 * sin(2 * t + 203d / 45) + 89d / 34 * sin(4 * t + 73d / 17)
+ 26d / 15 * sin(5 * t + 26d / 41) + 2d / 9 * sin(6 * t + 177d / 50)
+ 35d / 71 * sin(7 * t + 66d / 31) + 10805d / 33) * theta(15 * pi - t)
* theta(t - 11 * pi)
+ (-20d / 23 * sin(38d / 29 - 11 * t) - 31d / 18 * sin(46d / 37 - 9 * t)
- 497d / 108 * sin(9d / 16 - 5 * t) - 2375d / 26 * sin(3d / 29 - t)
+ 970d / 41 * sin(2 * t + 35d / 32) + 1011d / 92 * sin(3 * t + 7d / 38)
+ 131d / 27 * sin(4 * t + 91d / 90) + 24d / 71 * sin(6 * t + 34d / 37)
+ 90d / 29 * sin(7 * t + 14d / 23) + 21d / 16 * sin(8 * t + 25d / 12)
+ 21d / 38 * sin(10 * t + 89d / 19) + 7d / 27 * sin(12 * t + 68d / 15) - 10719d / 37)
* theta(11 * pi - t) * theta(t - 7 * pi)
+ (-11d / 37 * sin(4d / 7 - 6 * t) - 299d / 56 * sin(24d / 19 - 5 * t)
- 499d / 38 * sin(5d / 44 - 3 * t) - 6150d / 37 * sin(12d / 59 - t)
+ 1019d / 38 * sin(2 * t + 28d / 37) + 183d / 53 * sin(4 * t + 85d / 71)
+ 95d / 43 * sin(7 * t + 169d / 38) + 29d / 27 * sin(8 * t + 111d / 40)
+ 21d / 22 * sin(9 * t + 16d / 29) + 194d / 83 * sin(10 * t + 164d / 57)
+ 31d / 30 * sin(11 * t + 1d / 53) + 17d / 31 * sin(12 * t + 77d / 29) - 24819d / 82)
* theta(7 * pi - t) * theta(t - 3 * pi)
+ (-14d / 13 * sin(4d / 45 - 10 * t) - 229d / 26 * sin(16d / 23 - 7 * t)
- 222d / 17 * sin(28d / 23 - 5 * t) - 851d / 29 * sin(10d / 51 - 3 * t)
- 12070d / 13 * sin(12d / 11 - t) + 270d / 31 * sin(2 * t + 62d / 15)
+ 53d / 7 * sin(4 * t + 400d / 87) + 59d / 10 * sin(6 * t + 12d / 13)
+ 141d / 31 * sin(8 * t + 30d / 17) + 79d / 40 * sin(9 * t + 121d / 26) + 5838d / 29)
* theta(3 * pi - t) * theta(t + pi)) * theta(Math.Sqrt(Math.Sign(sin(t / 2))));
var model = new PlotModel { Title = "Angelina Jolie curve", PlotType = PlotType.Cartesian };
var fs = new FunctionSeries(xt, yt, 0, Math.PI * 120, 10000);
model.Series.Add(fs);
// Insert breaks at discontinuities
// TODO: this should be improved...
for (int i = 0; i + 1 < fs.Points.Count; i++)
{
var dx = fs.Points[i + 1].X - fs.Points[i].X;
var dy = fs.Points[i + 1].Y - fs.Points[i].Y;
if ((dx * dx) + (dy * dy) > 100000)
{
fs.Points.Insert(i + 1, new DataPoint(double.NaN, double.NaN));
i++;
}
}
return model;
}
///
/// Gets the stream for the specified embedded resource.
///
/// The name of the resource.
/// A stream.
private static Stream GetResourceStream(string name)
{
return typeof(MiscExamples).GetTypeInfo().Assembly.GetManifestResourceStream("ExampleLibrary.Resources." + name);
}
///
/// Renders the Mandelbrot set as an image inside the current plot area.
///
public class MandelbrotSetSeries : XYAxisSeries
{
///
/// Initializes a new instance of the class.
///
public MandelbrotSetSeries()
{
this.TrackerFormatString = "X: {0:0.000}\r\nY: {1:0.000}\r\nIterations: {2}";
}
///
/// Gets or sets the color axis.
///
/// The color axis.
/// The Maximum value of the ColorAxis defines the maximum number of iterations.
public LinearColorAxis ColorAxis { get; protected set; }
///
/// Gets or sets the color axis key.
///
/// The color axis key.
public string ColorAxisKey { get; set; }
///
/// Gets the point on the series that is nearest the specified point.
///
/// The point.
/// Interpolate the series if this flag is set to true.
/// A TrackerHitResult for the current hit.
public override TrackerHitResult GetNearestPoint(ScreenPoint point, bool interpolate)
{
var p = this.InverseTransform(point);
var it = this.Solve(p.X, p.Y, (int)this.ColorAxis.ActualMaximum + 1);
return new TrackerHitResult
{
Series = this,
DataPoint = p,
Position = point,
Item = null,
Index = -1,
Text = StringHelper.Format(this.ActualCulture, this.TrackerFormatString, null, p.X, p.Y, it)
};
}
///
/// Renders the series on the specified render context.
///
/// The rendering context.
public override void Render(IRenderContext rc)
{
var p0 = this.Transform(this.XAxis.ActualMinimum, this.YAxis.ActualMinimum);
var p1 = this.Transform(this.XAxis.ActualMaximum, this.YAxis.ActualMaximum);
var w = (int)(p1.X - p0.X);
var h = (int)(p0.Y - p1.Y);
int maxIterations = (int)this.ColorAxis.ActualMaximum + 1;
var pixels = new OxyColor[w, h];
ParallelFor(
0,
h,
i =>
{
double y = this.YAxis.ActualMaximum - ((double)i / (h - 1) * (this.YAxis.ActualMaximum - this.YAxis.ActualMinimum));
for (int j = 0; j < w; j++)
{
double x = this.XAxis.ActualMinimum
+ ((double)j / (w - 1)
* (this.XAxis.ActualMaximum - this.XAxis.ActualMinimum));
var iterations = Solve(x, y, maxIterations);
pixels[j, i] = this.ColorAxis.GetColor((double)iterations);
}
});
var bitmap = OxyImage.Create(pixels, ImageFormat.Png);
rc.DrawImage(bitmap, p0.X, p1.Y, p1.X - p0.X, p0.Y - p1.Y, 1, true);
}
///
/// Calculates the escape time for the specified point.
///
/// The x0.
/// The y0.
/// The max number of iterations.
/// The number of iterations.
protected virtual int Solve(double x0, double y0, int maxIterations)
{
int iteration = 0;
double x = 0;
double y = 0;
while ((x * x) + (y * y) <= 4 && iteration < maxIterations)
{
double xtemp = (x * x) - (y * y) + x0;
y = (2 * x * y) + y0;
x = xtemp;
iteration++;
}
return iteration;
}
///
/// Ensures that the axes of the series is defined.
///
protected override void EnsureAxes()
{
base.EnsureAxes();
this.ColorAxis = this.ColorAxisKey != null ?
this.PlotModel.GetAxis(this.ColorAxisKey) as LinearColorAxis :
this.PlotModel.DefaultColorAxis as LinearColorAxis;
}
///
/// Executes a serial for loop.
///
/// The start index (inclusive).
/// The end index (exclusive).
/// The action that is invoked once per iteration.
private static void SerialFor(int i0, int i1, Action action)
{
for (int i = i0; i < i1; i++)
{
action(i);
}
}
///
/// Executes a parallel for loop using ThreadPool.
///
/// The start index (inclusive).
/// The end index (exclusive).
/// The action that is invoked once per iteration.
private static void ParallelFor(int i0, int i1, Action action)
{
// Environment.ProcessorCount is not available here. Use 4 processors.
int p = 4;
// Initialize wait handles
var doneEvents = new WaitHandle[p];
for (int i = 0; i < p; i++)
{
doneEvents[i] = new ManualResetEvent(false);
}
// Invoke the action of a partition of the range
Action invokePartition = (k, j0, j1) =>
{
for (int i = j0; i < j1; i++)
{
action(i);
}
((ManualResetEvent)doneEvents[k]).Set();
};
// Start p background threads
int n = (i1 - i0 + p - 1) / p;
for (int i = 0; i < p; i++)
{
int k = i;
int j0 = i0 + (i * n);
var j1 = Math.Min(j0 + n, i1);
Task.Factory.StartNew(
() => invokePartition(k, j0, j1),
CancellationToken.None,
TaskCreationOptions.LongRunning,
TaskScheduler.Default);
}
// Wait for the threads to finish
foreach (var wh in doneEvents)
{
wh.WaitOne();
}
}
}
private class JuliaSetSeries : MandelbrotSetSeries
{
public double C1 { get; set; }
public double C2 { get; set; }
protected override int Solve(double x0, double y0, int maxIterations)
{
int iteration = 0;
double x = x0;
double y = y0;
double cr = this.C1;
double ci = this.C2;
while ((x * x) + (y * y) <= 4 && iteration < maxIterations)
{
double xtemp = (x * x) - (y * y) + cr;
y = (2 * x * y) + ci;
x = xtemp;
iteration++;
}
return iteration;
}
}
private class CustomAxis : LinearAxis
{
public IList MajorTicks { get; } = new List();
public IList MinorTicks { get; } = new List();
public IList Labels { get; } = new List();
public override void GetTickValues(out IList majorLabelValues, out IList majorTickValues, out IList minorTickValues)
{
majorTickValues = majorLabelValues = this.MajorTicks.Where(d => d >= this.ActualMinimum && d <= this.ActualMaximum).ToList();
minorTickValues = this.MinorTicks.Where(d => d >= this.ActualMinimum && d <= this.ActualMaximum).ToList();
}
protected override string FormatValueOverride(double x)
{
return this.Labels[this.MajorTicks.IndexOf(x)];
}
}
}
}