Add ScottPlot.WinForms using Manage NuGet packages.<\/p>\n
Form1.cs<\/p>\n
\r\nusing System.Data;\r\nusing System.Drawing;\r\nusing System.Linq;\r\nusing System.Text;\r\nusing System.Threading.Tasks;\r\nusing System.Windows.Forms;\r\nusing ScottPlot;\r\n\r\nnamespace Spline\r\n{\r\n public partial class Form1 : Form\r\n {\r\n public static class Cubic\r\n {\r\n \/\/\/ <summary>\r\n \/\/\/ Generate a smooth (interpolated) curve that follows the path of the given X\/Y points\r\n \/\/\/ <\/summary>\r\n public static (double[] xs, double[] ys) InterpolateXY(double[] xs, double[] ys, int count)\r\n {\r\n if (xs is null || ys is null || xs.Length != ys.Length)\r\n throw new ArgumentException($"{nameof(xs)} and {nameof(ys)} must have same length");\r\n\r\n int inputPointCount = xs.Length;\r\n double[] inputDistances = new double[inputPointCount];\r\n for (int i = 1; i < inputPointCount; i++)\r\n {\r\n double dx = xs[i] - xs[i - 1];\r\n double dy = ys[i] - ys[i - 1];\r\n double distance = Math.Sqrt(dx * dx + dy * dy);\r\n inputDistances[i] = inputDistances[i - 1] + distance;\r\n }\r\n\r\n double meanDistance = inputDistances.Last() \/ (count - 1);\r\n double[] evenDistances = Enumerable.Range(0, count).Select(x => x * meanDistance).ToArray();\r\n double[] xsOut = Interpolate(inputDistances, xs, evenDistances);\r\n double[] ysOut = Interpolate(inputDistances, ys, evenDistances);\r\n return (xsOut, ysOut);\r\n }\r\n\r\n private static double[] Interpolate(double[] xOrig, double[] yOrig, double[] xInterp)\r\n {\r\n (double[] a, double[] b) = FitMatrix(xOrig, yOrig);\r\n\r\n double[] yInterp = new double[xInterp.Length];\r\n for (int i = 0; i < yInterp.Length; i++)\r\n {\r\n int j;\r\n for (j = 0; j < xOrig.Length - 2; j++)\r\n if (xInterp[i] <= xOrig[j + 1])\r\n break;\r\n\r\n double dx = xOrig[j + 1] - xOrig[j];\r\n double t = (xInterp[i] - xOrig[j]) \/ dx;\r\n double y = (1 - t) * yOrig[j] + t * yOrig[j + 1] +\r\n t * (1 - t) * (a[j] * (1 - t) + b[j] * t);\r\n yInterp[i] = y;\r\n }\r\n return yInterp;\r\n }\r\n private static (double[] a, double[] b) FitMatrix(double[] x, double[] y)\r\n {\r\n int n = x.Length;\r\n double[] a = new double[n - 1];\r\n double[] b = new double[n - 1];\r\n double[] r = new double[n];\r\n double[] A = new double[n];\r\n double[] B = new double[n];\r\n double[] C = new double[n];\r\n\r\n double dx1, dx2, dy1, dy2;\r\n\r\n dx1 = x[1] - x[0];\r\n C[0] = 1.0f \/ dx1;\r\n B[0] = 2.0f * C[0];\r\n r[0] = 3 * (y[1] - y[0]) \/ (dx1 * dx1);\r\n\r\n for (int i = 1; i < n - 1; i++)\r\n {\r\n dx1 = x[i] - x[i - 1];\r\n dx2 = x[i + 1] - x[i];\r\n A[i] = 1.0f \/ dx1;\r\n C[i] = 1.0f \/ dx2;\r\n B[i] = 2.0f * (A[i] + C[i]);\r\n dy1 = y[i] - y[i - 1];\r\n dy2 = y[i + 1] - y[i];\r\n r[i] = 3 * (dy1 \/ (dx1 * dx1) + dy2 \/ (dx2 * dx2));\r\n }\r\n\r\n dx1 = x[n - 1] - x[n - 2];\r\n dy1 = y[n - 1] - y[n - 2];\r\n A[n - 1] = 1.0f \/ dx1;\r\n B[n - 1] = 2.0f * A[n - 1];\r\n r[n - 1] = 3 * (dy1 \/ (dx1 * dx1));\r\n\r\n double[] cPrime = new double[n];\r\n cPrime[0] = C[0] \/ B[0];\r\n for (int i = 1; i < n; i++)\r\n cPrime[i] = C[i] \/ (B[i] - cPrime[i - 1] * A[i]);\r\n\r\n double[] dPrime = new double[n];\r\n dPrime[0] = r[0] \/ B[0];\r\n for (int i = 1; i < n; i++)\r\n dPrime[i] = (r[i] - dPrime[i - 1] * A[i]) \/ (B[i] - cPrime[i - 1] * A[i]);\r\n\r\n double[] k = new double[n];\r\n k[n - 1] = dPrime[n - 1];\r\n for (int i = n - 2; i >= 0; i--)\r\n k[i] = dPrime[i] - cPrime[i] * k[i + 1];\r\n\r\n for (int i = 1; i < n; i++)\r\n {\r\n dx1 = x[i] - x[i - 1];\r\n dy1 = y[i] - y[i - 1];\r\n a[i - 1] = k[i - 1] * dx1 - dy1;\r\n b[i - 1] = -k[i] * dx1 + dy1;\r\n }\r\n\r\n return (a, b);\r\n }\r\n }\r\n\r\n public Form1()\r\n {\r\n InitializeComponent();\r\n }\r\n\r\n private void Form1_Load(object sender, EventArgs e)\r\n {\r\n Random rand = new(1268);\r\n int pointCount = 15;\r\n double[] xs1 = DataGen.Consecutive(pointCount);\r\n double[] ys1 = new double[pointCount];\r\n for (int i = 1; i < pointCount; i++)\r\n {\r\n \/\/xs1[i] = xs1[i - 1] + rand.NextDouble() - .5;\r\n ys1[i] = ys1[i - 1] + rand.NextDouble() - .5;\r\n }\r\n\r\n \/\/ Use cubic interpolation to smooth the original data\r\n (double[] xs2, double[] ys2) = Cubic.InterpolateXY(xs1, ys1, 200);\r\n\r\n \/\/ Plot the original vs. interpolated data\r\n var plt = new ScottPlot.Plot(900, 500);\r\n plt.AddScatter(xs1, ys1, label: "original", markerSize: 7);\r\n plt.AddScatter(xs2, ys2, label: "interpolated", markerSize: 3);\r\n plt.Style(Style.Seaborn);\r\n plt.Title("Cubic Spline");\r\n plt.XLabel("x axis");\r\n plt.YLabel("y axis");\r\n plt.Legend();\r\n plt.SaveFig("interpolation.png");\r\n pictureBox1.ImageLocation = "interpolation.png";\r\n }\r\n }\r\n}\r\n<\/pre>\n![\"\"](\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2022\/11\/interpolation.png?resize=900%2C500&ssl=1\")
<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"