# 1DTupleInterpolation

VTKExamples/Cxx/Math/1DTupleInterpolation

### Description

Contributed by: Lars Friedrich

A simple example that shows how to use vtkTupleInterpolator for the purpose of interpolating 1D functions. Internally the program investigates two functions: sine and Runge function with sparsely distributed supporting points. The application uses different interpolation modes: '''linear''', '''cardinal spline''' and '''Kochanek spline'''. Moreover, the example offers the "--csv-output" (or "-co") option which causes the program to generate CSV-sheets reflecting the interpolated data. In order to demonstrate the spline interpolation behavior at the edge regions, we use the '''open''' and '''closed''' interval spline options as well. For example, a Kochanek-interpolation of the Runge function:

### Program Usage

    ./1DTupleInterpolation [](options)

      -h or --help ... print this short help
      -nv or --no-verbose ... no verbose messages to std::cout
      -co or --csv-output ... CSV (comma separated values) file outputs

Note

optional arguments are case-sensitive!

### Code

1DTupleInterpolation.cxx

    //
    #include <cstdlib>
    #include <iostream>
    #include <string>
    #include <fstream>
    #include <cmath>
    #ifndef M_PI
      #define M_PI 3.14159265358979323846
    #endif
    #include <ctime>

    #include <vtkSmartPointer.h>
    #include <vtkTupleInterpolator.h>
    #include <vtkCardinalSpline.h>
    #include <vtkKochanekSpline.h>

    #define VERBOSE(x) \
    { \
      if (Verbose) \
      {\
        std::cout x; \
        std::cout.flush(); \
      }\
    }

    // verbose flag
    bool Verbose = true;
    // CSV output flag
    bool CSVOutput = false;

    /**
     * Print example usage information.
     **/
    void PrintUsage(char *binname)
    {
      std::string progname = "<binary-name>";
      if (binname)
        progname = std::string(binname);
      std::cout << "\n";
      std::cout << "   *** E X A M P L E   U S A G E ***\n";
      std::cout << "\n";
      std::cout << progname << " [options]\n";
      std::cout << "\n";
      std::cout << "  -h or --help ... print this short help\n";
      std::cout << "  -nv or --no-verbose ... no verbose messages to std::cout\n";
      std::cout << "  -co or --csv-output ... CSV (comma separated values) file outputs\n";
      std::cout << "\n";
      std::cout << "  NOTE: optional arguments are case-sensitive!\n";
      std::cout << "\n";
      std::cout << "  Author: ---\n";
      std::cout << "  Affiliation: ---\n";
      std::cout << "\n";
    }

    /** Runge function. **/
    double FRunge(double x)
    {
      return 1.0 / (1.0 + x * x);
    }

    /** Sine function. **/
    double FSin(double x)
    {
      return sin(x);
    }

    /** Execute a specific tuple interpolation method with pre-initialized tuple interpolator. **/
    bool TestInterpolation(vtkSmartPointer<vtkTupleInterpolator> tupInt, double
        tolerance, const char *csvFileName, double (*mathFunc)(double), double *x,
        double *y, double N, double symmetricIntervalWidth)
    {
      bool ok = true;
      std::ofstream csvint;
      if (CSVOutput)
      {
        csvint.open(csvFileName, std::ios::out);
        if (csvint.is_open())
          csvint << "x;y;e\n";
        else
          ok = false;
      }
      double yt[1];
      for (int i = 0; i < N; i++) // re-define supporting points
      {
        yt[0] = y[i];
        tupInt->AddTuple(x[i], yt);
      }
      // draw random samples from interval and test against mathFunc:
      for (int i = 0; i < 1000; i++)
      {
        double f = (double) (rand() % 100001) / 100000.;
        double xi = (f * 2.0 - 1.0) * symmetricIntervalWidth;
        double yi[1];
        tupInt->InterpolateTuple(xi, yi);
        double ei = std::abs(yi[0] - mathFunc(xi));
        // we have a tolerance within [-PI;+PI] - empirical!
        if (xi >= -symmetricIntervalWidth && xi <= symmetricIntervalWidth &&
            ei > tolerance)
          ok = false;
        if (CSVOutput && csvint.is_open())
          csvint << xi << ";" << yi[0] << ";" << ei << "\n";
      }
      if (CSVOutput && csvint.is_open())
        csvint.close();
      return ok;
    }

    /** \brief Demonstrate base functionality of VTK-based tuple interpolation (1D).
     * Demonstrate base functionality of VTK-based tuple interpolation (1D).
     *
     * Application result is 0 if SUCCESSFUL.
     *
     * Arguments: <br>
     * -h or --help ... print short help <br>
     * -nv or --no-verbose ... message output (verbose) <br>
     * -co or --csv-output ... CSV (comma separated values) file outputs <br>
     *
     * @author ---
     * @version 1.2
     */
    int main(int argc, char *argv[])
    {
      // arguments check
      for (int i = 1; i < argc; i++)
      {
        if (std::string(argv[i]) == "-nv" || std::string(argv[i]) == "--no-verbose")
          Verbose = false;
        if (std::string(argv[i]) == "-h" || std::string(argv[i]) == "--help")
        {
          if (argc > 0)
            PrintUsage(argv[0]);
          else
            PrintUsage(NULL);
          return EXIT_FAILURE;
        }
        if (std::string(argv[i]) == "-co" || std::string(argv[i]) == "--csv-output")
          CSVOutput = true;
      }

      VERBOSE(<< "\nDemonstrating VTK-based 1-tuple interpolation capabilities.\n")
      bool ok = true;

      VERBOSE(<< "  * Generate supporting points ... ")
      bool lok = true; // local OK
      // - SINE -
      const int N1 = 13;
      double *xs = new double[N1];
      double *ys = new double[N1];
      std::ofstream csv;
      if (CSVOutput)
      {
        csv.open("sine.csv", std::ios::out);
        if (csv.is_open())
          csv << "x;y\n";
        else
          lok = false;
      }
      // prepare the supporting points (sine):
      for (int i = 0; i < N1; i++)
      {
        xs[i] = -M_PI + (double) i / (double) (N1 - 1) * (2. * M_PI);
        ys[i] = FSin(xs[i]);

        if (CSVOutput && csv.is_open())
          csv << xs[i] << ";" << ys[i] << "\n";
      }
      if (CSVOutput && csv.is_open())
        csv.close();
      // - RUNGE -
      const int N2 = 10;
      double *xr = new double[N2];
      double *yr = new double[N2];
      if (CSVOutput)
      {
        csv.open("runge.csv", std::ios::out);
        if (csv.is_open())
          csv << "x;y\n";
        else
          lok = false;
      }
      // prepare the supporting points (sine):
      for (int i = 0; i < N2; i++)
      {
        xr[i] = -5.0 + (double) i / (double) (N2 - 1) * (2. * 5.0);
        yr[i] = FRunge(xr[i]);

        if (CSVOutput && csv.is_open())
          csv << xr[i] << ";" << yr[i] << "\n";
      }
      if (CSVOutput && csv.is_open())
        csv.close();
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of sine using linear method ... ")
      // initialize the tuple interpolator (1D):
      vtkSmartPointer<vtkTupleInterpolator> tupInt = vtkSmartPointer<vtkTupleInterpolator>::New();
      tupInt->SetInterpolationTypeToLinear(); // linear
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.04, "sin_linear_int.csv", FSin, xs, ys, N1, M_PI);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of sine using cardinal spline method (open interval) ... ")
      // initialize the tuple interpolator (1D):
      tupInt->SetInterpolationTypeToSpline(); // spline (implicit reset!)
      vtkSmartPointer<vtkCardinalSpline> cardSpline = vtkSmartPointer<vtkCardinalSpline>::New();
      cardSpline->SetClosed(false);
      tupInt->SetInterpolatingSpline(cardSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.1, "sin_card_spline_open_int.csv", FSin, xs, ys, N1, M_PI);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of sine using cardinal spline method (closed interval) ... ")
      // initialize the tuple interpolator (1D):
      tupInt->Initialize(); // reset
      tupInt->SetInterpolationTypeToSpline(); // spline
      cardSpline->SetClosed(true);
      tupInt->SetInterpolatingSpline(cardSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.05, "sin_card_spline_closed_int.csv", FSin, xs, ys, N1, M_PI);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of sine using Kochanek spline (default setup) method (open interval) ... ")
      // initialize the tuple interpolator (1D):
      tupInt->Initialize(); // reset
      tupInt->SetInterpolationTypeToSpline(); // spline
      vtkSmartPointer<vtkKochanekSpline> kochSpline = vtkSmartPointer<vtkKochanekSpline>::New();
      kochSpline->SetClosed(false);
      tupInt->SetInterpolatingSpline(kochSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.1, "sin_koch_spline_open_int.csv", FSin, xs, ys, N1, M_PI);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of sine using Kochanek spline (default setup) method (closed interval) ... ")
      // initialize the tuple interpolator (1D):
      tupInt->Initialize(); // reset
      tupInt->SetInterpolationTypeToSpline(); // spline
      kochSpline->SetClosed(true);
      tupInt->SetInterpolatingSpline(kochSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.06, "sin_koch_spline_closed_int.csv", FSin, xs, ys, N1, M_PI);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of Runge using linear method ... ")
      // initialize the tuple interpolator (1D):
      tupInt->Initialize();
      tupInt->SetInterpolationTypeToLinear(); // linear
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.25 /* around 0! */, "runge_linear_int.csv", FRunge, xr, yr, N2, 5.0);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of Runge using cardinal spline method ... ")
      // initialize the tuple interpolator (1D):
      tupInt->SetInterpolationTypeToSpline(); // spline (implicit reset!)
      cardSpline->SetClosed(false);
      tupInt->SetInterpolatingSpline(cardSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.15 /* around 0! */, "runge_card_spline_int.csv", FRunge, xr, yr, N2, 5.0);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      VERBOSE(<< "  * Interpolation of Runge using Kochanek spline method ... ")
      // initialize the tuple interpolator (1D):
      tupInt->Initialize(); // reset
      tupInt->SetInterpolationTypeToSpline(); // spline (implicit reset!)
      kochSpline->SetClosed(false);
      tupInt->SetInterpolatingSpline(kochSpline);
      tupInt->SetNumberOfComponents(1); // 1D (NOTE: set #components AFTER interpolation-type!)
      lok = TestInterpolation(tupInt, 0.18 /* around 0! */, "runge_koch_spline_int.csv", FRunge, xr, yr, N2, 5.0);
      ok = ok && lok;
      VERBOSE(<< (lok ? "OK" : "FAILURE") << "\n")

      delete[] xs;
      delete[] ys;
      delete[] xr;
      delete[] yr;
      cardSpline = NULL;
      kochSpline = NULL;
      tupInt = NULL;

      VERBOSE(<< "Application result: ")
      if (ok)
      {
        VERBOSE(<< "OK\n\n")
        return EXIT_SUCCESS;
      }
      else
      {
        VERBOSE(<< "FAILURE\n\n")
        return EXIT_FAILURE;
      }
    }

### CMakeLists.txt

    cmake_minimum_required(VERSION 2.8)

    PROJECT(1DTupleInterpolation)

    find_package(VTK REQUIRED)
    include(${VTK_USE_FILE})

    add_executable(1DTupleInterpolation MACOSX_BUNDLE 1DTupleInterpolation.cxx)

    target_link_libraries(1DTupleInterpolation ${VTK_LIBRARIES})

### Download and Build 1DTupleInterpolation

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Click here to download 1DTupleInterpolation and its CMakeLists.txt file. Once the tarball 1DTupleInterpolation.tar has been downloaded and extracted,

    cd 1DTupleInterpolation/build

If VTK is installed:

    cmake ..

If VTK is not installed but compiled on your system, you will need to specify the path to your VTK build:

    cmake -DVTK_DIR:PATH=/home/me/vtk_build ..

Build the project:

    make

and run it:

    ./1DTupleInterpolation

WINDOWS USERS PLEASE NOTE: Be sure to add the VTK bin directory to your path. This will resolve the VTK dll's at run time.