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1DTupleInterpolation

vtk-examples/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!

Question

If you have a question about this example, please use the VTK Discourse Forum

Code

1DTupleInterpolation.cxx

//
#include <cmath>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <string>
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#include <vtkCardinalSpline.h>
#include <vtkKochanekSpline.h>
#include <vtkNew.h>
#include <vtkTupleInterpolator.h>

#include <ctime>
#include <vector>

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

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

namespace {
/**
 * Print example usage information.
 **/
void PrintUsage(char* binname);

/** 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(vtkTupleInterpolator* tupInt, double tolerance,
                       const char* csvFileName, double (*mathFunc)(double),
                       std::vector<double>& x, const std::vector<double>& y,
                       double N, double symmetricIntervalWidth);

} // namespace

/** \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(nullptr);
      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 -
  constexpr int N1 = 13;
  std::vector<double> xs(N1, 0);
  std::vector<double> ys(N1, 0);
  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;
  std::vector<double> xr(N2, 0);
  std::vector<double> yr(N2, 0);
  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):
  vtkNew<vtkTupleInterpolator> tupInt;
  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!)
  vtkNew<vtkCardinalSpline> cardSpline;
  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
  vtkNew<vtkKochanekSpline> kochSpline;
  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")

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

namespace {
/**
 * 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";
}

/** Execute a specific tuple interpolation method with pre-initialized tuple
 * interpolator. **/
bool TestInterpolation(vtkTupleInterpolator* tupInt, double tolerance,
                       const char* csvFileName, double (*mathFunc)(double),
                       std::vector<double>& x, const std::vector<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;
}

} // namespace

CMakeLists.txt

cmake_minimum_required(VERSION 3.3 FATAL_ERROR)

project(1DTupleInterpolation)

find_package(VTK COMPONENTS 
  vtkCommonComputationalGeometry
  vtkCommonCore
  vtkInteractionStyle
  vtkRenderingContextOpenGL2
  vtkRenderingCore
  vtkRenderingFreeType
  vtkRenderingGL2PSOpenGL2
  vtkRenderingOpenGL2
  QUIET
)

if (NOT VTK_FOUND)
  message("Skipping 1DTupleInterpolation: ${VTK_NOT_FOUND_MESSAGE}")
  return ()
endif()
message (STATUS "VTK_VERSION: ${VTK_VERSION}")
if (VTK_VERSION VERSION_LESS "8.90.0")
  # old system
  include(${VTK_USE_FILE})
  add_executable(1DTupleInterpolation MACOSX_BUNDLE 1DTupleInterpolation.cxx )
  target_link_libraries(1DTupleInterpolation PRIVATE ${VTK_LIBRARIES})
else ()
  # include all components
  add_executable(1DTupleInterpolation MACOSX_BUNDLE 1DTupleInterpolation.cxx )
  target_link_libraries(1DTupleInterpolation PRIVATE ${VTK_LIBRARIES})
  # vtk_module_autoinit is needed
  vtk_module_autoinit(
    TARGETS 1DTupleInterpolation
    MODULES ${VTK_LIBRARIES}
    )
endif ()

Download and Build 1DTupleInterpolation

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

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