Lorenz

VTKExamples/Cxx/Visualization/Lorenz


Description

This example visualizes a Lorenz strange attractor by integrating the Lorenz equations in a volume. The number of visits in each voxel is recorded as a scalar function. The surface is extracted via vtkMarchingCubes using a visit value of 50. The number of integration steps is 10 million, in a volume of dimensions 200^3. The surface roughness is caused by the discrete nature of the evaluation function.

Code

Lorenz.cxx

// 
/*
* Create an iso-surface of the Lorenz attractor.
*
* Here we visualize a Lorenz strange attractor by integrating the Lorenz equations in a volume.
* The number of visits in each voxel is recorded as a scalar function.
* The surface is extracted via marching cubes using a visit value of 50.
* The number of integration steps is 10 million, in a volume of dimensions 200 x 200 * x 200.
* The surface roughness is caused by the discrete nature of the evaluation function.
*/

#include <vtkActor.h>
#include <vtkContourFilter.h>
#include <vtkMath.h>
#include <vtkNamedColors.h>
#include <vtkPointData.h>
#include <vtkPolyDataMapper.h>
#include <vtkProperty.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkRenderer.h>
#include <vtkShortArray.h>
#include <vtkStructuredPoints.h>

int main( int, char *[] )
{
  double    Pr = 10.0;  // The Lorenz parameters
  double    b = 2.667;
  double    r = 28.0;
  double    x, y, z;    // starting (and current) x, y, z 
  double    h = 0.01;   // integration step size 
  int           resolution=200; // slice resolution 
  int           iter = 10000000;    // number of iterations 
  double    xmin = -30.0;   // x, y, z range for voxels 
  double    xmax = 30.0;
  double    ymin = -30.0;
  double    ymax = 30.0;
  double    zmin = -10.0;
  double    zmax = 60.0;

  double xIncr, yIncr, zIncr;

  double    xx, yy, zz;
  short xxx, yyy, zzz;
  int   sliceSize;

  short *s;
  void options(int, char**);
  int numPts, index;

  // take a stab at an integration step size
  xIncr = resolution / (xmax - xmin);
  yIncr = resolution / (ymax - ymin);
  zIncr = resolution / (zmax - zmin);

  printf ("The Lorenz Attractor\n");
  printf (" Pr = %f\n", Pr);
  printf (" b = %f\n", b);
  printf (" r = %f\n", r);
  printf (" integration step size = %f\n", h);
  printf (" slice resolution = %d\n", resolution);
  printf (" # of iterations = %d\n", iter);
  printf (" specified range:\n");
  printf ("     x: %f, %f\n", xmin, xmax);
  printf ("     y: %f, %f\n", ymin, ymax);
  printf ("     z: %f, %f\n", zmin, zmax);

  x = vtkMath::Random(xmin,xmax);
  y = vtkMath::Random(ymin,ymax);
  z = vtkMath::Random(zmin,zmax);
  printf (" starting at %f, %f, %f\n", x, y, z);

  // allocate memory for the slices
  sliceSize = resolution * resolution;
  numPts = sliceSize * resolution;
  vtkSmartPointer<vtkShortArray> scalars =
    vtkSmartPointer<vtkShortArray>::New();
  s = scalars->WritePointer(0,numPts);
  for (auto i=0; i < numPts; i++)
  {
    s[i] = 0;
  }
  for (auto j = 0; j < iter; j++) 
  {
    // integrate to next time step
    xx = x + h * Pr * (y - x);
    yy = y + h * (x * (r - z) - y);
    zz = z + h * (x * y - (b * z));

    x = xx; y = yy; z = zz;

    // calculate voxel index
    if (x < xmax && x > xmin && y < ymax && y > ymin && z < zmax && z > zmin) 
    {
      xxx = (short) ((double)(xx - xmin) * xIncr);
      yyy = (short) ((double)(yy - ymin) * yIncr);
      zzz = (short) ((double)(zz - zmin) * zIncr);
      index = xxx + yyy*resolution + zzz*sliceSize;
      s[index] += 1;
    }
  }

  vtkSmartPointer<vtkNamedColors> colors =
    vtkSmartPointer<vtkNamedColors>::New();

  vtkSmartPointer<vtkStructuredPoints> volume =
    vtkSmartPointer<vtkStructuredPoints>::New();
  volume->GetPointData()->SetScalars(scalars);
  volume->SetDimensions(resolution,resolution,resolution);
  volume->SetOrigin(xmin,ymin,zmin);
  volume->SetSpacing((xmax-xmin)/resolution, (ymax-ymin)/resolution,
                     (zmax-zmin)/resolution);

  printf (" contouring...\n");
  // do the graphics dance
  vtkSmartPointer<vtkRenderer> renderer =
    vtkSmartPointer<vtkRenderer>::New();
  vtkSmartPointer<vtkRenderWindow> renWin =
    vtkSmartPointer<vtkRenderWindow>::New();
  renWin->AddRenderer(renderer);

  vtkSmartPointer<vtkRenderWindowInteractor> iren =
    vtkSmartPointer<vtkRenderWindowInteractor>::New();
  iren->SetRenderWindow(renWin);

  // create iso-surface
  vtkSmartPointer<vtkContourFilter> contour =
    vtkSmartPointer<vtkContourFilter>::New();
  contour->SetInputData(volume);
  contour->SetValue(0,50);

  // create mapper
  vtkSmartPointer<vtkPolyDataMapper> mapper =
    vtkSmartPointer<vtkPolyDataMapper>::New();
  mapper->SetInputConnection(contour->GetOutputPort());
  mapper->ScalarVisibilityOff();

  // create actor
  vtkSmartPointer<vtkActor> actor =
    vtkSmartPointer<vtkActor>::New();
  actor->SetMapper(mapper);
  actor->GetProperty()->SetColor(colors->GetColor3d("PaleTurquoise").GetData());

  renderer->AddActor(actor);
  renderer->SetBackground(colors->GetColor3d("PeachPuff").GetData());

  renWin->SetSize(640, 480);

  // interact with data
  renWin->Render();

  iren->Start();

  return EXIT_SUCCESS;
}

CMakeLists.txt

cmake_minimum_required(VERSION 2.8)

PROJECT(Lorenz)

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

add_executable(Lorenz MACOSX_BUNDLE Lorenz.cxx )

target_link_libraries(Lorenz ${VTK_LIBRARIES})

Download and Build Lorenz

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

cd Lorenz/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:

./Lorenz

WINDOWS USERS

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