# DisplayQuadraticSurfaces

VTKExamples/Cxx/Visualization/DisplayQuadraticSurfaces

### Description

This example demonstrates how to display several types of quadratic surfaces.

### Code

DisplayQuadraticSurfaces.cxx

    #include <vtkQuadric.h>
    #include <vtkSampleFunction.h>
    #include <vtkContourFilter.h>
    #include <vtkOutlineFilter.h>
    #include <vtkPolyDataMapper.h>
    #include <vtkActor.h>
    #include <vtkProperty.h>
    #include <vtkRenderWindow.h>
    #include <vtkRenderer.h>
    #include <vtkRenderWindowInteractor.h>
    #include <vtkImageData.h>
    #include <vtkSmartPointer.h>

    void Other();
    void Sphere();
    void Cone();
    void Ellipsoid();
    void Cylinder();
    void HyperboloidOneSheet();
    void HyperboloidTwoSheets();
    void HyperbolicParaboloid();
    void EllipticParaboloid();

    void PlotFunction(vtkQuadric* quadric, double value);

    int main (int, char *[])
    {
      //Other();
      //Sphere();
      //Cone();
      //Ellipsoid();
      //Cylinder();
      //HyperboloidOneSheet();
      //HyperboloidTwoSheets();
      //HyperbolicParaboloid();
      EllipticParaboloid();

      return 0;
    }

    void Sphere()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,1,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2 + 1*z^2

      PlotFunction(quadric, 1.0);
    }

    void EllipticParaboloid()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,0,0,0,0,0,0,-1,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2

      PlotFunction(quadric, 0.0);
    }

    void HyperbolicParaboloid()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,-1,0,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 - 1*y^2

      PlotFunction(quadric, 1.0);
    }

    void Cylinder()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,0,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2

      PlotFunction(quadric, 1.0);
    }

    void HyperboloidOneSheet()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,-1,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2

      PlotFunction(quadric, 1.0);
    }

    void HyperboloidTwoSheets()
    {
        // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,-1,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2

      PlotFunction(quadric, -1.0);
    }

    void Ellipsoid()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,2,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2 + 1*z^2

      PlotFunction(quadric, 1.0);
    }

    void Cone()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(1,1,-1,0,0,0,0,0,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 1*x^2 + 1*y^2 - 1*z^2
      PlotFunction(quadric, 0.0);

    }

    void Other()
    {
      // create the quadric function definition
      vtkSmartPointer<vtkQuadric> quadric = vtkSmartPointer<vtkQuadric>::New();
      quadric->SetCoefficients(.5,1,.2,0,.1,0,0,.2,0,0);

      // F(x,y,z) = a0*x^2 + a1*y^2 + a2*z^2 + a3*x*y + a4*y*z + a5*x*z + a6*x + a7*y + a8*z + a9
      // F(x,y,z) = 0.5*x^2 + 1*y^2 + 0.2*z^2 + 0*x*y + 0.1*y*z + 0*x*z + 0*x + 0.2*y + 0*z + 0
      PlotFunction(quadric, 1.0);

    }

    void PlotFunction(vtkQuadric* quadric, double value)
    {

      // sample the quadric function
      vtkSmartPointer<vtkSampleFunction> sample = vtkSmartPointer<vtkSampleFunction>::New();
      sample->SetSampleDimensions(50,50,50);
      sample->SetImplicitFunction(quadric);
      //double xmin = 0, xmax=1, ymin=0, ymax=1, zmin=0, zmax=1;
      double xmin = -10, xmax=11, ymin=-10, ymax=10, zmin=-10, zmax=10;
      sample->SetModelBounds(xmin, xmax, ymin, ymax, zmin, zmax);

      // Create five surfaces F(x,y,z) = constant between range specified
      /*
      vtkContourFilter *contours = vtkContourFilter::New();
      contours->SetInput(sample->GetOutput());
      contours->GenerateValues(5, 0.0, 1.2);
      */

      //create the 0 isosurface
      vtkSmartPointer<vtkContourFilter> contours = vtkSmartPointer<vtkContourFilter>::New();
      contours->SetInputConnection(sample->GetOutputPort());
      contours->GenerateValues(1, value, value);

      // map the contours to graphical primitives
      vtkSmartPointer<vtkPolyDataMapper> contourMapper = vtkSmartPointer<vtkPolyDataMapper>::New();
      contourMapper->SetInputConnection(contours->GetOutputPort());
      contourMapper->SetScalarRange(0.0, 1.2);

      // create an actor for the contours
      vtkSmartPointer<vtkActor> contourActor = vtkSmartPointer<vtkActor>::New();
      contourActor->SetMapper(contourMapper);

      // -- create a box around the function to indicate the sampling volume --

      // create outline
      vtkSmartPointer<vtkOutlineFilter> outline = vtkSmartPointer<vtkOutlineFilter>::New();
      outline->SetInputConnection(sample->GetOutputPort());

      // map it to graphics primitives
      vtkSmartPointer<vtkPolyDataMapper> outlineMapper = vtkSmartPointer<vtkPolyDataMapper>::New();
      outlineMapper->SetInputConnection(outline->GetOutputPort());

      // create an actor for it
      vtkSmartPointer<vtkActor> outlineActor = vtkSmartPointer<vtkActor>::New();
      outlineActor->SetMapper(outlineMapper);
      outlineActor->GetProperty()->SetColor(0,0,0);

      // setup the window
      vtkSmartPointer<vtkRenderer> ren1 = vtkSmartPointer<vtkRenderer>::New();
      vtkSmartPointer<vtkRenderWindow> renWin = vtkSmartPointer<vtkRenderWindow>::New();
      renWin->AddRenderer(ren1);
      vtkSmartPointer<vtkRenderWindowInteractor> iren = vtkSmartPointer<vtkRenderWindowInteractor>::New();
      iren->SetRenderWindow(renWin);

      // add the actors to the scene
      ren1->AddActor(contourActor);
      ren1->AddActor(outlineActor);
      ren1->SetBackground(1,1,1); // Background color white

      // render and interact
      renWin->Render();
      iren->Start();
    }

### CMakeLists.txt

    cmake_minimum_required(VERSION 2.8)

    PROJECT(DisplayQuadraticSurfaces)

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

    add_executable(DisplayQuadraticSurfaces MACOSX_BUNDLE DisplayQuadraticSurfaces.cxx )

    target_link_libraries(DisplayQuadraticSurfaces ${VTK_LIBRARIES})

### Download and Build DisplayQuadraticSurfaces

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

    cd DisplayQuadraticSurfaces/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:

    ./DisplayQuadraticSurfaces

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.