# QuadraticSurface

VTKExamples/Python/Visualization/QuadraticSurface

### Description

- Converted from c++ by Jim McCusker

### Code

QuadraticSurface.py

    #!/usr/bin/python

    import vtk

    def Sphere():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def EllipticParaboloid():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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, 10.0)

    def HyperbolicParaboloid():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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, 10.0)

    def Cylinder():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def HyperboloidOneSheet():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def HyperboloidTwoSheets():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def Ellipsoid():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def Cone():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def Other():
        # create the quadric function definition
        quadric = vtk.vtkQuadric()
        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)

    def PlotFunction(quadric, value):
        # sample the quadric function
        sample = vtk.vtkSampleFunction()
        sample.SetSampleDimensions(50, 50, 50)
        sample.SetImplicitFunction(quadric)
        # double xmin = 0, xmax=1, ymin=0, ymax=1, zmin=0, zmax=1
        xmin = -10
        xmax = 11
        ymin = -10
        ymax = 10
        zmin = -10
        zmax = 10
        sample.SetModelBounds(xmin, xmax, ymin, ymax, zmin, zmax)

        # create the 0 isosurface
        contours = vtk.vtkContourFilter()
        contours.SetInputConnection(sample.GetOutputPort())
        contours.GenerateValues(1, value, value)

        # map the contours to graphical primitives
        contourMapper = vtk.vtkPolyDataMapper()
        contourMapper.SetInputConnection(contours.GetOutputPort())
        contourMapper.SetScalarRange(0.0, 1.2)

        # create an actor for the contours
        contourActor = vtk.vtkActor()
        contourActor.SetMapper(contourMapper)

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

        # create outline
        outline = vtk.vtkOutlineFilter()
        outline.SetInputConnection(sample.GetOutputPort())

        # map it to graphics primitives
        outlineMapper = vtk.vtkPolyDataMapper()
        outlineMapper.SetInputConnection(outline.GetOutputPort())

        # create an actor for it
        outlineActor = vtk.vtkActor()
        outlineActor.SetMapper(outlineMapper)
        outlineActor.GetProperty().SetColor(0, 0, 0)

        # setup the window
        ren1 = vtk.vtkRenderer()
        renWin = vtk.vtkRenderWindow()
        renWin.AddRenderer(ren1)
        iren = vtk.vtkRenderWindowInteractor()
        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()

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