QuadraticSurface

#!/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):
    colors = vtk.vtkNamedColors()

    # 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(colors.GetColor3d('Black'))

    # 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(colors.GetColor3d('AliceBlue'))

    # render and interact
    renWin.Render()
    iren.Start()


def main():
    #  Choose one!

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


if __name__ == '__main__':
    main()