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# IsoparametricCellsDemo

VTKEx/Python/GeometricObjects/IsoparametricCellsDemo

### Description

This example shows the isoparametric cells supported by the VTK. These cells are nonlinear and contain one or more mid-side vertices. Isoparametric elements are typically used in finite element analysis. The term isoparametric is derived from the use of the same shape functions (or interpolation functions) to define the element's geometric shape as are used to define the displacements within the element.

This example illustrates each cell's representation using its parametric coordinates (pcoords) as the vertices of the cell. In practice, the vertices will correspond to physical points in a finite element model. Use vtkTessellatorFilter to better see the shape of the cell. See for example, QuadraticHexahedronDemo and QuadraticTetraDemo.

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See (Cxx)

Question

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### Code

IsoparametricCellsDemo.py

    #!/usr/bin/env python
    # -*- coding: utf-8 -*-

    import vtk

    def main():
        titles = list()
        textMappers = list()
        textActors = list()

        uGrids = list()
        mappers = list()
        actors = list()
        renderers = list()

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticEdge()))
        titles.append("VTK_QUADRATIC_EDGE (= 21)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticTriangle()))
        titles.append("VTK_QUADRATIC_TRIANGLE (= 22)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticQuad()))
        titles.append("VTK_QUADRATIC_QUAD (= 23)")

        uGrids.append(MakeQuadraticPolygon())
        titles.append("VTK_QUADRATIC_POLYGON (= 36)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticTetra()))
        titles.append("VTK_QUADRATIC_TETRA (= 24)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticHexahedron()))
        titles.append("VTK_QUADRATIC_HEXAHEDRON (= 25)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticWedge()))
        titles.append("VTK_QUADRATIC_WEDGE (= 26)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticPyramid()))
        titles.append("VTK_QUADRATIC_PYRAMID (= 27)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkBiQuadraticQuad()))
        titles.append("VTK_BIQUADRATIC_QUAD (= 28)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkTriQuadraticHexahedron()))
        titles.append("VTK_TRIQUADRATIC_HEXAHEDRON (= 29)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticLinearQuad()))
        titles.append("VTK_QUADRATIC_LINEAR_QUAD (= 30)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkQuadraticLinearWedge()))
        titles.append("VTK_QUADRATIC_LINEAR_WEDGE (= 31)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkBiQuadraticQuadraticWedge()))
        titles.append("VTK_BIQUADRATIC_QUADRATIC_WEDGE (= 32)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkBiQuadraticQuadraticHexahedron()))
        titles.append("VTK_BIQUADRATIC_QUADRATIC_HEXAHEDRON (= 33)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkBiQuadraticTriangle()))
        titles.append("VTK_BIQUADRATIC_TRIANGLE (= 34)")

        uGrids.append(MakeUnstructuredGrid(
            vtk.vtkCubicLine()))
        titles.append("VTK_CUBIC_LINE (= 35)")

        colors = vtk.vtkNamedColors()

        renWin = vtk.vtkRenderWindow()
        renWin.SetSize(600, 600)
        renWin.SetWindowName("Isoparametric Cell")

        iRen = vtk.vtkRenderWindowInteractor()
        iRen.SetRenderWindow(renWin)

        # Create one sphere for all
        sphere = vtk.vtkSphereSource()
        sphere.SetPhiResolution(21)
        sphere.SetThetaResolution(21)
        sphere.SetRadius(.08)

        # Create one text property for all
        textProperty = vtk.vtkTextProperty()
        textProperty.SetFontSize(10)
        textProperty.SetJustificationToCentered()

        # Create and link the mappers actors and renderers together.
        for i in range(0, len(uGrids)):
            print("Creating:", titles[i])
            textMappers.append(vtk.vtkTextMapper())
            textActors.append(vtk.vtkActor2D())

            textMappers[i].GetTextProperty().SetFontSize(10)
            textMappers[i].GetTextProperty().ShadowOn()
            mappers.append(vtk.vtkDataSetMapper())
            actors.append(vtk.vtkActor())
            renderers.append(vtk.vtkRenderer())
            mappers[i].SetInputData(uGrids[i])
            actors[i].SetMapper(mappers[i])
            actors[i].GetProperty().SetColor(colors.GetColor3d("Tomato"))
            actors[i].GetProperty().EdgeVisibilityOn()
            actors[i].GetProperty().SetLineWidth(3)
            actors[i].GetProperty().SetOpacity(.5)
            renderers[i].AddViewProp(actors[i])

            textMappers[i].SetInput(titles[i])
            textActors[i].SetMapper(textMappers[i])
            textActors[i].SetPosition(50, 10)
            renderers[i].AddViewProp(textActors[i])

            # Label the points
            labelMapper = vtk.vtkLabeledDataMapper()
            labelMapper.SetInputData(uGrids[i])
            labelActor = vtk.vtkActor2D()
            labelActor.SetMapper(labelMapper)
            renderers[i].AddViewProp(labelActor)

            # Glyph the points
            pointMapper = vtk.vtkGlyph3DMapper()
            pointMapper.SetInputData(uGrids[i])
            pointMapper.SetSourceConnection(sphere.GetOutputPort())
            pointMapper.ScalingOff()
            pointMapper.ScalarVisibilityOff()

            pointActor = vtk.vtkActor()
            pointActor.SetMapper(pointMapper)
            pointActor.GetProperty().SetDiffuseColor(colors.GetColor3d("Banana"))
            pointActor.GetProperty().SetSpecular(.6)
            pointActor.GetProperty().SetSpecularColor(1.0, 1.0, 1.0)
            pointActor.GetProperty().SetSpecularPower(100)
            renderers[i].AddViewProp(pointActor)

            renWin.AddRenderer(renderers[i])

        # Setup the viewports
        xGridDimensions = 4
        yGridDimensions = 4
        rendererSize = 240
        renWin.SetSize(rendererSize * xGridDimensions, rendererSize * yGridDimensions)
        for row in range(0, yGridDimensions):
            for col in range(0, xGridDimensions):
                index = row * xGridDimensions + col

                # (xmin, ymin, xmax, ymax)
                viewport = [float(col) / xGridDimensions,
                            float(yGridDimensions - (row + 1)) / yGridDimensions,
                            float(col + 1) / xGridDimensions,
                            float(yGridDimensions - row) / yGridDimensions]

                if index > (len(actors) - 1):
                    # Add a renderer even if there is no actor.
                    # This makes the render window background all the same color.
                    ren = vtk.vtkRenderer()
                    ren.SetBackground(colors.GetColor3d("SlateGray"))
                    ren.SetViewport(viewport)
                    renWin.AddRenderer(ren)
                    continue

                renderers[index].SetViewport(viewport)
                renderers[index].SetBackground(colors.GetColor3d("SlateGray"))
                renderers[index].ResetCamera()
                renderers[index].GetActiveCamera().Azimuth(30)
                renderers[index].GetActiveCamera().Elevation(-30)
                renderers[index].ResetCameraClippingRange()

        iRen.Initialize()
        renWin.Render()
        iRen.Start()

    # These functions return a vtkUnstructured grid corresponding to the object.

    def MakeUnstructuredGrid(aCell):
        pcoords = aCell.GetParametricCoords()
        for i in range(0, aCell.GetNumberOfPoints()):
            aCell.GetPointIds().SetId(i, i)
            aCell.GetPoints().SetPoint(i, (pcoords[3 * i]), (pcoords[3 * i + 1]), (pcoords[3 * i + 2]))

        ug = vtk.vtkUnstructuredGrid()
        ug.SetPoints(aCell.GetPoints())
        ug.InsertNextCell(aCell.GetCellType(), aCell.GetPointIds())
        return ug

    def MakeQuadraticPolygon():
        quadraticPolygon = vtk.vtkQuadraticPolygon()

        quadraticPolygon.GetPointIds().SetNumberOfIds(8)
        quadraticPolygon.GetPointIds().SetId(0, 0)
        quadraticPolygon.GetPointIds().SetId(1, 1)
        quadraticPolygon.GetPointIds().SetId(2, 2)
        quadraticPolygon.GetPointIds().SetId(3, 3)
        quadraticPolygon.GetPointIds().SetId(4, 4)
        quadraticPolygon.GetPointIds().SetId(5, 5)
        quadraticPolygon.GetPointIds().SetId(6, 6)
        quadraticPolygon.GetPointIds().SetId(7, 7)

        quadraticPolygon.GetPoints().SetNumberOfPoints(8)
        quadraticPolygon.GetPoints().SetPoint(0, 0.0, 0.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(1, 2.0, 0.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(2, 2.0, 2.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(3, 0.0, 2.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(4, 1.0, 0.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(5, 2.0, 1.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(6, 1.0, 2.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(7, 0.0, 1.0, 0.0)
        quadraticPolygon.GetPoints().SetPoint(5, 3.0, 1.0, 0.0)

        ug = vtk.vtkUnstructuredGrid()
        ug.SetPoints(quadraticPolygon.GetPoints())
        ug.InsertNextCell(quadraticPolygon.GetCellType(), quadraticPolygon.GetPointIds())
        return ug

    if __name__ == '__main__':
        main()