example3_volume Program

Uses

  • program~~example3_volume~~UsesGraph program~example3_volume example3_volume module~forcad forcad program~example3_volume->module~forcad module~forcad_nurbs_curve forcad_nurbs_curve module~forcad->module~forcad_nurbs_curve module~forcad_nurbs_surface forcad_nurbs_surface module~forcad->module~forcad_nurbs_surface module~forcad_nurbs_volume forcad_nurbs_volume module~forcad->module~forcad_nurbs_volume module~forcad_utils forcad_utils module~forcad->module~forcad_utils module~forcad_nurbs_curve->module~forcad_utils module~forcad_nurbs_surface->module~forcad_utils module~forcad_nurbs_volume->module~forcad_utils stdlib_quadrature stdlib_quadrature module~forcad_utils->stdlib_quadrature

This program demonstrates the usage of a NURBS (Non-Uniform Rational B-Spline) volume object to create and finalize a NURBS volume. It sets up control points, weights, and knot vectors for all three dimensions, generates the volume, and exports the control points and the volume to VTK files.

Define the control points for the NURBS volume

Define weights for the control points (optional) Define knot vectors for all three dimensions Set knot vectors, control points, and weights for the NURBS volume object Wc is optional.

Deallocate local arrays

Export the control points to a VTK file

Generate the NURBS volume with resolutions of 20, 20, and 20 in the three dimensions

Export the generated volume to a VTK file

Show the control geometry and geometry using PyVista

Print size of knot vectors Insert knots 0.25 and 0.75 in all three directions Print size of knot vectors after inserting knots Print degrees

Elevate degree by 2 in all three directions Print degrees after elevating

Print size of knot vectors Print size of knot vectors after removing knots Generate the refined NURBS volume with resolutions of 40, 40, and 40 in the three dimensions

Export updated control points to a VTK file

Export the refined generated volume to a VTK file

Show the control geometry and geometry using PyVista

Rotate the control points

Rotate the generated curve

Translate the control points

Translate the generated curve

Export the transformed control points to a VTK file

Export the transformed generated volume to a VTK file

Show the control geometry and geometry using PyVista

first compute and set the connectivities of volume elements

get the connectivity of the face1 of the first element get the degree of the faces Finalize the NURBS volume object


Calls

program~~example3_volume~~CallsGraph program~example3_volume example3_volume none~get_degree nurbs_volume%get_degree program~example3_volume->none~get_degree none~get_knot nurbs_volume%get_knot program~example3_volume->none~get_knot none~set nurbs_volume%set program~example3_volume->none~set proc~cmp_degreeface nurbs_volume%cmp_degreeFace program~example3_volume->proc~cmp_degreeface proc~cmp_elem nurbs_volume%cmp_elem program~example3_volume->proc~cmp_elem proc~cmp_elemface nurbs_volume%cmp_elemFace program~example3_volume->proc~cmp_elemface proc~create nurbs_volume%create program~example3_volume->proc~create proc~elevate_degree nurbs_volume%elevate_degree program~example3_volume->proc~elevate_degree proc~export_xc nurbs_volume%export_Xc program~example3_volume->proc~export_xc proc~export_xg nurbs_volume%export_Xg program~example3_volume->proc~export_xg proc~finalize nurbs_volume%finalize program~example3_volume->proc~finalize proc~generate_xc~2 generate_Xc program~example3_volume->proc~generate_xc~2 proc~insert_knots nurbs_volume%insert_knots program~example3_volume->proc~insert_knots proc~remove_knots nurbs_volume%remove_knots program~example3_volume->proc~remove_knots proc~rotate_xc nurbs_volume%rotate_Xc program~example3_volume->proc~rotate_xc proc~rotate_xg nurbs_volume%rotate_Xg program~example3_volume->proc~rotate_xg proc~set_elem nurbs_volume%set_elem program~example3_volume->proc~set_elem proc~show nurbs_volume%show program~example3_volume->proc~show proc~translate_xc nurbs_volume%translate_Xc program~example3_volume->proc~translate_xc proc~translate_xg nurbs_volume%translate_Xg program~example3_volume->proc~translate_xg proc~get_degree_all nurbs_volume%get_degree_all none~get_degree->proc~get_degree_all proc~get_degree_dir nurbs_volume%get_degree_dir none~get_degree->proc~get_degree_dir proc~get_knot_all nurbs_volume%get_knot_all none~get_knot->proc~get_knot_all proc~get_knoti nurbs_volume%get_knoti none~get_knot->proc~get_knoti proc~set1 nurbs_volume%set1 none~set->proc~set1 proc~set2 nurbs_volume%set2 none~set->proc~set2 proc~set3 nurbs_volume%set3 none~set->proc~set3 proc~set4 nurbs_volume%set4 none~set->proc~set4 interface~elemconn_cn elemConn_Cn proc~cmp_elem->interface~elemconn_cn interface~unique unique proc~cmp_elem->interface~unique proc~get_multiplicity nurbs_volume%get_multiplicity proc~cmp_elem->proc~get_multiplicity interface~compute_xg compute_Xg proc~create->interface~compute_xg interface~ndgrid ndgrid proc~create->interface~ndgrid proc~is_rational nurbs_volume%is_rational proc~create->proc~is_rational proc~elevate_degree->none~get_knot proc~elevate_degree->none~set proc~elevate_degree_a_5_9 elevate_degree_A_5_9 proc~elevate_degree->proc~elevate_degree_a_5_9 proc~cmp_elem_xc_vis nurbs_volume%cmp_elem_Xc_vis proc~export_xc->proc~cmp_elem_xc_vis proc~cmp_elem_xg_vis nurbs_volume%cmp_elem_Xg_vis proc~export_xg->proc~cmp_elem_xg_vis proc~insert_knots->none~get_knot proc~insert_knots->none~set interface~compute_multiplicity compute_multiplicity proc~insert_knots->interface~compute_multiplicity proc~findspan findspan proc~insert_knots->proc~findspan proc~insert_knot_a_5_1 insert_knot_A_5_1 proc~insert_knots->proc~insert_knot_a_5_1 proc~remove_knots->none~get_knot proc~remove_knots->none~set proc~remove_knots->interface~compute_multiplicity proc~remove_knots->proc~findspan proc~remove_knots_a_5_8 remove_knots_A_5_8 proc~remove_knots->proc~remove_knots_a_5_8 proc~rotation rotation proc~rotate_xc->proc~rotation proc~rotate_xg->proc~rotation proc~compute_multiplicity1 compute_multiplicity1 interface~compute_multiplicity->proc~compute_multiplicity1 proc~compute_multiplicity2 compute_multiplicity2 interface~compute_multiplicity->proc~compute_multiplicity2 proc~cmp_elemconn_cn_l cmp_elemConn_Cn_L interface~elemconn_cn->proc~cmp_elemconn_cn_l proc~cmp_elemconn_cn_s cmp_elemConn_Cn_S interface~elemconn_cn->proc~cmp_elemconn_cn_s proc~cmp_elemconn_cn_v cmp_elemConn_Cn_V interface~elemconn_cn->proc~cmp_elemconn_cn_v proc~ndgrid2 ndgrid2 interface~ndgrid->proc~ndgrid2 proc~ndgrid3 ndgrid3 interface~ndgrid->proc~ndgrid3 proc~unique_integer unique_integer interface~unique->proc~unique_integer proc~unique_real unique_real interface~unique->proc~unique_real interface~elemconn_c0 elemConn_C0 proc~cmp_elem_xc_vis->interface~elemconn_c0 proc~cmp_elem_xg_vis->interface~elemconn_c0 proc~elevate_degree_a_5_9->interface~compute_multiplicity proc~bincoeff bincoeff proc~elevate_degree_a_5_9->proc~bincoeff proc~get_multiplicity->interface~compute_multiplicity cosd cosd proc~rotation->cosd sind sind proc~rotation->sind proc~cmp_degree nurbs_volume%cmp_degree proc~set1->proc~cmp_degree proc~cmp_nc nurbs_volume%cmp_nc proc~set1->proc~cmp_nc proc~set2->proc~cmp_nc proc~compute_knot_vector compute_knot_vector proc~set2->proc~compute_knot_vector proc~set3->proc~cmp_degree proc~cmp_elemconn_c0_l cmp_elemConn_C0_L interface~elemconn_c0->proc~cmp_elemconn_c0_l proc~cmp_elemconn_c0_s cmp_elemConn_C0_S interface~elemconn_c0->proc~cmp_elemconn_c0_s proc~cmp_elemconn_c0_v cmp_elemConn_C0_V interface~elemconn_c0->proc~cmp_elemconn_c0_v proc~factln factln proc~bincoeff->proc~factln proc~cmp_degree->proc~get_multiplicity proc~cmp_nc->interface~compute_multiplicity proc~repelem repelem proc~compute_knot_vector->proc~repelem

Variables

Type Attributes Name Initial
real(kind=rk), allocatable :: Wc(:)

Arrays for control points and weights
real(kind=rk), allocatable :: Xc(:,:)

Arrays for control points and weights
real(kind=rk) :: knot1(4)

Arrays for knot vectors in all three dimensions
real(kind=rk) :: knot2(4)

Arrays for knot vectors in all three dimensions
real(kind=rk) :: knot3(4)

Arrays for knot vectors in all three dimensions
type(nurbs_volume) :: nurbs

Declare a NURBS volume object

Functions

function generate_Xc(L) result(control_points)

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: L

Return Value real(kind=rk), allocatable, (:,:)


Source Code

program example3_volume

    use forcad, only: rk, nurbs_volume

    implicit none
    type(nurbs_volume) :: nurbs              !! Declare a NURBS volume object
    real(rk), allocatable :: Xc(:,:), Wc(:)  !! Arrays for control points and weights
    real(rk) :: knot1(4), knot2(4), knot3(4) !! Arrays for knot vectors in all three dimensions

    !-----------------------------------------------------------------------------
    ! Setting up the NURBS volume
    !-----------------------------------------------------------------------------

    !> Define the control points for the NURBS volume
    Xc = generate_Xc(5.0_rk)

    !> Define weights for the control points (optional)
    allocate(Wc(size(Xc,1)), source=1.0_rk)
    Wc(2) = 5.0_rk

    !> Define knot vectors for all three dimensions
    knot1 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk]
    knot2 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk]
    knot3 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk]

    !> Set knot vectors, control points, and weights for the NURBS volume object
    !> Wc is optional.
    call nurbs%set(knot1, knot2, knot3, Xc, Wc)

    !> Deallocate local arrays
    deallocate(Xc, Wc)

    !> Export the control points to a VTK file
    call nurbs%export_Xc('vtk/nurbs_volume_Xc.vtk')

    !-----------------------------------------------------------------------------
    ! Creating the NURBS volume
    !-----------------------------------------------------------------------------

    !> Generate the NURBS volume with resolutions of 20, 20, and 20 in the three dimensions
    call nurbs%create(20, 20, 20)

    !> Export the generated volume to a VTK file
    call nurbs%export_Xg('vtk/nurbs_volume_Xg.vtk')

    !-----------------------------------------------------------------------------
    ! Visualization using PyVista
    ! Note: PyVista is required for visualization. Install it using `pip install pyvista`
    !-----------------------------------------------------------------------------

    !> Show the control geometry and geometry using PyVista
    call nurbs%show('vtk/nurbs_volume_Xc.vtk','vtk/nurbs_volume_Xg.vtk')

    !-----------------------------------------------------------------------------
    ! Refinements
    !-----------------------------------------------------------------------------

    !> Print size of knot vectors
    print*, size(nurbs%get_knot(1))
    print*, size(nurbs%get_knot(2))
    print*, size(nurbs%get_knot(3))

    !> Insert knots 0.25 and 0.75 in all three directions
    call nurbs%insert_knots(1, [0.25_rk, 0.75_rk], [1,1]) ! direction 1
    call nurbs%insert_knots(2, [0.25_rk, 0.75_rk], [1,1]) ! direction 2
    call nurbs%insert_knots(3, [0.25_rk, 0.75_rk], [1,1]) ! direction 3

    !> Print size of knot vectors after inserting knots
    print*, size(nurbs%get_knot(1))
    print*, size(nurbs%get_knot(2))
    print*, size(nurbs%get_knot(3))

    !> Print degrees
    print*, nurbs%get_degree()

    !> Elevate degree by 2 in all three directions
    call nurbs%elevate_degree(1, 2) ! direction 1
    call nurbs%elevate_degree(2, 2) ! direction 2
    call nurbs%elevate_degree(3, 2) ! direction 3

    !> Print degrees after elevating
    print*, nurbs%get_degree()

    !> Print size of knot vectors
    print*, size(nurbs%get_knot(1))
    print*, size(nurbs%get_knot(2))
    print*, size(nurbs%get_knot(3))

    call nurbs%remove_knots(1, [0.25_rk, 0.75_rk], [1,1]) ! direction 1
    call nurbs%remove_knots(2, [0.25_rk, 0.75_rk], [1,1]) ! direction 2
    call nurbs%remove_knots(3, [0.25_rk, 0.75_rk], [1,1]) ! direction 3

    !> Print size of knot vectors after removing knots
    print*, size(nurbs%get_knot(1))
    print*, size(nurbs%get_knot(2))
    print*, size(nurbs%get_knot(3))

    !> Generate the refined NURBS volume with resolutions of 40, 40, and 40 in the three dimensions
    call nurbs%create()

    !> Export updated control points to a VTK file
    call nurbs%export_Xc('vtk/nurbs_volume_Xc2.vtk')

    !> Export the refined generated volume to a VTK file
    call nurbs%export_Xg('vtk/nurbs_volume_Xg2.vtk')

    !-----------------------------------------------------------------------------
    ! Visualization using PyVista
    ! Note: PyVista is required for visualization. Install it using `pip install pyvista`
    !-----------------------------------------------------------------------------

    !> Show the control geometry and geometry using PyVista
    call nurbs%show('vtk/nurbs_volume_Xc2.vtk','vtk/nurbs_volume_Xg2.vtk')

    !-----------------------------------------------------------------------------
    ! Transformations
    !-----------------------------------------------------------------------------

    !> Rotate the control points
    call nurbs%rotate_Xc(alpha=-45.0_rk, beta=0.0_rk, theta=90.0_rk)

    !> Rotate the generated curve
    call nurbs%rotate_Xg(alpha=-45.0_rk, beta=0.0_rk, theta=90.0_rk)

    !> Translate the control points
    call nurbs%translate_Xc([1.0_rk, 2.0_rk, -3.0_rk])

    !> Translate the generated curve
    call nurbs%translate_Xg([1.0_rk, 2.0_rk, -3.0_rk])

    !> Export the transformed control points to a VTK file
    call nurbs%export_Xc('vtk/nurbs_volume_Xc3.vtk')

    !> Export the transformed generated volume to a VTK file
    call nurbs%export_Xg('vtk/nurbs_volume_Xg3.vtk')

    !-----------------------------------------------------------------------------
    ! Visualization using PyVista
    ! Note: PyVista is required for visualization. Install it using `pip install pyvista`
    !-----------------------------------------------------------------------------

    !> Show the control geometry and geometry using PyVista
    call nurbs%show('vtk/nurbs_volume_Xc3.vtk','vtk/nurbs_volume_Xg3.vtk')

    !-----------------------------------------------------------------------------
    ! Extract faces
    !-----------------------------------------------------------------------------

    !> first compute and set the connectivities of volume elements
    call nurbs%set_elem(nurbs%cmp_elem())

    !> get the connectivity of the face1 of the first element
    print*, 'Face 1 of element 1:', nurbs%cmp_elemFace(elem=1, face=1)
    print*, 'Face 2 of element 1:', nurbs%cmp_elemFace(elem=1, face=2)
    print*, 'Face 3 of element 1:', nurbs%cmp_elemFace(elem=1, face=3)
    print*, 'Face 4 of element 1:', nurbs%cmp_elemFace(elem=1, face=4)
    print*, 'Face 5 of element 1:', nurbs%cmp_elemFace(elem=1, face=5)
    print*, 'Face 6 of element 1:', nurbs%cmp_elemFace(elem=1, face=6)

    !> get the degree of the faces
    print*, 'Degree of face 1:', nurbs%cmp_degreeFace(face=1)
    print*, 'Degree of face 2:', nurbs%cmp_degreeFace(face=2)
    print*, 'Degree of face 3:', nurbs%cmp_degreeFace(face=3)
    print*, 'Degree of face 4:', nurbs%cmp_degreeFace(face=4)
    print*, 'Degree of face 5:', nurbs%cmp_degreeFace(face=5)
    print*, 'Degree of face 6:', nurbs%cmp_degreeFace(face=6)
    
    !-----------------------------------------------------------------------------
    ! Finalizing
    !-----------------------------------------------------------------------------

    !> Finalize the NURBS volume object
    call nurbs%finalize()

contains

    !-----------------------------------------------------------------------------
    function generate_Xc(L) result(control_points)
        implicit none
        real(rk), intent(in) :: L
        real(rk), allocatable :: control_points(:,:)
        real(rk) :: L2
        L2 = L / 2.0_rk
        allocate(control_points(8, 3))
        control_points(1,:) = [ L2, -L2,  L2]
        control_points(2,:) = [ L2, -L2, -L2]
        control_points(3,:) = [-L2, -L2,  L2]
        control_points(4,:) = [-L2, -L2, -L2]
        control_points(5,:) = [ L2,  L2,  L2]
        control_points(6,:) = [ L2,  L2, -L2]
        control_points(7,:) = [-L2,  L2,  L2]
        control_points(8,:) = [-L2,  L2, -L2]
    end function
    !-----------------------------------------------------------------------------

end program example3_volume