example3_surface Program

Uses

  • program~~example3_surface~~UsesGraph program~example3_surface example3_surface module~forcad forcad program~example3_surface->module~forcad module~forcad_kinds forcad_kinds module~forcad->module~forcad_kinds 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_kinds module~forcad_nurbs_curve->module~forcad_utils module~forcad_nurbs_surface->module~forcad_kinds module~forcad_nurbs_surface->module~forcad_utils module~forcad_nurbs_volume->module~forcad_kinds module~forcad_nurbs_volume->module~forcad_utils module~forcad_utils->module~forcad_kinds

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

Define control points for the NURBS surface

Define weights for the control points Define knot vectors for both dimensions Set knot vectors, control points, and weights for the NURBS surface object

Deallocate local arrays

Export parameter space to a VTK file

Export the control points to a VTK file

Generate the NURBS surface with resolutions of 30 in both dimensions

Export the generated surface to a VTK file

Export the NURBS surface to an IGES file

Show the control geometry and geometry using PyVista

Print size of the knot vectors Insert knots 0.25, twice and 0.75, once in both directions Print size of the knot vectors after inserting knots Print the degrees

Elevate degree by 2 in both directions Print the degrees after elevating

Print size of the knot vectors Remove knots 0.25, twice and 0.75, once in both directions Print size of the knot vectors after removing knots Generate the refined NURBS surface with resolutions of 30 in both dimensions

Export refined parameter space to a VTK file

Export updated control points to a VTK file

Export the refined generated surface to a VTK file

Export the NURBS surface to an IGES 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 parameter space to a VTK file

Export the transformed control points to a VTK file

Export the transformed generated volume to a VTK file

Export the transformed NURBS surface to an IGES file

Show the control geometry and geometry using PyVista

Finalize the NURBS surface object


Calls

program~~example3_surface~~CallsGraph program~example3_surface example3_surface none~get_degree nurbs_surface%get_degree program~example3_surface->none~get_degree none~get_knot nurbs_surface%get_knot program~example3_surface->none~get_knot none~set nurbs_surface%set program~example3_surface->none~set proc~create nurbs_surface%create program~example3_surface->proc~create proc~elevate_degree nurbs_surface%elevate_degree program~example3_surface->proc~elevate_degree proc~export_iges nurbs_surface%export_iges program~example3_surface->proc~export_iges proc~export_xc nurbs_surface%export_Xc program~example3_surface->proc~export_xc proc~export_xg nurbs_surface%export_Xg program~example3_surface->proc~export_xg proc~export_xth nurbs_surface%export_Xth program~example3_surface->proc~export_xth proc~finalize nurbs_surface%finalize program~example3_surface->proc~finalize proc~generate_xc~3 generate_Xc program~example3_surface->proc~generate_xc~3 proc~insert_knots nurbs_surface%insert_knots program~example3_surface->proc~insert_knots proc~remove_knots nurbs_surface%remove_knots program~example3_surface->proc~remove_knots proc~rotate_xc nurbs_surface%rotate_Xc program~example3_surface->proc~rotate_xc proc~rotate_xg nurbs_surface%rotate_Xg program~example3_surface->proc~rotate_xg proc~show nurbs_surface%show program~example3_surface->proc~show proc~translate_xc nurbs_surface%translate_Xc program~example3_surface->proc~translate_xc proc~translate_xg nurbs_surface%translate_Xg program~example3_surface->proc~translate_xg proc~get_degree_all nurbs_surface%get_degree_all none~get_degree->proc~get_degree_all proc~get_degree_dir nurbs_surface%get_degree_dir none~get_degree->proc~get_degree_dir proc~get_knot_all nurbs_surface%get_knot_all none~get_knot->proc~get_knot_all proc~get_knoti nurbs_surface%get_knoti none~get_knot->proc~get_knoti proc~set1 nurbs_surface%set1 none~set->proc~set1 proc~set2 nurbs_surface%set2 none~set->proc~set2 proc~set3 nurbs_surface%set3 none~set->proc~set3 proc~set4 nurbs_surface%set4 none~set->proc~set4 interface~compute_xg compute_Xg proc~create->interface~compute_xg interface~ndgrid ndgrid proc~create->interface~ndgrid proc~is_rational nurbs_surface%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~elevate_degree->proc~is_rational append append proc~export_iges->append delete delete proc~export_iges->delete init init proc~export_iges->init makedpsections makedpsections proc~export_iges->makedpsections makegsection makegsection proc~export_iges->makegsection makessection makessection proc~export_iges->makessection proc~export_iges->proc~is_rational writeigesfile writeigesfile proc~export_iges->writeigesfile proc~cmp_elem_xc_vis nurbs_surface%cmp_elem_Xc_vis proc~export_xc->proc~cmp_elem_xc_vis proc~export_vtk_legacy export_vtk_legacy proc~export_xc->proc~export_vtk_legacy proc~cmp_elem_xg_vis nurbs_surface%cmp_elem_Xg_vis proc~export_xg->proc~cmp_elem_xg_vis proc~export_xg->proc~export_vtk_legacy proc~export_xth->none~set proc~export_xth->interface~ndgrid interface~unique unique proc~export_xth->interface~unique proc~cmp_elem nurbs_surface%cmp_elem proc~export_xth->proc~cmp_elem proc~export_xth->proc~export_vtk_legacy 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~insert_knots->proc~is_rational 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->proc~is_rational 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~compute_xg_bspline_2d compute_Xg_bspline_2d interface~compute_xg->proc~compute_xg_bspline_2d proc~compute_xg_bspline_2d_1point compute_Xg_bspline_2d_1point interface~compute_xg->proc~compute_xg_bspline_2d_1point proc~compute_xg_nurbs_2d compute_Xg_nurbs_2d interface~compute_xg->proc~compute_xg_nurbs_2d proc~compute_xg_nurbs_2d_1point compute_Xg_nurbs_2d_1point interface~compute_xg->proc~compute_xg_nurbs_2d_1point 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 proc~cmp_elem->interface~unique interface~elemconn_cn elemConn_Cn proc~cmp_elem->interface~elemconn_cn proc~get_multiplicity nurbs_surface%get_multiplicity proc~cmp_elem->proc~get_multiplicity 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 cosd cosd proc~rotation->cosd sind sind proc~rotation->sind proc~cmp_degree nurbs_surface%cmp_degree proc~set1->proc~cmp_degree proc~cmp_nc nurbs_surface%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~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~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 proc~basis_bspline basis_bspline proc~compute_xg_bspline_2d->proc~basis_bspline proc~kron kron proc~compute_xg_bspline_2d->proc~kron proc~compute_xg_bspline_2d_1point->proc~basis_bspline proc~compute_xg_bspline_2d_1point->proc~kron proc~cmp_tgc_2d cmp_Tgc_2d proc~compute_xg_nurbs_2d->proc~cmp_tgc_2d proc~compute_xg_nurbs_2d_1point->proc~basis_bspline proc~compute_xg_nurbs_2d_1point->proc~kron proc~get_multiplicity->interface~compute_multiplicity proc~cmp_tgc_2d->proc~basis_bspline proc~cmp_tgc_2d->proc~kron

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(6)

Arrays for knot vectors in both dimensions
real(kind=rk) :: knot2(6)

Arrays for knot vectors in both dimensions
type(nurbs_surface) :: nurbs

Declare a NURBS surface object

Functions

function generate_Xc(num_rows, num_cols, peak_height) result(control_points)

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: num_rows
integer, intent(in) :: num_cols
real(kind=rk), intent(in) :: peak_height

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


Source Code

program example3_surface

    use forcad

    implicit none

    type(nurbs_surface) :: nurbs            !! Declare a NURBS surface object
    real(rk), allocatable :: Xc(:,:), Wc(:) !! Arrays for control points and weights
    real(rk) :: knot1(6), knot2(6)          !! Arrays for knot vectors in both dimensions

    !-----------------------------------------------------------------------------
    ! Setting up the NURBS surface
    !-----------------------------------------------------------------------------

    !> Define control points for the NURBS surface
    Xc = generate_Xc(3, 3, 1.0_rk)

    !> Define weights for the control points
    allocate(Wc(size(Xc, 1)))
    Wc = 1.0_rk
    Wc(2) = 2.0_rk

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

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

    !> Deallocate local arrays
    deallocate(Xc, Wc)

    !> Export parameter space to a VTK file
    call nurbs%export_Xth('vtk/nurbs_surface_Xth.vtk')

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

    !-----------------------------------------------------------------------------
    ! Creating the NURBS surface
    !-----------------------------------------------------------------------------

    !> Generate the NURBS surface with resolutions of 30 in both dimensions
    call nurbs%create(30, 30)

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

    !> Export the NURBS surface to an IGES file
    call nurbs%export_iges('iges/nurbs_surface.iges')

    !-----------------------------------------------------------------------------
    ! 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_surface_Xc.vtk','vtk/nurbs_surface_Xg.vtk')

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

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

    !> Insert knots 0.25, twice and 0.75, once in both directions
    call nurbs%insert_knots(1, [0.25_rk, 0.75_rk], [2,1]) ! direction 1
    call nurbs%insert_knots(2, [0.25_rk, 0.75_rk], [2,1]) ! direction 2

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

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

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

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

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

    !> Remove knots 0.25, twice and 0.75, once in both directions
    call nurbs%remove_knots(1, [0.25_rk, 0.75_rk], [2,1]) ! direction 1
    call nurbs%remove_knots(2, [0.25_rk, 0.75_rk], [2,1]) ! direction 2

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

    !> Generate the refined NURBS surface with resolutions of 30 in both dimensions
    call nurbs%create()

    !> Export refined parameter space to a VTK file
    call nurbs%export_Xth('vtk/nurbs_surface_Xth2.vtk')

    !> Export updated control points to a VTK file
    call nurbs%export_Xc('vtk/nurbs_surface_Xc2.vtk')

    !> Export the refined generated surface to a VTK file
    call nurbs%export_Xg('vtk/nurbs_surface_Xg2.vtk')

    !> Export the NURBS surface to an IGES file
    call nurbs%export_iges('iges/nurbs_surface2.iges')

    !-----------------------------------------------------------------------------
    ! 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_surface_Xc2.vtk','vtk/nurbs_surface_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 parameter space to a VTK file
    call nurbs%export_Xth('vtk/nurbs_surface_Xth3.vtk')

    !> Export the transformed control points to a VTK file
    call nurbs%export_Xc('vtk/nurbs_surface_Xc3.vtk')

    !> Export the transformed generated volume to a VTK file
    call nurbs%export_Xg('vtk/nurbs_surface_Xg3.vtk')

    !> Export the transformed NURBS surface to an IGES file
    call nurbs%export_iges('iges/nurbs_surface3.iges')

    !-----------------------------------------------------------------------------
    ! 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_surface_Xc3.vtk','vtk/nurbs_surface_Xg3.vtk')

    !-----------------------------------------------------------------------------
    ! Finalizing
    !-----------------------------------------------------------------------------

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

contains

    !-----------------------------------------------------------------------------
    function generate_Xc(num_rows, num_cols, peak_height) result(control_points)
        integer, intent(in) :: num_rows, num_cols
        real(rk), intent(in) :: peak_height
        real(rk), allocatable :: control_points(:,:)
        integer :: i, j
        real(rk) :: x_spacing, y_spacing, x_offset, y_offset
        x_spacing = 1.0_rk / real(num_cols - 1, rk)
        y_spacing = 1.0_rk / real(num_rows - 1, rk)
        x_offset = -0.5_rk
        y_offset = -0.5_rk
        allocate(control_points(num_rows * num_cols, 3))
        do i = 1, num_rows
            do j = 1, num_cols
                control_points((i - 1) * num_cols + j, 1) = x_offset + real(j - 1, rk) * x_spacing
                control_points((i - 1) * num_cols + j, 2) = y_offset + real(i - 1, rk) * y_spacing
                control_points((i - 1) * num_cols + j, 3) = &
                    peak_height * exp(-((control_points((i - 1) * num_cols + j, 1) ** 2) &
                    + (control_points((i - 1) * num_cols + j, 2) ** 2))) + 0.5_rk * peak_height * 0.2_rk
            end do
        end do
    end function
    !-----------------------------------------------------------------------------

end program example3_surface