!> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> This module defines the 'nurbs_curve' type for representing a Non-Uniform Rational B-Spline (NURBS) curve. module forcad_nurbs_curve use forcad_utils, only: rk, basis_bspline, elemConn_C0, compute_multiplicity, compute_knot_vector, basis_bspline_der,& insert_knot_A_5_1, findspan, elevate_degree_A_5_9, remove_knots_A_5_8, & elemConn_Cn, unique, rotation, dyad, gauss_leg implicit none private public nurbs_curve !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause type nurbs_curve real(rk), allocatable, private :: Xc(:,:) !! Control points (2D array: [nc, dim]) real(rk), allocatable, private :: Xg(:,:) !! Geometry points (2D array: [ng, dim]) real(rk), allocatable, private :: Wc(:) !! Weights for control points (1D array: [nc]) real(rk), allocatable, private :: Xt(:) !! Evaluation points (1D array: [ng]) real(rk), allocatable, private :: knot(:) !! Knot vector (1D array) integer, private :: degree !! Degree (order) of the curve integer, private :: nc !! Number of control points integer, private :: ng !! Number of geometry points integer, allocatable, private :: elemConn_Xc_vis(:,:) !! Connectivity for visualization of control points integer, allocatable, private :: elemConn_Xg_vis(:,:) !! Connectivity for visualization of geometry points integer, allocatable, private :: elemConn(:,:) !! IGA element connectivity contains procedure :: set1 !!> Set knot vector, control points and weights for the NURBS curve object procedure :: set1a procedure :: set2 !!> Set NURBS curve using nodes of parameter space, degree, continuity, control points and weights procedure :: set3 !!> Set Bezier or Rational Bezier curve using control points and weights procedure :: set4 !!> Set NURBS curve using degree, number of control points, control points and weights generic :: set => set1, set1a, set2, set3, set4 !!> Set NURBS curve procedure :: create !!> Generate geometry points procedure :: cmp_Xg !!> Compute geometry points procedure, private :: get_Xc_all !!> Get all control points procedure, private :: get_Xci !!> Get i-th control point procedure, private :: get_Xcid !!> Get i-th control point in a specific direction generic :: get_Xc => get_Xc_all, get_Xci, get_Xcid !!> Get control points procedure, private :: get_Xg_all !!> Get all geometry points procedure, private :: get_Xgi !!> Get i-th geometry point procedure, private :: get_Xgid !!> Get i-th geometry point in a specific direction generic :: get_Xg => get_Xg_all, get_Xgi, get_Xgid !!> Get geometry points procedure, private :: get_Wc_all !!> Get all weights procedure, private :: get_Wci !!> Get i-th weight generic :: get_Wc => get_Wc_all, get_Wci !!> Get weights procedure :: get_Xt !!> Get parameter values procedure, private :: get_knot_all !!> Get all knot vectors procedure, private :: get_knoti !!> Get i-th knot value generic :: get_knot => get_knoti, get_knot_all !!> Get knot vector procedure :: get_ng !!> Get number of geometry points procedure :: cmp_degree !!> Compute degree of the NURBS curve procedure :: get_degree !!> Get degree of the NURBS curve procedure :: finalize !!> Finalize the NURBS curve object procedure :: cmp_elem_Xc_vis !!> Generate connectivity for control points procedure :: cmp_elem_Xg_vis !!> Generate connectivity for geometry points procedure :: cmp_elem !!> Generate IGA element connectivity procedure :: get_elem_Xc_vis !!> Get connectivity for control points procedure :: get_elem_Xg_vis !!> Get connectivity for geometry points procedure :: get_elem !!> Get IGA element connectivity procedure :: set_elem_Xc_vis !!> Set connectivity for control points procedure :: set_elem_Xg_vis !!> Set connectivity for geometry points procedure :: set_elem !!> Set IGA element connectivity procedure :: export_Xc !!> Export control points to VTK file procedure :: export_Xg !!> Export geometry points to VTK file procedure :: modify_Xc !!> Modify control points procedure :: modify_Wc !!> Modify weights procedure :: get_multiplicity !!> Compute and return the multiplicity of the knots procedure :: get_continuity !!> Compute and return the continuity of the curve procedure :: cmp_nc !!> Compute number of required control points procedure :: get_nc !!> Get number of control points procedure :: insert_knots !!> Insert knots into the knot vector procedure :: elevate_degree !!> Elevate the degree of the curve procedure, private :: basis_vector !!> Compute the basis functions of the NURBS curve procedure, private :: basis_scalar !!> Compute the basis functions of the NURBS curve generic :: basis => basis_vector, basis_scalar !!> Compute the basis functions of the NURBS curve procedure, private :: derivative_vector !!> Compute the derivative of the NURBS curve procedure, private :: derivative_scalar !!> Compute the derivative of the NURBS curve generic :: derivative => derivative_vector, derivative_scalar !!> Compute the derivative of the NURBS curve procedure, private :: derivative2_vector !!> Compute the second derivative of the NURBS curve procedure, private :: derivative2_scalar !!> Compute the second derivative of the NURBS curve generic :: derivative2 => derivative2_vector, derivative2_scalar !!> Compute the second derivative of the NURBS curve procedure :: is_rational !!> Check if the NURBS curve is rational procedure :: remove_knots !!> Remove knots from the knot vector procedure :: rotate_Xc !!> Rotate control points procedure :: rotate_Xg !!> Rotate geometry points procedure :: translate_Xc !!> Translate control points procedure :: translate_Xg !!> Translate geometry points procedure :: show !!> Show the NURBS object using PyVista procedure :: nearest_point !!> Find the nearest point on the NURBS curve (Approximation) procedure :: nearest_point2 !!> Find the nearest point on the NURBS curve (Minimization - Newton's method) procedure :: ansatz !!> Compute the shape functions, derivative of shape functions and dL procedure :: cmp_length !!> Compute the length of the NURBS curve ! Shapes procedure :: set_circle !!> Set a circle procedure :: set_half_circle !!> Set a half circle procedure :: set_C !!> Set a C-shape end type !=============================================================================== interface compute_Xg pure function compute_Xg_nurbs_1d(f_Xt, f_knot, f_degree, f_nc, f_ng, f_Xc, f_Wc) result(f_Xg) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Xc(:,:) real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable :: f_Xg(:,:) end function pure function compute_Xg_bspline_1d(f_Xt, f_knot, f_degree, f_nc, f_ng, f_Xc) result(f_Xg) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Xc(:,:) real(rk), allocatable :: f_Xg(:,:) end function pure function compute_Xg_nurbs_1d_1point(f_Xt, f_knot, f_degree, f_nc, f_Xc, f_Wc) result(f_Xg) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), intent(in), contiguous :: f_Xc(:,:) real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable :: f_Xg(:) end function pure function compute_Xg_bspline_1d_1point(f_Xt, f_knot, f_degree, f_nc, f_Xc) result(f_Xg) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), intent(in), contiguous :: f_Xc(:,:) real(rk), allocatable :: f_Xg(:) end function end interface interface compute_d2Tgc pure subroutine compute_d2Tgc_nurbs_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng, f_Wc, f_d2Tgc, f_dTgc, f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable, intent(out) :: f_d2Tgc(:,:) real(rk), allocatable, intent(out) :: f_dTgc(:,:) real(rk), allocatable, intent(out) :: f_Tgc(:,:) end subroutine pure subroutine compute_d2Tgc_bspline_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng, f_d2Tgc, f_dTgc, f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), allocatable, intent(out) :: f_d2Tgc(:,:) real(rk), allocatable, intent(out) :: f_dTgc(:,:) real(rk), allocatable, intent(out) :: f_Tgc(:,:) end subroutine pure subroutine compute_d2Tgc_nurbs_1d_scalar(f_Xt, f_knot, f_degree, f_nc, f_Wc, f_d2Tgc, f_dTgc, f_Tgc) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable, intent(out) :: f_d2Tgc(:) real(rk), allocatable, intent(out) :: f_dTgc(:) real(rk), allocatable, intent(out) :: f_Tgc(:) end subroutine pure subroutine compute_d2Tgc_bspline_1d_scalar(f_Xt, f_knot, f_degree, f_nc, f_d2Tgc, f_dTgc, f_Tgc) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), allocatable, intent(out) :: f_d2Tgc(:) real(rk), allocatable, intent(out) :: f_dTgc(:) real(rk), allocatable, intent(out) :: f_Tgc(:) end subroutine end interface interface compute_dTgc pure subroutine compute_dTgc_nurbs_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng, f_Wc, f_dTgc, f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable, intent(out) :: f_dTgc(:,:) real(rk), allocatable, intent(out) :: f_Tgc(:,:) end subroutine pure subroutine compute_dTgc_bspline_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng, f_dTgc, f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), allocatable, intent(out) :: f_dTgc(:,:) real(rk), allocatable, intent(out) :: f_Tgc(:,:) end subroutine pure subroutine compute_dTgc_nurbs_1d_scalar(f_Xt, f_knot, f_degree, f_nc, f_Wc, f_dTgc, f_Tgc, f_elem) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable, intent(out) :: f_dTgc(:) real(rk), allocatable, intent(out) :: f_Tgc(:) integer, intent(in), optional :: f_elem(:) end subroutine pure subroutine compute_dTgc_bspline_1d_scalar(f_Xt, f_knot, f_degree, f_nc, f_dTgc, f_Tgc, f_elem) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), allocatable, intent(out) :: f_dTgc(:) real(rk), allocatable, intent(out) :: f_Tgc(:) integer, intent(in), optional :: f_elem(:) end subroutine end interface interface compute_Tgc pure function compute_Tgc_nurbs_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng, f_Wc) result(f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable :: f_Tgc(:,:) end function pure function compute_Tgc_bspline_1d_vector(f_Xt, f_knot, f_degree, f_nc, f_ng) result(f_Tgc) import :: rk real(rk), intent(in), contiguous :: f_Xt(:) real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc integer, intent(in) :: f_ng real(rk), allocatable :: f_Tgc(:,:) end function pure function compute_Tgc_nurbs_1d_scalar(f_Xt, f_knot, f_degree, f_nc, f_Wc) result(f_Tgc) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), intent(in), contiguous :: f_Wc(:) real(rk), allocatable :: f_Tgc(:) end function pure function compute_Tgc_bspline_1d_scalar(f_Xt, f_knot, f_degree, f_nc) result(f_Tgc) import :: rk real(rk), intent(in) :: f_Xt real(rk), intent(in), contiguous :: f_knot(:) integer, intent(in) :: f_degree integer, intent(in) :: f_nc real(rk), allocatable :: f_Tgc(:) end function end interface interface pure function nearest_point_help_1d(f_ng, f_Xg, f_point_Xg) result(f_distances) import :: rk integer, intent(in) :: f_ng real(rk), intent(in), contiguous :: f_Xg(:,:) real(rk), intent(in), contiguous :: f_point_Xg(:) real(rk), allocatable :: f_distances(:) end function end interface contains !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set knot vector, control points and weights for the NURBS curve object. pure subroutine set1(this, knot, Xc, Wc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: knot(:) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%knot)) deallocate(this%knot) if (allocated(this%Xc)) deallocate(this%Xc) this%knot = knot call this%cmp_degree() this%Xc = Xc this%nc = size(this%Xc, 1) if (present(Wc)) then if (size(Wc) /= this%nc) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) deallocate(this%Wc) this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set knot vector, control points and weights for the NURBS curve object. pure subroutine set1a(this, knot, Xc, Wc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: knot(:) real(rk), intent(in), contiguous :: Xc(:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%knot)) deallocate(this%knot) if (allocated(this%Xc)) deallocate(this%Xc) this%knot = knot call this%cmp_degree() allocate(this%Xc(size(Xc), 3), source = 0.0_rk) this%Xc(:,1) = Xc this%nc = size(this%Xc, 1) if (present(Wc)) then if (size(Wc) /= this%nc) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) deallocate(this%Wc) this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set NURBS curve using nodes of parameter space (Xth), degree, continuity, control points and weights. pure subroutine set2(this, Xth_dir, degree, continuity, Xc, Wc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: Xth_dir(:) integer, intent(in) :: degree integer, intent(in), contiguous :: continuity(:) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%knot)) deallocate(this%knot) if (allocated(this%Xc)) deallocate(this%Xc) this%knot = compute_knot_vector(Xth_dir, degree, continuity) this%degree = degree this%Xc = Xc this%nc = size(this%Xc, 1) if (present(Wc)) then if (size(Wc) /= this%nc) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) deallocate(this%Wc) this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set Bezier or Rational Bezier curve using control points and weights. pure subroutine set3(this, Xc, Wc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%knot)) deallocate(this%knot) if (allocated(this%Xc)) deallocate(this%Xc) this%Xc = Xc this%nc = size(this%Xc, 1) if (allocated(this%knot)) deallocate(this%knot) allocate(this%knot(2*this%nc)) this%knot(1:this%nc) = 0.0_rk this%knot(this%nc+1:2*this%nc) = 1.0_rk call this%cmp_degree() if (present(Wc)) then if (size(Wc) /= this%nc) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) deallocate(this%Wc) this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set4(this, degree, nc, Xc, Wc) class(nurbs_curve), intent(inout) :: this integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) integer :: m, i if (allocated(this%Xc)) deallocate(this%Xc) this%Xc = Xc this%nc = nc this%degree = degree ! Size of knot vectors m = nc + degree + 1 if (allocated(this%knot)) deallocate(this%knot) allocate(this%knot(m)) this%knot(1:degree+1) = 0.0_rk this%knot(degree+2:m-degree-1) = [(real(i, rk)/(m-2*degree-1), i=1, m-2*degree-2)] this%knot(m-degree:m) = 1.0_rk if (present(Wc)) then if (size(Wc) /= nc) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) deallocate(this%Wc) this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine create(this, res, Xt) class(nurbs_curve), intent(inout) :: this integer, intent(in), optional :: res real(rk), intent(in), contiguous, optional :: Xt(:) integer :: i ! check if (.not.allocated(this%Xc)) then error stop 'Control points are not set.' end if if (.not.allocated(this%knot)) then error stop 'Knot vector is not set.' end if ! Set parameter values if (present(Xt)) then if (allocated(this%Xt)) deallocate(this%Xt) this%Xt = Xt elseif (present(res)) then if (allocated(this%Xt)) deallocate(this%Xt) allocate(this%Xt(res)) this%Xt = [(real(i-1, rk) / real(res-1, rk), i=1, res)] ! else ! this%Xt = this%Xt end if ! Set number of geometry points this%ng = size(this%Xt) ! Allocate memory for geometry points if (allocated(this%Xg)) deallocate(this%Xg) if (this%is_rational()) then ! NURBS this%Xg = compute_Xg(& this%Xt, this%knot, this%degree, this%nc, this%ng, this%Xc, this%Wc) else ! B-Spline this%Xg = compute_Xg(& this%Xt, this%knot, this%degree, this%nc, this%ng, this%Xc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_Xg(this, Xt) result(Xg) class(nurbs_curve), intent(in) :: this real(rk), intent(in) :: Xt real(rk), allocatable :: Xg(:) ! check if (.not.allocated(this%Xc)) then error stop 'Control points are not set.' end if if (.not.allocated(this%knot)) then error stop 'Knot vector is not set.' end if if (this%is_rational()) then ! NURBS Xg = compute_Xg(Xt, this%knot, this%degree, this%nc, this%Xc, this%Wc) else ! B-Spline Xg = compute_Xg(Xt, this%knot, this%degree, this%nc, this%Xc) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xc_all(this) result(Xc) class(nurbs_curve), intent(in) :: this real(rk), allocatable :: Xc(:,:) if (allocated(this%Xc)) then Xc = this%Xc else error stop 'Control points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xci(this, n) result(Xc) class(nurbs_curve), intent(in) :: this integer, intent(in) :: n real(rk), allocatable :: Xc(:) if (allocated(this%Xc)) then if (n<lbound(this%Xc,1) .or. n>ubound(this%Xc,1)) then error stop 'Invalid index for control points.' end if Xc = this%Xc(n,:) else error stop 'Control points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xcid(this, n, dir) result(Xc) class(nurbs_curve), intent(in) :: this integer, intent(in) :: n integer, intent(in) :: dir real(rk) :: Xc if (allocated(this%Xc)) then if (n<lbound(this%Xc,1) .or. n>ubound(this%Xc,1)) then error stop 'Invalid index for control points.' end if if (dir<lbound(this%Xc,2) .or. dir>ubound(this%Xc,2)) then error stop 'Invalid index for control points.' end if Xc = this%Xc(n, dir) else error stop 'Control points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xg_all(this) result(Xg) class(nurbs_curve), intent(in) :: this real(rk), allocatable :: Xg(:,:) if (allocated(this%Xg)) then Xg = this%Xg else error stop 'Geometry points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xgi(this, n) result(Xg) class(nurbs_curve), intent(in) :: this integer, intent(in) :: n real(rk), allocatable :: Xg(:) if (allocated(this%Xg)) then if (n<lbound(this%Xg,1) .or. n>ubound(this%Xg,1)) then error stop 'Invalid index for geometry points.' end if Xg = this%Xg(n,:) else error stop 'Control points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xgid(this, n, dir) result(Xg) class(nurbs_curve), intent(in) :: this integer, intent(in) :: n integer, intent(in) :: dir real(rk) :: Xg if (allocated(this%Xg)) then if (n<lbound(this%Xg,1) .or. n>ubound(this%Xg,1)) then error stop 'Invalid index for geometry points.' end if if (dir<lbound(this%Xg,2) .or. dir>ubound(this%Xg,2)) then error stop 'Invalid index for geometry points.' end if Xg = this%Xg(n, dir) else error stop 'Control points are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Wc_all(this) result(Wc) class(nurbs_curve), intent(in) :: this real(rk), allocatable :: Wc(:) if (allocated(this%Wc)) then Wc = this%Wc else error stop 'The NURBS curve is not rational or weights are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Wci(this, n) result(Wc) class(nurbs_curve), intent(in) :: this integer, intent(in) :: n real(rk) :: Wc if (allocated(this%Wc)) then if (n<lbound(this%Wc,1) .or. n>ubound(this%Wc,1)) then error stop 'Invalid index for weights.' end if Wc = this%Wc(n) else error stop 'The NURBS curve is not rational or weights are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_Xt(this) result(Xt) class(nurbs_curve), intent(in) :: this real(rk), allocatable :: Xt(:) if (allocated(this%Xt)) then Xt = this%Xt else error stop 'Parameter values are not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_ng(this) result(ng) class(nurbs_curve), intent(in) :: this integer :: ng ng = this%ng end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_degree(this) class(nurbs_curve), intent(inout) :: this integer, allocatable :: m(:) m = this%get_multiplicity() this%degree = m(1) - 1 end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_degree(this) result(degree) class(nurbs_curve), intent(in) :: this integer :: degree degree = this%degree end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_knot_all(this) result(knot) class(nurbs_curve), intent(in) :: this real(rk), allocatable :: knot(:) if (allocated(this%knot)) then knot = this%knot else error stop 'Knot vector is not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_knoti(this,i) result(knot) class(nurbs_curve), intent(in) :: this integer, intent(in) :: i real(rk) :: knot if (allocated(this%knot)) then if (i < 1 .or. i > size(this%knot)) then error stop 'Invalid index for knot vector.' else knot = this%knot(i) end if else error stop 'Knot vector is not set.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine finalize(this) class(nurbs_curve), intent(inout) :: this if (allocated(this%Xc)) deallocate(this%Xc) if (allocated(this%Xg)) deallocate(this%Xg) if (allocated(this%Wc)) deallocate(this%Wc) if (allocated(this%Xt)) deallocate(this%Xt) if (allocated(this%knot)) deallocate(this%knot) if (allocated(this%elemConn_Xc_vis)) deallocate(this%elemConn_Xc_vis) if (allocated(this%elemConn_Xg_vis)) deallocate(this%elemConn_Xg_vis) if (allocated(this%elemConn)) deallocate(this%elemConn) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elem_Xc_vis(this, p) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) integer, intent(in), optional :: p if (present(p)) then elemConn = elemConn_C0(this%nc,p) else elemConn = elemConn_C0(this%nc,1) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elem_Xg_vis(this, p) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) integer, intent(in), optional :: p if (present(p)) then elemConn = elemConn_C0(this%ng,p) else elemConn = elemConn_C0(this%ng,1) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine export_Xc(this, filename) class(nurbs_curve), intent(in) :: this character(len=*), intent(in) :: filename integer :: i, nc, nunit integer, allocatable :: elemConn(:,:) ! check if (.not.allocated(this%Xc)) then error stop 'Control points are not set.' end if if (.not.allocated(this%elemConn_Xc_vis)) then elemConn = this%cmp_elem_Xc_vis() else elemConn = this%elemConn_Xc_vis end if nc = size(this%Xc, 1) open(newunit=nunit, file=filename, action='write') write(nunit,'(a)') '# vtk DataFile Version 2.0' write(nunit,'(a)') 'Generated by ForCAD' write(nunit,'(a)') 'ASCII' write(nunit,'(a)') 'DATASET UNSTRUCTURED_GRID' write(nunit,'(a," ",g0," ",a)') 'POINTS', nc, 'double' if (size(this%Xc, 2) == 2) then write(nunit,'(g0," ",g0," ",g0)') (this%Xc(i,1), this%Xc(i,2), 0.0_rk , i = 1, nc) elseif (size(this%Xc, 2) == 3) then write(nunit,'(g0," ",g0," ",g0)') (this%Xc(i,1), this%Xc(i,2), this%Xc(i,3) , i = 1, nc) else error stop 'Invalid dimension of the control points.' end if write(nunit,'(a," ",g0," ",g0)') 'CELLS', size(elemConn,1), size(elemConn,1)*(size(elemConn,2)+1) write(nunit,'(g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0)')& (2, elemConn(i,1)-1,elemConn(i,2)-1, i = 1, size(elemConn,1)) write(nunit,'(a," ",g0)') 'CELL_TYPES', size(elemConn,1) write(nunit,'(g0)') (3 , i = 1, size(elemConn,1)) close(nunit) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine export_Xg(this, filename) class(nurbs_curve), intent(in) :: this character(len=*), intent(in) :: filename integer :: i, ng, nunit integer, allocatable :: elemConn(:,:) ! check if (.not.allocated(this%Xg)) then error stop 'Geometry points are not set.' end if if (.not.allocated(this%elemConn_Xg_vis)) then elemConn = this%cmp_elem_Xg_vis() else elemConn = this%elemConn_Xg_vis end if ng = size(this%Xg, 1) open(newunit=nunit, file=filename, action='write') write(nunit,'(a)') '# vtk DataFile Version 2.0' write(nunit,'(a)') 'Generated by ForCAD' write(nunit,'(a)') 'ASCII' write(nunit,'(a)') 'DATASET UNSTRUCTURED_GRID' write(nunit,'(a," ",g0," ",a)') 'POINTS', ng, 'double' if (size(this%Xg, 2) == 2) then write(nunit,'(g0," ",g0," ",g0)') (this%Xg(i,1), this%Xg(i,2), 0.0_rk , i = 1, ng) elseif (size(this%Xg, 2) == 3) then write(nunit,'(g0," ",g0," ",g0)') (this%Xg(i,1), this%Xg(i,2), this%Xg(i,3) , i = 1, ng) else error stop 'Invalid dimension of the geometry points.' end if write(nunit,'(a," ",g0," ",g0)') 'CELLS', size(elemConn,1), size(elemConn,1)*(size(elemConn,2)+1) write(nunit,'(g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0," ",g0)')& (2, elemConn(i,1)-1,elemConn(i,2)-1, i = 1, size(elemConn,1)) write(nunit,'(a," ",g0)') 'CELL_TYPES', size(elemConn,1) write(nunit,'(g0)') (3 , i = 1, size(elemConn,1)) close(nunit) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine modify_Xc(this,X,num,dir) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: X integer, intent(in) :: num integer, intent(in) :: dir if (allocated(this%Xc)) then this%Xc(num,dir) = X if (allocated(this%Wc)) then call this%set(knot=this%get_knot(), Xc=this%get_Xc(), Wc=this%get_Wc()) else call this%set(knot=this%get_knot(), Xc=this%get_Xc()) end if else error stop 'Control points are not set.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine modify_Wc(this,W,num) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: W integer, intent(in) :: num if (allocated(this%Wc)) then this%Wc(num) = W if (allocated(this%knot)) then call this%set(knot=this%get_knot(), Xc=this%get_Xc(), Wc=this%get_Wc()) else call this%set(Xc=this%get_Xc(), Wc=this%get_Wc()) end if else error stop 'The NURBS curve is not rational.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_multiplicity(this) result(m) class(nurbs_curve), intent(in) :: this integer, allocatable :: m(:) ! check if (.not.allocated(this%knot)) then error stop 'Knot vector is not set.' else m = compute_multiplicity(this%knot) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_continuity(this) result(c) class(nurbs_curve), intent(in) :: this integer, allocatable :: c(:) ! check if (.not.allocated(this%knot)) then error stop 'Knot vector is not set.' else c = this%degree - compute_multiplicity(this%knot) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_nc(this) class(nurbs_curve), intent(inout) :: this this%nc = sum(compute_multiplicity(this%knot)) - this%degree - 1 end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_nc(this) result(nc) class(nurbs_curve), intent(in) :: this integer :: nc nc = this%nc end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine insert_knots(this,Xth,r) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: Xth(:) integer, intent(in), contiguous :: r(:) integer :: k, i, s, dim, j, n_new real(rk), allocatable :: Xcw(:,:), Xcw_new(:,:), Xc_new(:,:), Wc_new(:), knot_new(:) if (this%is_rational()) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc-1,this%degree,Xth(i),this%knot) if (this%knot(k+1) == Xth(i)) then s = compute_multiplicity(this%knot,Xth(i)) else s = 0 end if dim = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),dim+1)) do j = 1, size(this%Xc,1) Xcw(j,1:dim) = this%Xc(j,1:dim)*this%Wc(j) end do Xcw(:,dim+1) = this%Wc(:) call insert_knot_A_5_1(& this%degree,& this%knot,& Xcw,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xcw_new) allocate(Xc_new(1:n_new+1,1:dim)) allocate(Wc_new(1:n_new+1)) do j = 1, n_new+1 Xc_new(j,1:dim) = Xcw_new(j-1,1:dim)/Xcw_new(j-1,dim+1) Wc_new(j) = Xcw_new(j-1,dim+1) end do call this%set(knot=knot_new, Xc=Xc_new, Wc=Wc_new) deallocate(Xcw, Xcw_new, Xc_new, Wc_new) end do else ! B-Spline do i = 1, size(Xth) k = findspan(this%nc-1,this%degree,Xth(i),this%knot) if (this%knot(k+1) == Xth(i)) then s = compute_multiplicity(this%knot,Xth(i)) else s = 0 end if call insert_knot_A_5_1(& this%degree,& this%knot,& this%Xc,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xc_new) call this%set(knot=knot_new, Xc=Xc_new) end do end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine elevate_degree(this, t) class(nurbs_curve), intent(inout) :: this integer, intent(in) :: t real(rk), allocatable :: Xcw(:,:), Xcw_new(:,:), knot_new(:), Xc_new(:,:), Wc_new(:) integer :: dim, j, nc_new if (this%is_rational()) then ! NURBS dim = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),dim+1)) do j = 1, size(this%Xc,1) Xcw(j,1:dim) = this%Xc(j,1:dim)*this%Wc(j) Xcw(j,dim+1) = this%Wc(j) end do call elevate_degree_A_5_9(t, this%knot, this%degree, Xcw, nc_new, knot_new, Xcw_new) allocate(Xc_new(1:nc_new,1:dim)) allocate(Wc_new(1:nc_new)) do j = 1, nc_new Xc_new(j,1:dim) = Xcw_new(j,1:dim)/Xcw_new(j,dim+1) end do Wc_new(:) = Xcw_new(:,dim+1) call this%set(knot=knot_new, Xc=Xc_new, Wc=Wc_new) deallocate(Xcw, Xcw_new, Xc_new, Wc_new) else ! B-Spline dim = size(this%Xc,2) call elevate_degree_A_5_9(t, this%knot, this%degree, this%Xc, nc_new, knot_new, Xc_new) call this%set(knot=knot_new, Xc=Xc_new) deallocate(Xc_new) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative_vector(this, res, Xt, dTgc, Tgc) class(nurbs_curve), intent(inout) :: this integer, intent(in), optional :: res real(rk), intent(in), contiguous, optional :: Xt(:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out), optional :: Tgc(:,:) integer :: i ! Set parameter values if (present(Xt)) then if (allocated(this%Xt)) deallocate(this%Xt) this%Xt = Xt elseif (present(res)) then if (allocated(this%Xt)) deallocate(this%Xt) allocate(this%Xt(res)) this%Xt = [(real(i-1, rk) / real(res-1, rk), i=1, res)] ! else ! this%Xt = this%Xt end if ! Set number of geometry points this%ng = size(this%Xt,1) if (this%is_rational()) then ! NURBS call compute_dTgc(this%Xt, this%knot, this%degree, this%nc, this%ng, this%Wc, dTgc, Tgc) else ! B-Spline call compute_dTgc(this%Xt, this%knot, this%degree, this%nc, this%ng, dTgc, Tgc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative_scalar(this, Xt, dTgc, Tgc, elem) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: Xt integer, intent(in), optional :: elem(:) real(rk), allocatable, intent(out) :: dTgc(:) real(rk), allocatable, intent(out), optional :: Tgc(:) if (this%is_rational()) then ! NURBS call compute_dTgc(Xt, this%knot, this%degree, this%nc, this%Wc, dTgc, Tgc, elem) else ! B-Spline call compute_dTgc(Xt, this%knot, this%degree, this%nc, dTgc, Tgc, elem) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative2_vector(this, res, Xt, d2Tgc, dTgc, Tgc) class(nurbs_curve), intent(inout) :: this integer, intent(in), optional :: res real(rk), intent(in), contiguous, optional :: Xt(:) real(rk), allocatable, intent(out) :: d2Tgc(:,:) real(rk), allocatable, intent(out), optional :: dTgc(:,:) real(rk), allocatable, intent(out), optional :: Tgc(:,:) integer :: i ! Set parameter values if (present(Xt)) then if (allocated(this%Xt)) deallocate(this%Xt) this%Xt = Xt elseif (present(res)) then if (allocated(this%Xt)) deallocate(this%Xt) allocate(this%Xt(res)) this%Xt = [(real(i-1, rk) / real(res-1, rk), i=1, res)] ! else ! this%Xt = this%Xt end if ! Set number of geometry points this%ng = size(this%Xt,1) if (this%is_rational()) then ! NURBS call compute_d2Tgc(this%Xt, this%knot, this%degree, this%nc, this%ng, this%Wc, d2Tgc, dTgc, Tgc) else ! B-Spline call compute_d2Tgc(this%Xt, this%knot, this%degree, this%nc, this%ng, d2Tgc, dTgc, Tgc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative2_scalar(this, Xt, d2Tgc, dTgc, Tgc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: Xt real(rk), allocatable, intent(out) :: d2Tgc(:) real(rk), allocatable, intent(out), optional :: dTgc(:) real(rk), allocatable, intent(out), optional :: Tgc(:) if (this%is_rational()) then ! NURBS call compute_d2Tgc(Xt, this%knot, this%degree, this%nc, this%Wc, d2Tgc, dTgc, Tgc) else ! B-Spline call compute_d2Tgc(Xt, this%knot, this%degree, this%nc, d2Tgc, dTgc, Tgc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine basis_vector(this, res, Xt, Tgc) class(nurbs_curve), intent(inout) :: this integer, intent(in), optional :: res real(rk), intent(in), contiguous, optional :: Xt(:) real(rk), allocatable, intent(out) :: Tgc(:,:) integer :: i ! Set parameter values if (present(Xt)) then if (allocated(this%Xt)) deallocate(this%Xt) this%Xt = Xt elseif (present(res)) then if (allocated(this%Xt)) deallocate(this%Xt) allocate(this%Xt(res)) this%Xt = [(real(i-1, rk) / real(res-1, rk), i=1, res)] ! else ! this%Xt = this%Xt end if ! Set number of geometry points this%ng = size(this%Xt,1) if (this%is_rational()) then ! NURBS Tgc = compute_Tgc(this%Xt, this%knot, this%degree, this%nc, this%ng, this%Wc) else ! B-Spline Tgc = compute_Tgc(this%Xt, this%knot, this%degree, this%nc, this%ng) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine basis_scalar(this, Xt, Tgc) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: Xt real(rk), allocatable, intent(out) :: Tgc(:) if (this%is_rational()) then ! NURBS Tgc = compute_Tgc(Xt, this%knot, this%degree, this%nc, this%Wc) else ! B-Spline Tgc = compute_Tgc(Xt, this%knot, this%degree, this%nc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function is_rational(this) result(r) class(nurbs_curve), intent(in) :: this logical :: r r = .false. if (allocated(this%Wc)) then if (any(this%Wc /= this%Wc(1))) then r = .true. end if end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_elem_Xc_vis(this, elemConn) class(nurbs_curve), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn_Xc_vis)) deallocate(this%elemConn_Xc_vis) this%elemConn_Xc_vis = elemConn end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_elem_Xg_vis(this, elemConn) class(nurbs_curve), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn_Xg_vis)) deallocate(this%elemConn_Xg_vis) this%elemConn_Xg_vis = elemConn end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_elem(this, elemConn) class(nurbs_curve), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn)) deallocate(this%elemConn) this%elemConn = elemConn end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_elem_Xc_vis(this) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) elemConn = this%elemConn_Xc_vis end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_elem_Xg_vis(this) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) elemConn = this%elemConn_Xg_vis end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_elem(this) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) elemConn = this%elemConn end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine remove_knots(this,Xth,r) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: Xth(:) integer, intent(in), contiguous :: r(:) integer :: k, i, s, dim, j, nc_new, t real(rk), allocatable :: Xcw(:,:), Xcw_new(:,:), Xc_new(:,:), Wc_new(:), knot_new(:) if (this%is_rational()) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc-1,this%degree,Xth(i),this%knot) if (this%knot(k+1) == Xth(i)) then s = compute_multiplicity(this%knot,Xth(i)) else s = 0 end if k = k + 1 dim = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),dim+1)) do j = 1, size(this%Xc,1) Xcw(j,1:dim) = this%Xc(j,1:dim)*this%Wc(j) end do Xcw(:,dim+1) = this%Wc(:) call remove_knots_A_5_8(& this%degree,& this%knot,& Xcw,& Xth(i),& k,& s,& r(i),& t,& knot_new,& Xcw_new) if (allocated(Xcw)) deallocate(Xcw) if (t == 0) then ! no change else nc_new = size(Xcw_new,1) allocate(Xc_new(nc_new,dim)) allocate(Wc_new(nc_new)) do j = 1, nc_new Xc_new(j,:) = Xcw_new(j,1:dim)/Xcw_new(j,dim+1) end do Wc_new(:) = Xcw_new(:,dim+1) call this%set(knot=knot_new, Xc=Xc_new, Wc=Wc_new) if (allocated(Xcw_new)) deallocate(Xcw_new) if (allocated(Xc_new)) deallocate(Xc_new) if (allocated(Wc_new)) deallocate(Wc_new) end if end do else ! B-Spline do i = 1, size(Xth) k = findspan(this%nc-1,this%degree,Xth(i),this%knot) if (this%knot(k+1) == Xth(i)) then s = compute_multiplicity(this%knot,Xth(i)) else s = 0 end if k = k + 1 call remove_knots_A_5_8(& this%degree,& this%knot,& this%Xc,& Xth(i),& k,& s,& r(i),& t,& knot_new,& Xc_new) if (t == 0) then ! no change else call this%set(knot=knot_new, Xc=Xc_new) end if end do end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_circle(this, center, radius) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius real(rk), allocatable :: Xc(:,:), Wc(:), knot(:) integer :: i ! Define control points for circle allocate(Xc(7, 3)) Xc(1,:)= [ 1.0_rk, 0.0_rk, 0.0_rk] Xc(2,:)= [ 1.0_rk, sqrt(3.0_rk), 0.0_rk] Xc(3,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(4,:)= [-2.0_rk, 0.0_rk, 0.0_rk] Xc(5,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(6,:)= [ 1.0_rk, -sqrt(3.0_rk), 0.0_rk] Xc(7,:)= [ 1.0_rk, 0.0_rk, 0.0_rk] ! Scale and translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) * radius end do ! Define weights for the control points Wc = [1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk] ! Define knot vector knot = [0.0_rk, 0.0_rk, 0.0_rk, 1.0_rk/3.0_rk, 1.0_rk/3.0_rk, 2.0_rk/3.0_rk, 2.0_rk/3.0_rk, 1.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot, Xc, Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_C(this, center, radius) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius real(rk), allocatable :: Xc(:,:), Wc(:), knot(:) integer :: i ! Define control points for C-shape allocate(Xc(5, 3)) Xc(1,:)= [ 1.0_rk, 0.0_rk, 0.0_rk] Xc(2,:)= [ 1.0_rk, sqrt(3.0_rk), 0.0_rk] Xc(3,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(4,:)= [-2.0_rk, 0.0_rk, 0.0_rk] Xc(5,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, 0.0_rk] ! Scale and translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) * radius end do ! Define weights for the control points Wc = [1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk] ! Define knot vector knot = [0.0_rk, 0.0_rk, 0.0_rk, 1.0_rk/2.0_rk, 1.0_rk/2.0_rk, 1.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot, Xc, Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elem(this) result(elemConn) class(nurbs_curve), intent(in) :: this integer, allocatable :: elemConn(:,:) call elemConn_Cn(this%nc, this%degree, unique(this%knot), this%get_multiplicity(),& elemConn) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine rotate_Xc(this, alpha, beta, theta) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: alpha, beta, theta integer :: i do i = 1, this%nc this%Xc(i, :) = matmul(rotation(alpha,beta,theta), this%Xc(i, :)) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine rotate_Xg(this, alpha, beta, theta) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: alpha, beta, theta integer :: i do i = 1, this%ng this%Xg(i, :) = matmul(rotation(alpha,beta,theta), this%Xg(i, :)) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine translate_Xc(this, vec) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: vec(:) integer :: i do i = 1, this%nc this%Xc(i, :) = this%Xc(i, :) + vec end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine translate_Xg(this, vec) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: vec(:) integer :: i do i = 1, this%nc this%Xg(i, :) = this%Xg(i, :) + vec end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine show(this, vtkfile_Xc, vtkfile_Xg) class(nurbs_curve), intent(inout) :: this character(len=*), intent(in) :: vtkfile_Xc, vtkfile_Xg character(len=3000) :: pyvista_script pyvista_script = & "import pyvista as pv"//achar(10)//& "pv.global_theme.color = 'white'"//achar(10)//& "Xc = pv.read('"//trim(vtkfile_Xc)//"')"//achar(10)//& "Xg = pv.read('"//trim(vtkfile_Xg)//"')"//achar(10)//& "p = pv.Plotter(lighting='light kit')"//achar(10)//& "actor_Xcp = p.add_mesh("//achar(10)//& " Xc,"//achar(10)//& " style='points',"//achar(10)//& " point_size=10,"//achar(10)//& " color='red',"//achar(10)//& " render_points_as_spheres=True,"//achar(10)//& " opacity=0.5,"//achar(10)//& ")"//achar(10)//& "actor_Xcw = p.add_mesh("//achar(10)//& " Xc,"//achar(10)//& " show_edges=True,"//achar(10)//& " color='yellow',"//achar(10)//& " line_width=3,"//achar(10)//& " style='wireframe',"//achar(10)//& " opacity=0.2"//achar(10)//& ")"//achar(10)//& "actor_Xg = p.add_mesh("//achar(10)//& " Xg,"//achar(10)//& " show_edges=False,"//achar(10)//& " color='cyan',"//achar(10)//& " line_width=7,"//achar(10)//& " metallic=0.6,"//achar(10)//& " pbr=True,"//achar(10)//& " split_sharp_edges=True,"//achar(10)//& ")"//achar(10)//& "p.add_axes(interactive=False)"//achar(10)//& "def point_picker_callback(point):"//achar(10)//& " mesh = Xc"//achar(10)//& " point_id = mesh.find_closest_point(point)"//achar(10)//& " point_coords = mesh.points[point_id]"//achar(10)//& " label = f'ID: {point_id + 1}\n({point_coords[0]:.3f}, {point_coords[1]:.3f}, {point_coords[2]:.3f})'"//achar(10)//& " p.add_point_labels("//achar(10)//& " [point_coords],"//achar(10)//& " [label],"//achar(10)//& " font_size=14,"//achar(10)//& " text_color='black',"//achar(10)//& " show_points=False,"//achar(10)//& " fill_shape=False,"//achar(10)//& " shape=None,"//achar(10)//& " )"//achar(10)//& "picker = p.enable_point_picking(callback=point_picker_callback, show_message=False)"//achar(10)//& "window_size = p.window_size"//achar(10)//& "y_pos = window_size[1]"//achar(10)//& "def Xcp_toggle_vis(flag):"//achar(10)//& " actor_Xcp.SetVisibility(flag)"//achar(10)//& "def Xcw_toggle_vis(flag):"//achar(10)//& " actor_Xcw.SetVisibility(flag)"//achar(10)//& "def Xg_toggle_vis(flag):"//achar(10)//& " actor_Xg.SetVisibility(flag)"//achar(10)//& "p.add_checkbox_button_widget("//achar(10)//& " Xcp_toggle_vis,"//achar(10)//& " value=True,"//achar(10)//& " color_on='red',"//achar(10)//& " size=25,"//achar(10)//& " position=(0, y_pos - 1 * 25),"//achar(10)//& ")"//achar(10)//& "p.add_checkbox_button_widget("//achar(10)//& " Xcw_toggle_vis,"//achar(10)//& " value=True,"//achar(10)//& " color_on='yellow',"//achar(10)//& " size=25,"//achar(10)//& " position=(0, y_pos - 2 * 25),"//achar(10)//& ")"//achar(10)//& "p.add_checkbox_button_widget("//achar(10)//& " Xg_toggle_vis,"//achar(10)//& " value=True,"//achar(10)//& " color_on='cyan',"//achar(10)//& " size=25,"//achar(10)//& " position=(0, y_pos - 3 * 25),"//achar(10)//& ")"//achar(10)//& "p.add_text("//achar(10)//& " 'Xc (Points)',"//achar(10)//& " position=(25 + 3, y_pos - 1 * 25),"//achar(10)//& " font_size=8,"//achar(10)//& " color='black',"//achar(10)//& " font='times',"//achar(10)//& ")"//achar(10)//& "p.add_text("//achar(10)//& " 'Xc (Control geometry)',"//achar(10)//& " position=(25 + 3, y_pos - 2 * 25),"//achar(10)//& " font_size=8,"//achar(10)//& " color='black',"//achar(10)//& " font='times',"//achar(10)//& ")"//achar(10)//& "p.add_text("//achar(10)//& " 'Xg (Geometry)',"//achar(10)//& " position=(25 + 3, y_pos - 3 * 25),"//achar(10)//& " font_size=8,"//achar(10)//& " color='black',"//achar(10)//& " font='times',"//achar(10)//& ")"//achar(10)//& "p.add_text('ForCAD', position=(0.0, 10.0), font_size=14, color='black', font='times')"//achar(10)//& "p.add_text("//achar(10)//& " 'https://github.com/gha3mi/forcad',"//achar(10)//& " position=(0.0, 0.0),"//achar(10)//& " font_size=7,"//achar(10)//& " color='blue',"//achar(10)//& " font='times',"//achar(10)//& ")"//achar(10)//& "p.show(title='ForCAD', interactive=True)" call execute_command_line('python -c "'//trim(adjustl(pyvista_script))//'"') end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_half_circle(this, center, radius) class(nurbs_curve), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius real(rk), allocatable :: Xc(:,:), Wc(:), knot(:) integer :: i ! Define control points for half circle allocate(Xc(5, 3)) Xc(1,:) = [ 0.5_rk, 0.0_rk, 0.0_rk] Xc(2,:) = [ 0.5_rk, 0.5_rk, 0.0_rk] Xc(3,:) = [ 0.0_rk, 0.5_rk, 0.0_rk] Xc(4,:) = [-0.5_rk, 0.5_rk, 0.0_rk] Xc(5,:) = [-0.5_rk, 0.0_rk, 0.0_rk] ! Scale and translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) * radius end do ! Define weights for the control points Wc = [1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk] ! Define knot vector knot = [0.0_rk, 0.0_rk, 0.0_rk, 1.0_rk/2.0_rk, & 1.0_rk/2.0_rk, 1.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot, Xc, Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine nearest_point(this, point_Xg, nearest_Xg, nearest_Xt, id) class(nurbs_curve), intent(in) :: this real(rk), intent(in) :: point_Xg(:) real(rk), intent(out), allocatable, optional :: nearest_Xg(:) real(rk), intent(out), optional :: nearest_Xt integer, intent(out), optional :: id integer :: id_ real(rk), allocatable :: distances(:) allocate(distances(this%ng)) distances = nearest_point_help_1d(this%ng, this%Xg, point_Xg) id_ = minloc(distances, dim=1) if (present(id)) id = id_ if (present(nearest_Xg)) nearest_Xg = this%Xg(id_,:) if (present(nearest_Xt)) nearest_Xt = this%Xt(id_) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine nearest_point2(this, point_Xg, tol, maxit, nearest_Xt, nearest_Xg) class(nurbs_curve), intent(inout) :: this real(rk), intent(in) :: point_Xg(:) real(rk), intent(in) :: tol integer, intent(in) :: maxit real(rk), intent(out) :: nearest_Xt real(rk), allocatable, intent(out), optional :: nearest_Xg(:) real(rk):: xk, xkn, obj, grad, hess, dk, alphak, tau, beta, lower_bounds, upper_bounds real(rk), allocatable :: Xg(:), Tgc(:), dTgc(:), d2Tgc(:) integer :: k, l logical :: convergenz type(nurbs_curve) :: copy_this k = 0 ! lower and upper bounds lower_bounds = minval(this%knot) upper_bounds = maxval(this%knot) ! guess initial point copy_this = this call copy_this%create(10) call copy_this%nearest_point(point_Xg=point_Xg, nearest_Xt=xk) call copy_this%finalize() ! Check if xk is within the knot vector range if (xk < minval(this%knot)) then xk = minval(this%knot) else if (xk > maxval(this%knot)) then xk = maxval(this%knot) end if xkn = xk convergenz = .false. allocate(Xg(size(this%Xc,2))) ! allocate(dTgc(size(this%Xc,1))) ! allocate(d2Tgc(size(this%Xc,1))) do while (.not. convergenz .and. k < maxit) ! objection, gradient and hessian Xg = this%cmp_Xg(xk) call this%derivative2(Xt=xk, d2Tgc=d2Tgc, dTgc=dTgc, Tgc=Tgc) ! Tgc is not needed obj = norm2(Xg - point_Xg) + 0.001_rk ! add a small number to avoid division by zero grad = dot_product((Xg-point_Xg)/obj, matmul(dTgc,this%Xc)) hess = dot_product(matmul(dTgc,this%Xc) - (Xg-point_Xg)/obj*grad, matmul(dTgc,this%Xc))/obj& + dot_product((Xg-point_Xg)/obj, matmul(d2Tgc,this%Xc)) ! debug print '(i3,1x,e20.10,1x,e20.10)', k, xk, abs(grad) if (abs(grad) <= tol .or. (k>0 .and. abs(xk-xkn) <= tol)) then convergenz = .true. nearest_Xt = xk if (present(nearest_Xg)) nearest_Xg = this%cmp_Xg(nearest_Xt) else dk = - grad / hess ! Backtracking-Armijo Line Search alphak = 1.0_rk tau = 0.5_rk ! 0 < tau < 1 beta = 1.0e-4_rk ! 0 < beta < 1 l = 0 do while (.not. norm2(this%cmp_Xg(xk + alphak*dk) - point_Xg) <= obj + alphak*beta*grad*dk .and. l<50) alphak = tau * alphak l = l + 1 end do xkn = xk xk = xk + alphak*dk ! Check if xk is within the knot vector range xk = max(min(xk, upper_bounds), lower_bounds) k = k + 1 end if end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine ansatz(this, ie, ig, Tgc, dTgc_dXg, dL) class(nurbs_curve), intent(inout) :: this integer, intent(in) :: ie, ig real(rk), intent(out) :: dL real(rk), allocatable, intent(out) :: Tgc(:), dTgc_dXg(:,:) real(rk), allocatable :: Xth(:), Xth_e(:), Xc_eT(:,:), Xksi(:), Wksi(:) integer, allocatable :: elem_th(:,:), elem_c(:,:), elem_ce(:) type(nurbs_curve) :: th, th_e real(rk), allocatable :: dTtth_dXksi(:), Ttth(:), dTgc_dXt(:), dXg_dXt(:) real(rk) :: Xt, dXt_dXksi real(rk), allocatable :: dXg_dXksi(:) !! Jacobian matrix real(rk) :: det_dXg_dXksi !! Determinant of the Jacobian matrix call gauss_leg([0.0_rk, 1.0_rk], this%degree, Xksi, Wksi) Xth = unique(this%knot) call th%set([0.0_rk,Xth,1.0_rk], Xth) elem_th = th%cmp_elem() elem_c = this%cmp_elem() Xth_e = Xth(elem_th(ie,:)) call th_e%set([0.0_rk,0.0_rk,1.0_rk,1.0_rk], Xth_e) elem_ce = elem_c(ie,:) Xc_eT = transpose(this%Xc(elem_ce,:)) call th_e%derivative(Xksi(ig), dTtth_dXksi, Ttth) Xt = dot_product(Xth_e, Ttth) dXt_dXksi = dot_product(Xth_e, dTtth_dXksi) call this%derivative(Xt, dTgc_dXt, Tgc, elem_ce) dXg_dXt = matmul(Xc_eT, dTgc_dXt) dTgc_dXg = dyad(dTgc_dXt, dXg_dXt)/norm2(dXg_dXt) dXg_dXksi = dXg_dXt*dXt_dXksi det_dXg_dXksi = norm2(dXg_dXksi) dL = det_dXg_dXksi*Wksi(ig) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_length(this, length) class(nurbs_curve), intent(inout) :: this real(rk), intent(out) :: length real(rk), allocatable :: Tgc(:), dTgc_dXg(:,:) integer :: ie, ig real(rk) :: dL, dL_ig length = 0.0_rk do ie = 1, size(this%cmp_elem(),1) dL = 0.0_rk do ig = 1, size(this%cmp_elem(),2) call this%ansatz(ie, ig, Tgc, dTgc_dXg, dL_ig) dL = dL + dL_ig end do length = length + dL end do end subroutine !=============================================================================== end module forcad_nurbs_curve !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Xg_nurbs_1d(Xt, knot, degree, nc, ng, Xc, Wc) result(Xg) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Xg(:,:) real(rk), allocatable :: Tgc(:) integer :: i allocate(Xg(ng, size(Xc,2))) allocate(Tgc(nc)) !$OMP PARALLEL DO PRIVATE(Tgc) do i = 1, ng Tgc = basis_bspline(Xt(i), knot, nc, degree) Tgc = Tgc*(Wc/(dot_product(Tgc,Wc))) Xg(i,:) = matmul(Tgc, Xc) end do !$OMP END PARALLEL DO end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Xg_nurbs_1d_1point(Xt, knot, degree, nc, Xc, Wc) result(Xg) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Xg(:) real(rk), allocatable :: Tgc(:) allocate(Xg(size(Xc))) allocate(Tgc(nc)) Tgc = basis_bspline(Xt, knot, nc, degree) Tgc = Tgc*(Wc/(dot_product(Tgc,Wc))) Xg = matmul(Tgc, Xc) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Xg_bspline_1d(Xt, knot, degree, nc, ng, Xc) result(Xg) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), intent(in), contiguous :: Xc(:,:) real(rk), allocatable :: Xg(:,:) integer :: i allocate(Xg(ng, size(Xc,2))) !$OMP PARALLEL DO do i = 1, ng Xg(i,:) = matmul(basis_bspline(Xt(i), knot, nc, degree), Xc) end do !$OMP END PARALLEL DO end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Xg_bspline_1d_1point(Xt, knot, degree, nc, Xc) result(Xg) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Xc(:,:) real(rk), allocatable :: Xg(:) allocate(Xg(size(Xc))) Xg = matmul(basis_bspline(Xt, knot, nc, degree), Xc) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_dTgc_nurbs_1d_vector(Xt, knot, degree, nc, ng, Wc, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_der implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk), allocatable :: dBi(:), Bi(:) integer :: i allocate(dTgc(ng, nc), Tgc(ng, nc), dBi(nc), Bi(nc)) do i = 1, size(Xt) call basis_bspline_der(Xt(i), knot, nc, degree, dBi, Bi) Tgc(i,:) = Bi*(Wc/(dot_product(Bi,Wc))) dTgc(i,:) = ( dBi*Wc - Tgc(i,:)*dot_product(dBi,Wc) ) / dot_product(Bi,Wc) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_dTgc_nurbs_1d_scalar(Xt, knot, degree, nc, Wc, dTgc, Tgc, elem) use forcad_utils, only: rk, basis_bspline_der implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Wc(:) integer, intent(in), optional :: elem(:) real(rk), allocatable, intent(out) :: dTgc(:) real(rk), allocatable, intent(out) :: Tgc(:) real(rk), allocatable :: dBi(:), Bi(:) call basis_bspline_der(Xt, knot, nc, degree, dBi, Bi) if (.not. present(elem)) then allocate(dTgc(nc), Tgc(nc)) Tgc = Bi*(Wc/(dot_product(Bi,Wc))) dTgc = ( dBi*Wc - Tgc*dot_product(dBi,Wc) ) / dot_product(Bi,Wc) else allocate(dTgc(size(elem)), Tgc(size(elem))) Tgc = Bi(elem)*(Wc(elem)/(dot_product(Bi(elem),Wc(elem)))) dTgc = ( dBi(elem)*Wc(elem) - Tgc*dot_product(dBi(elem),Wc(elem)) ) / dot_product(Bi(elem),Wc(elem)) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_dTgc_bspline_1d_vector(Xt, knot, degree, nc, ng, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_der implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk), allocatable :: dBi(:), Bi(:) integer :: i allocate(dTgc(ng, nc), Tgc(ng, nc), dBi(nc), Bi(nc)) do i = 1, size(Xt) call basis_bspline_der(Xt(i), knot, nc, degree, dBi, Bi) Tgc(i,:) = Bi dTgc(i,:) = dBi end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_dTgc_bspline_1d_scalar(Xt, knot, degree, nc, dTgc, Tgc, elem) use forcad_utils, only: rk, basis_bspline_der implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in), optional :: elem(:) real(rk), allocatable, intent(out) :: dTgc(:) real(rk), allocatable, intent(out) :: Tgc(:) real(rk), allocatable :: dB(:), B(:) if (.not. present(elem)) then allocate(dTgc(nc), Tgc(nc)) call basis_bspline_der(Xt, knot, nc, degree, dTgc, Tgc) else allocate(dB(size(elem)), B(size(elem))) call basis_bspline_der(Xt, knot, nc, degree, dB, B) Tgc = B(elem) dTgc = dB(elem) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_d2Tgc_nurbs_1d_vector(Xt, knot, degree, nc, ng, Wc, d2Tgc, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_2der implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable, intent(out) :: d2Tgc(:,:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk), allocatable :: d2Bi(:), dBi(:), Tgci(:), dTgci(:), Bi(:) integer :: i allocate(d2Tgc(ng, nc), dTgc(ng, nc), Tgc(ng, nc), d2Bi(nc), dTgci(nc), dBi(nc), Tgci(nc), Bi(nc)) do i = 1, size(Xt) call basis_bspline_2der(Xt(i), knot, nc, degree, d2Bi, dBi, Bi) Tgci = Bi*(Wc/(dot_product(Bi,Wc))) Tgc(i,:) = Tgci dTgci = ( dBi*Wc - Tgci*dot_product(dBi,Wc) ) / dot_product(Bi,Wc) dTgc(i,:) = dTgci d2Tgc(i,:) = (d2Bi*Wc - 2.0_rk*dTgci*dot_product(dBi,Wc) - Tgci*dot_product(d2Bi,Wc)) / dot_product(Bi,Wc) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_d2Tgc_nurbs_1d_scalar(Xt, knot, degree, nc, Wc, d2Tgc, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_2der implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable, intent(out) :: d2Tgc(:) real(rk), allocatable, intent(out) :: dTgc(:) real(rk), allocatable, intent(out) :: Tgc(:) real(rk), allocatable :: d2Bi(:), dBi(:), Bi(:) allocate(d2Tgc(nc), dTgc(nc), Tgc(nc), d2Bi(nc), dBi(nc), Bi(nc)) call basis_bspline_2der(Xt, knot, nc, degree, d2Bi, dBi, Bi) Tgc = Bi*(Wc/(dot_product(Bi,Wc))) dTgc = ( dBi*Wc - Tgc*dot_product(dBi,Wc) ) / dot_product(Bi,Wc) d2Tgc = (d2Bi*Wc - 2.0_rk*dTgc*dot_product(dBi,Wc) - Tgc*dot_product(d2Bi,Wc)) / dot_product(Bi,Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_d2Tgc_bspline_1d_vector(Xt, knot, degree, nc, ng, d2Tgc, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_2der implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), allocatable, intent(out) :: d2Tgc(:,:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk), allocatable :: d2Tgci(:), dTgci(:), Tgci(:) integer :: i allocate(d2Tgc(ng, nc), dTgc(ng, nc), Tgc(ng, nc), dTgci(nc), Tgci(nc), d2Tgci(nc)) do i = 1, size(Xt) call basis_bspline_2der(Xt(i), knot, nc, degree, d2Tgci, dTgci, Tgci) Tgc(i,:) = Tgci dTgc(i,:) = dTgci d2Tgc(i,:) = d2Tgci end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine compute_d2Tgc_bspline_1d_scalar(Xt, knot, degree, nc, d2Tgc, dTgc, Tgc) use forcad_utils, only: rk, basis_bspline_2der implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), allocatable, intent(out) :: d2Tgc(:) real(rk), allocatable, intent(out) :: dTgc(:) real(rk), allocatable, intent(out) :: Tgc(:) allocate(d2Tgc(nc), dTgc(nc), Tgc(nc)) call basis_bspline_2der(Xt, knot, nc, degree, d2Tgc, dTgc, Tgc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Tgc_nurbs_1d_vector(Xt, knot, degree, nc, ng, Wc) result(Tgc) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Tgc(:,:) real(rk), allocatable :: Tgci(:) integer :: i allocate(Tgc(ng, nc), Tgci(nc)) !$OMP PARALLEL DO PRIVATE(Tgci) do i = 1, size(Xt,1) Tgci = basis_bspline(Xt(i), knot, nc, degree) Tgc(i,:) = Tgci*(Wc/(dot_product(Tgci,Wc))) end do !$OMP END PARALLEL DO end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Tgc_nurbs_1d_scalar(Xt, knot, degree, nc, Wc) result(Tgc) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Tgc(:) allocate(Tgc(nc)) Tgc = basis_bspline(Xt, knot, nc, degree) Tgc = Tgc*(Wc/(dot_product(Tgc,Wc))) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Tgc_bspline_1d_vector(Xt, knot, degree, nc, ng) result(Tgc) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc integer, intent(in) :: ng real(rk), allocatable :: Tgc(:,:) integer :: i allocate(Tgc(ng, nc)) !$OMP PARALLEL DO do i = 1, size(Xt,1) Tgc(i,:) = basis_bspline(Xt(i), knot, nc, degree) end do !$OMP END PARALLEL DO end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function compute_Tgc_bspline_1d_scalar(Xt, knot, degree, nc) result(Tgc) use forcad_utils, only: rk, basis_bspline implicit none real(rk), intent(in) :: Xt real(rk), intent(in), contiguous :: knot(:) integer, intent(in) :: degree integer, intent(in) :: nc real(rk), allocatable :: Tgc(:) allocate(Tgc(nc)) Tgc = basis_bspline(Xt, knot, nc, degree) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure function nearest_point_help_1d(ng, Xg, point_Xg) result(distances) use forcad_utils, only: rk implicit none integer, intent(in) :: ng real(rk), intent(in), contiguous :: Xg(:,:) real(rk), intent(in), contiguous :: point_Xg(:) real(rk), allocatable :: distances(:) integer :: i allocate(distances(ng)) !$OMP PARALLEL DO do i = 1, ng distances(i) = norm2(Xg(i,:) - point_Xg) end do !$OMP END PARALLEL DO end function !===============================================================================