!> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> This module defines the 'nurbs_volume' type for representing a Non-Uniform Rational B-Spline (NURBS) volume. module forcad_nurbs_volume use forcad_kinds, only: rk use forcad_utils, only: basis_bspline, elemConn_C0, kron, ndgrid, compute_multiplicity, compute_knot_vector, & basis_bspline_der, insert_knot_A_5_1, findspan, elevate_degree_A_5_9, hexahedron_Xc, remove_knots_A_5_8, & elemConn_Cn, unique, rotation, det, inv, gauss_leg, export_vtk_legacy, basis_bspline_2der implicit none private public nurbs_volume !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause type nurbs_volume real(rk), allocatable, private :: Xc(:,:) !! Control points (2D array: [nc(1)*nc(2)*nc(3), dim]) real(rk), allocatable, private :: Xg(:,:) !! Geometry points (2D array: [ng(1)*ng(2)*ng(3), dim]) real(rk), allocatable, private :: Wc(:) !! Weights for the control points (1D array: [nc(1)*nc(2)*nc(3)]) real(rk), allocatable, private :: Xt1(:) !! Evaluation parameter values in the first direction (1D array: [ng(1)]) real(rk), allocatable, private :: Xt2(:) !! Evaluation parameter values in the second direction (1D array: [ng(2)]) real(rk), allocatable, private :: Xt3(:) !! Evaluation parameter values in the third direction (1D array: [ng(3)]) real(rk), allocatable, private :: Xt(:,:) !! Evaluation parameter values (2D array: [ng(1)*ng(2)*ng(3), dim] real(rk), allocatable, private :: knot1(:) !! Knot vector in the first direction (1D array) real(rk), allocatable, private :: knot2(:) !! Knot vector in the second direction (1D array) real(rk), allocatable, private :: knot3(:) !! Knot vector in the third direction (1D array) integer, private :: degree(3) !! Degree (order) of the volume integer, private :: nc(3) !! Number of control points in each direction integer, private :: ng(3) !! Number of geometry points in each direction 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 vectors, control points and weights for the NURBS volume object procedure :: set2 !!> Set NURBS volume using nodes of parameter space, degree, continuity, control points and weights procedure :: set3 !!> Set Bezier or Rational Bezier volume using control points and weights procedure :: set4 !!> Set NURBS volume using degree, number of control points, control points and weights generic :: set => set1, set2, set3, set4 !!> Set NURBS volume 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, private :: get_nc_dir !!> Get number of control points in a specific direction procedure, private :: get_nc_all !!> Get number of control points in all directions generic :: get_nc => get_nc_all, get_nc_dir !!> Get number of control points procedure :: cmp_degree !!> Compute degree of the NURBS volume procedure, private :: get_degree_all!!> Get degree of the NURBS volume in all directions procedure, private :: get_degree_dir!!> Get degree of the NURBS volume in a specific direction generic :: get_degree => get_degree_all, get_degree_dir !!> Get degree of the NURBS volume procedure :: finalize !!> Finalize the NURBS volume 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 :: export_Xth !!> Export parameter space 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 NURBS volume procedure :: cmp_nc !!> Compute number of required control points procedure, private :: basis_vector !!> Compute the basis functions of the NURBS volume procedure, private :: basis_scalar !!> Compute the basis functions of the NURBS volume generic :: basis => basis_vector, basis_scalar !!> Compute the basis functions of the NURBS volume procedure, private :: derivative_vector !!> Compute the derivative of the NURBS volume procedure, private :: derivative_scalar !!> Compute the derivative of the NURBS volume generic :: derivative => derivative_vector, derivative_scalar !!> Compute the derivative of the NURBS volume procedure, private :: derivative2_vector !!> Compute the second derivative of the NURBS volume procedure, private :: derivative2_scalar !!> Compute the second derivative of the NURBS volume generic :: derivative2 => derivative2_vector, derivative2_scalar !!> Compute the second derivative of the NURBS volume procedure :: insert_knots !!> Insert knots into the knot vector procedure :: elevate_degree !!> Elevate the degree of the NURBS volume procedure :: is_rational !!> Check if the NURBS volume is rational procedure :: put_to_nurbs !!> Put a shape to a NURBS volume 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 volume (Approximation) procedure :: nearest_point2 !!> Find the nearest point on the NURBS volume (Minimization - Newtons method) procedure :: ansatz !!> Compute the shape functions, derivative of shape functions and dV procedure :: cmp_volume !!> Compute the volume of the NURBS volume procedure :: lsq_fit_bspline !!> Fit B-spline volume to structured data points using least squares ! Faces procedure :: cmp_elemFace_Xc_vis !!> Compute faces of the control points procedure :: cmp_elemFace_Xg_vis !!> Compute faces of the geometry points procedure :: cmp_elemFace !!> Compute faces of the IGA elements procedure :: cmp_degreeFace !!> Compute degrees of the faces ! Shapes procedure :: set_hexahedron !!> Set a hexahedron procedure :: set_ring !!> Set a ring procedure :: set_half_ring !!> Set a half ring procedure :: set_C !!> Set a C-shape end type !=============================================================================== interface compute_Xg module procedure compute_Xg_nurbs_3d module procedure compute_Xg_bspline_3d module procedure compute_Xg_nurbs_3d_1point module procedure compute_Xg_bspline_3d_1point end interface interface compute_Tgc module procedure compute_Tgc_nurbs_3d_vector module procedure compute_Tgc_bspline_3d_vector module procedure compute_Tgc_nurbs_3d_scalar module procedure compute_Tgc_bspline_3d_scalar end interface interface compute_dTgc module procedure compute_dTgc_nurbs_3d_vector module procedure compute_dTgc_bspline_3d_vector module procedure compute_dTgc_nurbs_3d_scalar module procedure compute_dTgc_bspline_3d_scalar end interface interface compute_d2Tgc module procedure compute_d2Tgc_nurbs_3d_vector module procedure compute_d2Tgc_bspline_3d_vector module procedure compute_d2Tgc_nurbs_3d_scalar module procedure compute_d2Tgc_bspline_3d_scalar end interface contains !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set control points and weights for the NURBS volume object. pure subroutine set1(this, knot1, knot2, knot3, Xc, Wc) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%knot1)) then if (size(this%knot1) /= size(knot1)) deallocate(this%knot1) end if if (allocated(this%knot2)) then if (size(this%knot2) /= size(knot2)) deallocate(this%knot2) end if if (allocated(this%knot3)) then if (size(this%knot3) /= size(knot3)) deallocate(this%knot3) end if if (allocated(this%Xc)) then if (size(this%Xc,1) /= size(Xc,1) .or. size(this%Xc,2) /= size(Xc,2)) deallocate(this%Xc) end if this%knot1 = knot1 this%knot2 = knot2 this%knot3 = knot3 call this%cmp_degree() call this%cmp_nc() this%Xc = Xc if (present(Wc)) then if (size(Wc) /= this%nc(1)*this%nc(2)*this%nc(3)) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) then if (size(this%Wc) /= size(Wc)) deallocate(this%Wc) end if this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set control points and weights for the NURBS volume object. pure subroutine set2(this, Xth_dir1, Xth_dir2, Xth_dir3, degree, continuity1, continuity2, continuity3, Xc, Wc) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: Xth_dir1(:), Xth_dir2(:), Xth_dir3(:) integer, intent(in), contiguous :: degree(:) integer, intent(in), contiguous :: continuity1(:), continuity2(:), continuity3(:) real(rk), intent(in), contiguous, optional :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) this%knot1 = compute_knot_vector(Xth_dir1, degree(1), continuity1) this%knot2 = compute_knot_vector(Xth_dir2, degree(2), continuity2) this%knot3 = compute_knot_vector(Xth_dir3, degree(3), continuity3) this%degree(1) = degree(1) this%degree(2) = degree(2) this%degree(3) = degree(3) call this%cmp_nc() if (present(Xc)) this%Xc = Xc if (present(Wc)) this%Wc = Wc end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause !> Set Bezier or Rational Bezier volume using control points and weights. pure subroutine set3(this, nc, Xc, Wc) class(nurbs_volume), intent(inout) :: this integer, intent(in), contiguous :: nc(:) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) if (allocated(this%Xc)) then if (size(this%Xc,1) /= nc(1)*nc(2)*nc(3) .or. size(this%Xc,2) /= size(Xc,2)) deallocate(this%Xc) end if this%Xc = Xc this%nc = nc if (allocated(this%knot1)) then if (size(this%knot1) /= 2*nc(1)) then deallocate(this%knot1) allocate(this%knot1(2*this%nc(1))) end if else allocate(this%knot1(2*this%nc(1))) end if this%knot1(1:this%nc(1)) = 0.0_rk this%knot1(this%nc(1)+1:2*this%nc(1)) = 1.0_rk if (allocated(this%knot2)) then if (size(this%knot2) /= 2*nc(2)) then deallocate(this%knot2) allocate(this%knot2(2*this%nc(2))) end if else allocate(this%knot2(2*this%nc(2))) end if this%knot2(1:this%nc(2)) = 0.0_rk this%knot2(this%nc(2)+1:2*this%nc(2)) = 1.0_rk if (allocated(this%knot3)) then if (size(this%knot3) /= 2*nc(3)) then deallocate(this%knot3) allocate(this%knot3(2*this%nc(3))) end if else allocate(this%knot3(2*this%nc(3))) end if this%knot3(1:this%nc(3)) = 0.0_rk this%knot3(this%nc(3)+1:2*this%nc(3)) = 1.0_rk call this%cmp_degree() if (present(Wc)) then if (size(Wc) /= this%nc(1)*this%nc(2)*this%nc(3)) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) then if (size(this%Wc) /= size(Wc)) deallocate(this%Wc) end if 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_volume), intent(inout) :: this integer, intent(in), contiguous :: degree(:) integer, intent(in), contiguous :: nc(:) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous, optional :: Wc(:) integer :: m(3), i if (allocated(this%Xc)) then if (size(this%Xc,1) /= nc(1)*nc(2)*nc(3) .or. size(this%Xc,2) /= size(Xc,2)) deallocate(this%Xc) end if this%Xc = Xc this%nc = nc this%degree = degree ! Size of knot vectors m = nc + degree + 1 if (allocated(this%knot1)) then if (size(this%knot1) /= m(1)) then deallocate(this%knot1) allocate(this%knot1(m(1))) end if else allocate(this%knot1(m(1))) end if this%knot1(1:degree(1)+1) = 0.0_rk this%knot1(degree(1)+2:m(1)-degree(1)-1) = [(real(i, rk)/(m(1)-2*degree(1)-1), i=1, m(1)-2*degree(1)-2)] this%knot1(m(1)-degree(1):m(1)) = 1.0_rk if (allocated(this%knot2)) then if (size(this%knot2) /= m(2)) then deallocate(this%knot2) allocate(this%knot2(m(2))) end if else allocate(this%knot2(m(2))) end if this%knot2(1:degree(2)+1) = 0.0_rk this%knot2(degree(2)+2:m(2)-degree(2)-1) = [(real(i, rk)/(m(2)-2*degree(2)-1), i=1, m(2)-2*degree(2)-2)] this%knot2(m(2)-degree(2):m(2)) = 1.0_rk if (allocated(this%knot3)) then if (size(this%knot3) /= m(3)) then deallocate(this%knot3) allocate(this%knot3(m(3))) end if else allocate(this%knot3(m(3))) end if this%knot3(1:degree(3)+1) = 0.0_rk this%knot3(degree(3)+2:m(3)-degree(3)-1) = [(real(i, rk)/(m(3)-2*degree(3)-1), i=1, m(3)-2*degree(3)-2)] this%knot3(m(3)-degree(3):m(3)) = 1.0_rk if (present(Wc)) then if (size(Wc) /= nc(1)*nc(2)*nc(3)) then error stop 'Number of weights does not match the number of control points.' else if (allocated(this%Wc)) then if (size(this%Wc) /= size(Wc)) deallocate(this%Wc) end if this%Wc = Wc end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine create(this, res1, res2, res3, Xt1, Xt2, Xt3, Xt) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: res1, res2, res3 real(rk), intent(in), contiguous, optional :: Xt1(:), Xt2(:), Xt3(:) 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%knot1) .or. .not.allocated(this%knot2) .or. .not.allocated(this%knot3)) then error stop 'Knot vector(s) is/are not set.' end if ! Set parameter values if (present(Xt1)) then if (allocated(this%Xt1)) then if (size(this%Xt1) /= size(Xt1)) deallocate(this%Xt1) end if this%Xt1 = Xt1 elseif (present(res1)) then if (allocated(this%Xt1)) then if (size(this%Xt1) /= res1) then deallocate(this%Xt1) allocate(this%Xt1(res1)) end if else allocate(this%Xt1(res1)) end if this%Xt1 = [(this%knot1(1)+(this%knot1(size(this%knot1))-this%knot1(1))*real(i-1,rk)/real(res1-1,rk), i=1, res1)] ! else ! this%Xt1 = this%Xt1 end if ! Set parameter values if (present(Xt2)) then if (allocated(this%Xt2)) then if (size(this%Xt2) /= size(Xt2)) deallocate(this%Xt2) end if this%Xt2 = Xt2 elseif (present(res2)) then if (allocated(this%Xt2)) then if (size(this%Xt2) /= res2) then deallocate(this%Xt2) allocate(this%Xt2(res2)) end if else allocate(this%Xt2(res2)) end if this%Xt2 = [(this%knot2(1)+(this%knot2(size(this%knot2))-this%knot2(1))*real(i-1,rk)/real(res2-1,rk), i=1, res2)] ! else ! this%Xt2 = this%Xt2 end if ! Set parameter values if (present(Xt3)) then if (allocated(this%Xt3)) then if (size(this%Xt3) /= size(Xt3)) deallocate(this%Xt3) end if this%Xt3 = Xt3 elseif (present(res3)) then if (allocated(this%Xt3)) then if (size(this%Xt3) /= res3) then deallocate(this%Xt3) allocate(this%Xt3(res3)) end if else allocate(this%Xt3(res3)) end if this%Xt3 = [(this%knot3(1)+(this%knot3(size(this%knot3))-this%knot3(1))*real(i-1,rk)/real(res3-1,rk), i=1, res3)] ! else ! this%Xt3 = this%Xt3 end if if (present(Xt)) then this%Xt = Xt else ! Set number of geometry points this%ng(1) = size(this%Xt1,1) this%ng(2) = size(this%Xt2,1) this%ng(3) = size(this%Xt3,1) call ndgrid(this%Xt1, this%Xt2, this%Xt3, this%Xt) end if if (allocated(this%Xg)) then if (size(this%Xg,1) /= product(this%ng) .or. size(this%Xg,2) /= size(this%Xc,2)) then deallocate(this%Xg) allocate(this%Xg(product(this%ng), size(this%Xc,2))) end if else allocate(this%Xg(product(this%ng), size(this%Xc,2))) end if if (this%is_rational()) then ! NURBS this%Xg = compute_Xg(& this%Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%ng, this%Xc, this%Wc) else ! B-Spline this%Xg = compute_Xg(& this%Xt, this%knot1, this%knot2, this%knot3, 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_volume), intent(in) :: this real(rk), intent(in), contiguous :: 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%knot1) .or. .not.allocated(this%knot2) .or. .not.allocated(this%knot3)) then error stop 'Knot vector(s) is/are not set.' end if if (this%is_rational()) then ! NURBS Xg = compute_Xg(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%Xc, this%Wc) else ! B-Spline Xg = compute_Xg(Xt, this%knot1, this%knot2, this%knot3, 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_volume), 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_volume), 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_volume), 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 direction 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_volume), 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_volume), 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_volume), 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 direction 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_volume), intent(in) :: this real(rk), allocatable :: Wc(:) if (allocated(this%Wc)) then Wc = this%Wc else error stop 'The NURBS volume 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_volume), 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 volume 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, dir) result(Xt) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir real(rk), allocatable :: Xt(:) if (dir == 1) then if (allocated(this%Xt1)) then Xt = this%Xt1 else error stop 'Parameter values are not set.' end if elseif (dir == 2) then if (allocated(this%Xt2)) then Xt = this%Xt2 else error stop 'Parameter values are not set.' end if elseif (dir == 3) then if (allocated(this%Xt3)) then Xt = this%Xt3 else error stop 'Parameter values are not set.' end if else error stop 'Invalid direction for parameter values.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_ng(this) result(ng) class(nurbs_volume), intent(in) :: this integer :: ng(3) ng = this%ng end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_degree(this, dir) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: dir integer, allocatable :: m1(:), m2(:), m3(:) if (present(dir)) then if (dir == 1) then m1 = this%get_multiplicity(1) this%degree(1) = m1(1) - 1 else if (dir == 2) then m2 = this%get_multiplicity(2) this%degree(2) = m2(1) - 1 else if (dir == 3) then m3 = this%get_multiplicity(3) this%degree(3) = m3(1) - 1 else error stop 'Invalid direction for degree.' end if else m1 = this%get_multiplicity(1) this%degree(1) = m1(1) - 1 m2 = this%get_multiplicity(2) this%degree(2) = m2(1) - 1 m3 = this%get_multiplicity(3) this%degree(3) = m3(1) - 1 end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_degree_all(this) result(degree) class(nurbs_volume), intent(in) :: this integer :: degree(3) degree(1) = this%degree(1) degree(2) = this%degree(2) degree(3) = this%degree(3) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_degree_dir(this, dir) result(degree) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir integer :: degree if (dir == 1) then degree = this%degree(1) else if (dir == 2) then degree = this%degree(2) else if (dir == 3) then degree = this%degree(3) else error stop 'Invalid direction for degree.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_knot_all(this, dir) result(knot) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir real(rk), allocatable :: knot(:) if (dir == 1) then if (allocated(this%knot1)) then knot = this%knot1 else error stop 'Knot vector is not set.' end if elseif (dir == 2) then if (allocated(this%knot2)) then knot = this%knot2 else error stop 'Knot vector is not set.' end if elseif (dir == 3) then if (allocated(this%knot3)) then knot = this%knot3 else error stop 'Knot vector is not set.' end if else error stop 'Invalid direction for knot vector.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_knoti(this, dir, i) result(knot) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir integer, intent(in) :: i real(rk) :: knot if (dir == 1) then if (allocated(this%knot1)) then if (i < 1 .or. i > size(this%knot1)) then error stop 'Invalid index for knot vector.' else knot = this%knot1(i) end if else error stop 'Knot vector is not set.' end if elseif (dir == 2) then if (allocated(this%knot2)) then if (i < 1 .or. i > size(this%knot2)) then error stop 'Invalid index for knot vector.' else knot = this%knot2(i) end if else error stop 'Knot vector is not set.' end if elseif (dir == 3) then if (allocated(this%knot3)) then if (i < 1 .or. i > size(this%knot3)) then error stop 'Invalid index for knot vector.' else knot = this%knot3(i) end if else error stop 'Knot vector is not set.' end if else error stop 'Invalid direction for knot vector.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine finalize(this) class(nurbs_volume), 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%Xt1)) deallocate(this%Xt1) if (allocated(this%Xt2)) deallocate(this%Xt2) if (allocated(this%Xt3)) deallocate(this%Xt3) if (allocated(this%Xt)) deallocate(this%Xt) if (allocated(this%knot1)) deallocate(this%knot1) if (allocated(this%knot2)) deallocate(this%knot2) if (allocated(this%knot3)) deallocate(this%knot3) 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_volume), intent(in) :: this integer, allocatable :: elemConn(:,:) integer, intent(in), contiguous, optional :: p(:) if (present(p)) then elemConn = elemConn_C0(this%nc(1), this%nc(2), this%nc(3), p(1), p(2), p(3)) else elemConn = elemConn_C0(this%nc(1), this%nc(2), this%nc(3), 1, 1, 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_volume), intent(in) :: this integer, allocatable :: elemConn(:,:) integer, intent(in), contiguous, optional :: p(:) if (present(p)) then elemConn = elemConn_C0(this%ng(1), this%ng(2), this%ng(3), p(1), p(2), p(3)) else elemConn = elemConn_C0(this%ng(1), this%ng(2), this%ng(3), 1, 1, 1) end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine export_Xc(this, filename, point_data, field_names, encoding) class(nurbs_volume), intent(in) :: this character(len=*), intent(in) :: filename real(rk), intent(in), optional :: point_data(:,:) character(len=*), intent(in), optional :: field_names(:) character(len=*), intent(in), optional :: encoding 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 call export_vtk_legacy(filename=filename, points=this%Xc, elemConn=elemConn, vtkCellType=12, & point_data=point_data, field_names=field_names, encoding=encoding) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine export_Xg(this, filename, point_data, field_names, encoding) class(nurbs_volume), intent(in) :: this character(len=*), intent(in) :: filename real(rk), intent(in), optional :: point_data(:,:) character(len=*), intent(in), optional :: field_names(:) character(len=*), intent(in), optional :: encoding 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 call export_vtk_legacy(filename=filename, points=this%Xg, elemConn=elemConn, vtkCellType=12, & point_data=point_data, field_names=field_names, encoding=encoding) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause impure subroutine export_Xth(this, filename, point_data, field_names, encoding) class(nurbs_volume), intent(in) :: this character(len=*), intent(in) :: filename real(rk), intent(in), optional :: point_data(:,:) character(len=*), intent(in), optional :: field_names(:) character(len=*), intent(in), optional :: encoding integer, allocatable :: elemConn(:,:) real(rk), allocatable :: Xth(:,:), Xth1(:), Xth2(:), Xth3(:) type(nurbs_volume) :: th Xth1 = unique(this%knot1) Xth2 = unique(this%knot2) Xth3 = unique(this%knot3) call ndgrid(Xth1, Xth2, Xth3, Xth) call th%set(& [this%knot1(1),Xth1,this%knot1(size(this%knot1))],& [this%knot2(1),Xth2,this%knot2(size(this%knot2))],& [this%knot3(1),Xth3,this%knot3(size(this%knot3))], Xth) elemConn = th%cmp_elem() call export_vtk_legacy(filename=filename, points=Xth, elemConn=elemConn, vtkCellType=12, & point_data=point_data, field_names=field_names, encoding=encoding) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine modify_Xc(this,X,num,dir) class(nurbs_volume), 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(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=this%get_knot(3),& Xc=this%get_Xc(), Wc=this%get_Wc()) else call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=this%get_knot(3),& 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_volume), intent(inout) :: this real(rk), intent(in) :: W integer, intent(in) :: num if (allocated(this%Wc)) then this%Wc(num) = W if (allocated(this%knot1) .and. allocated(this%knot2) .and. allocated(this%knot3)) then call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=this%get_knot(3),& Xc=this%get_Xc(), Wc=this%get_Wc()) else call this%set(nc=this%nc, Xc=this%get_Xc(), Wc=this%get_Wc()) end if else error stop 'The NURBS volume is not rational.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_multiplicity(this, dir) result(m) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir integer, allocatable :: m(:) if (dir == 1) then ! check if (.not.allocated(this%knot1)) then error stop 'Knot vector is not set.' else m = compute_multiplicity(this%knot1) end if elseif (dir == 2) then ! check if (.not.allocated(this%knot2)) then error stop 'Knot vector is not set.' else m = compute_multiplicity(this%knot2) end if elseif (dir == 3) then ! check if (.not.allocated(this%knot3)) then error stop 'Knot vector is not set.' else m = compute_multiplicity(this%knot3) end if else error stop 'Invalid direction.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_continuity(this, dir) result(c) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir integer, allocatable :: c(:) if (dir == 1) then ! check if (.not.allocated(this%knot1)) then error stop 'Knot vector is not set.' else c = this%degree(1) - compute_multiplicity(this%knot1) end if elseif (dir == 2) then ! check if (.not.allocated(this%knot2)) then error stop 'Knot vector is not set.' else c = this%degree(2) - compute_multiplicity(this%knot2) end if elseif (dir == 3) then ! check if (.not.allocated(this%knot3)) then error stop 'Knot vector is not set.' else c = this%degree(3) - compute_multiplicity(this%knot3) end if else error stop 'Invalid direction.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_nc(this, dir) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: dir if (present(dir)) then if (dir == 1) then ! check if (.not.allocated(this%knot1)) then error stop 'Knot vector is not set.' else this%nc(1) = sum(compute_multiplicity(this%knot1)) - this%degree(1) - 1 end if elseif (dir == 2) then ! check if (.not.allocated(this%knot2)) then error stop 'Knot vector is not set.' else this%nc(2) = sum(compute_multiplicity(this%knot2)) - this%degree(2) - 1 end if elseif (dir == 3) then ! check if (.not.allocated(this%knot3)) then error stop 'Knot vector is not set.' else this%nc(3) = sum(compute_multiplicity(this%knot3)) - this%degree(3) - 1 end if else error stop 'Invalid direction.' end if else ! check if (.not.allocated(this%knot1)) then error stop 'Knot vector is not set.' else this%nc(1) = sum(compute_multiplicity(this%knot1)) - this%degree(1) - 1 end if ! check if (.not.allocated(this%knot2)) then error stop 'Knot vector is not set.' else this%nc(2) = sum(compute_multiplicity(this%knot2)) - this%degree(2) - 1 end if ! check if (.not.allocated(this%knot3)) then error stop 'Knot vector is not set.' else this%nc(3) = sum(compute_multiplicity(this%knot3)) - this%degree(3) - 1 end if end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_nc_all(this) result(nc) class(nurbs_volume), intent(in) :: this integer :: nc(3) nc = this%nc end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_nc_dir(this, dir) result(nc) class(nurbs_volume), intent(in) :: this integer, intent(in) :: dir integer :: nc if (dir == 1) then ! check if (.not.allocated(this%knot1)) then error stop 'Knot vector is not set.' else nc = sum(compute_multiplicity(this%knot1)) - this%degree(1) - 1 end if elseif (dir == 2) then ! check if (.not.allocated(this%knot2)) then error stop 'Knot vector is not set.' else nc = sum(compute_multiplicity(this%knot2)) - this%degree(2) - 1 end if elseif (dir == 3) then ! check if (.not.allocated(this%knot3)) then error stop 'Knot vector is not set.' else nc = sum(compute_multiplicity(this%knot3)) - this%degree(3) - 1 end if else error stop 'Invalid direction.' end if end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, dTgc, Tgc) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: res1, res2, res3 real(rk), intent(in), contiguous, optional :: Xt1(:), Xt2(:), Xt3(:) real(rk), allocatable, intent(out) :: dTgc(:,:,:) real(rk), allocatable, intent(out), optional :: Tgc(:,:) integer :: i real(rk), allocatable :: Xt(:,:) ! Set parameter values if (present(Xt1)) then if (allocated(this%Xt1)) then if (size(Xt1,1) /= size(this%Xt1,1)) deallocate(this%Xt1) end if this%Xt1 = Xt1 elseif (present(res1)) then if (allocated(this%Xt1)) then if (size(this%Xt1,1) /= res1) then deallocate(this%Xt1) allocate(this%Xt1(res1)) end if else allocate(this%Xt1(res1)) end if this%Xt1 = [(this%knot1(1)+(this%knot1(size(this%knot1))-this%knot1(1))*real(i-1,rk)/real(res1-1,rk), i=1, res1)] ! else ! this%Xt1 = this%Xt1 end if ! Set parameter values if (present(Xt2)) then if (allocated(this%Xt2)) then if (size(Xt2,1) /= size(this%Xt2,1)) deallocate(this%Xt2) end if this%Xt2 = Xt2 elseif (present(res2)) then if (allocated(this%Xt2)) then if (size(this%Xt2,1) /= res2) then deallocate(this%Xt2) allocate(this%Xt2(res2)) end if else allocate(this%Xt2(res2)) end if this%Xt2 = [(this%knot2(1)+(this%knot2(size(this%knot2))-this%knot2(1))*real(i-1,rk)/real(res2-1,rk), i=1, res2)] ! else ! this%Xt2 = this%Xt2 end if ! Set parameter values if (present(Xt3)) then if (allocated(this%Xt3)) then if (size(Xt3,1) /= size(this%Xt3,1)) deallocate(this%Xt3) end if this%Xt3 = Xt3 elseif (present(res3)) then if (allocated(this%Xt3)) then if (size(this%Xt3,1) /= res3) then deallocate(this%Xt3) allocate(this%Xt3(res3)) end if else allocate(this%Xt3(res3)) end if this%Xt3 = [(this%knot3(1)+(this%knot3(size(this%knot3))-this%knot3(1))*real(i-1,rk)/real(res3-1,rk), i=1, res3)] ! else ! this%Xt3 = this%Xt3 end if ! Set number of geometry points this%ng(1) = size(this%Xt1,1) this%ng(2) = size(this%Xt2,1) this%ng(3) = size(this%Xt3,1) call ndgrid(this%Xt1, this%Xt2, this%Xt3, Xt) if (this%is_rational()) then ! NURBS call compute_dTgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%ng, this%Wc, dTgc, Tgc) else call compute_dTgc(Xt, this%knot1, this%knot2, this%knot3, 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_volume), intent(inout) :: this real(rk), intent(in), contiguous :: 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%knot1, this%knot2, this%knot3, this%degree, this%nc, this%Wc, dTgc, Tgc, elem) else call compute_dTgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, dTgc, Tgc, elem) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine derivative2_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, d2Tgc, dTgc, Tgc) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: res1, res2, res3 real(rk), intent(in), contiguous, optional :: Xt1(:), Xt2(:), Xt3(:) real(rk), allocatable, intent(out) :: d2Tgc(:,:,:) real(rk), allocatable, intent(out), optional :: dTgc(:,:,:) real(rk), allocatable, intent(out), optional :: Tgc(:,:) integer :: i real(rk), allocatable :: Xt(:,:) ! Set parameter values if (present(Xt1)) then if (allocated(this%Xt1)) then if (size(Xt1,1) /= size(this%Xt1,1)) deallocate(this%Xt1) end if this%Xt1 = Xt1 elseif (present(res1)) then if (allocated(this%Xt1)) then if (size(this%Xt1,1) /= res1) then deallocate(this%Xt1) allocate(this%Xt1(res1)) end if else allocate(this%Xt1(res1)) end if this%Xt1 = [(this%knot1(1)+(this%knot1(size(this%knot1))-this%knot1(1))*real(i-1,rk)/real(res1-1,rk), i=1, res1)] ! else ! this%Xt1 = this%Xt1 end if ! Set parameter values if (present(Xt2)) then if (allocated(this%Xt2)) then if (size(Xt2,1) /= size(this%Xt2,1)) deallocate(this%Xt2) end if this%Xt2 = Xt2 elseif (present(res2)) then if (allocated(this%Xt2)) then if (size(this%Xt2,1) /= res2) then deallocate(this%Xt2) allocate(this%Xt2(res2)) end if else allocate(this%Xt2(res2)) end if this%Xt2 = [(this%knot2(1)+(this%knot2(size(this%knot2))-this%knot2(1))*real(i-1,rk)/real(res2-1,rk), i=1, res2)] ! else ! this%Xt2 = this%Xt2 end if ! Set parameter values if (present(Xt3)) then if (allocated(this%Xt3)) then if (size(Xt3,1) /= size(this%Xt3,1)) deallocate(this%Xt3) end if this%Xt3 = Xt3 elseif (present(res3)) then if (allocated(this%Xt3)) then if (size(this%Xt3,1) /= res3) then deallocate(this%Xt3) allocate(this%Xt3(res3)) end if else allocate(this%Xt3(res3)) end if this%Xt3 = [(this%knot3(1)+(this%knot3(size(this%knot3))-this%knot3(1))*real(i-1,rk)/real(res3-1,rk), i=1, res3)] ! else ! this%Xt3 = this%Xt3 end if ! Set number of geometry points this%ng(1) = size(this%Xt1,1) this%ng(2) = size(this%Xt2,1) this%ng(3) = size(this%Xt3,1) call ndgrid(this%Xt1, this%Xt2, this%Xt3, Xt) if (this%is_rational()) then ! NURBS call compute_d2Tgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%ng, this%Wc, d2Tgc, dTgc, Tgc) else call compute_d2Tgc(Xt, this%knot1, this%knot2, this%knot3, 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_volume), intent(inout) :: this real(rk), intent(in), contiguous :: 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%knot1, this%knot2, this%knot3, this%degree, this%nc, this%Wc, d2Tgc, dTgc, Tgc) else call compute_d2Tgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, d2Tgc, dTgc, Tgc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine basis_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, Tgc) class(nurbs_volume), intent(inout) :: this integer, intent(in), optional :: res1, res2, res3 real(rk), intent(in), contiguous, optional :: Xt1(:), Xt2(:), Xt3(:) real(rk), allocatable, intent(out) :: Tgc(:,:) integer :: i real(rk), allocatable :: Xt(:,:) ! Set parameter values if (present(Xt1)) then if (allocated(this%Xt1)) then if (size(Xt1,1) /= size(this%Xt1,1)) deallocate(this%Xt1) end if this%Xt1 = Xt1 elseif (present(res1)) then if (allocated(this%Xt1)) then if (size(this%Xt1,1) /= res1) then deallocate(this%Xt1) allocate(this%Xt1(res1)) end if else allocate(this%Xt1(res1)) end if this%Xt1 = [(this%knot1(1)+(this%knot1(size(this%knot1))-this%knot1(1))*real(i-1,rk)/real(res1-1,rk), i=1, res1)] ! else ! this%Xt1 = this%Xt1 end if ! Set parameter values if (present(Xt2)) then if (allocated(this%Xt2)) then if (size(Xt2,1) /= size(this%Xt2,1)) deallocate(this%Xt2) end if this%Xt2 = Xt2 elseif (present(res2)) then if (allocated(this%Xt2)) then if (size(this%Xt2,1) /= res2) then deallocate(this%Xt2) allocate(this%Xt2(res2)) end if else allocate(this%Xt2(res2)) end if this%Xt2 = [(this%knot2(1)+(this%knot2(size(this%knot2))-this%knot2(1))*real(i-1,rk)/real(res2-1,rk), i=1, res2)] ! else ! this%Xt2 = this%Xt2 end if ! Set parameter values if (present(Xt3)) then if (allocated(this%Xt3)) then if (size(Xt3,1) /= size(this%Xt3,1)) deallocate(this%Xt3) end if this%Xt3 = Xt3 elseif (present(res3)) then if (allocated(this%Xt3)) then if (size(this%Xt3,1) /= res3) then deallocate(this%Xt3) allocate(this%Xt3(res3)) end if else allocate(this%Xt3(res3)) end if this%Xt3 = [(this%knot3(1)+(this%knot3(size(this%knot3))-this%knot3(1))*real(i-1,rk)/real(res3-1,rk), i=1, res3)] ! else ! this%Xt3 = this%Xt3 end if ! Set number of geometry points this%ng(1) = size(this%Xt1,1) this%ng(2) = size(this%Xt2,1) this%ng(3) = size(this%Xt3,1) call ndgrid(this%Xt1, this%Xt2, this%Xt3, Xt) if (this%is_rational()) then ! NURBS Tgc = compute_Tgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%ng, this%Wc) else Tgc = compute_Tgc(Xt, this%knot1, this%knot2, this%knot3, 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_volume), intent(inout) :: this real(rk), intent(in), contiguous :: Xt(:) real(rk), allocatable, intent(out) :: Tgc(:) if (this%is_rational()) then ! NURBS Tgc = compute_Tgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc, this%Wc) else Tgc = compute_Tgc(Xt, this%knot1, this%knot2, this%knot3, this%degree, this%nc) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine insert_knots(this, dir ,Xth,r) class(nurbs_volume), intent(inout) :: this integer, intent(in) :: dir real(rk), intent(in), contiguous :: Xth(:) integer, intent(in), contiguous :: r(:) integer :: k, i, s, d, j, n_new real(rk), allocatable :: Xc(:,:), Xcw(:,:), Xcw_new(:,:), Xc_new(:,:), Wc_new(:), knot_new(:) real(rk), allocatable :: Xc4(:,:,:,:) if (dir == 1) then ! direction 1 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(1)-1,this%degree(1),Xth(i),this%knot1) ! if (this%knot1(k+1) == Xth(i)) then if (abs(this%knot1(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot1, Xth(i)) else s = 0 end if d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xcw = reshape(Xcw,[this%nc(1),this%nc(2)*this%nc(3)*(d+1)]) call insert_knot_A_5_1(& this%degree(1),& this%knot1,& Xcw,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xcw_new) Xcw_new = reshape(Xcw_new,[(n_new+1)*this%nc(2)*this%nc(3),d+1]) allocate(Xc_new(1:(n_new+1)*this%nc(2)*this%nc(3),1:d)) allocate(Wc_new(1:(n_new+1)*this%nc(2)*this%nc(3))) do j = 1, (n_new+1)*this%nc(2)*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), 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)-1,this%degree(1),Xth(i),this%knot1) ! if (this%knot1(k+1) == Xth(i)) then if (abs(this%knot1(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot1, Xth(i)) else s = 0 end if d = size(this%Xc,2) Xc = reshape(this%Xc,[this%nc(1),this%nc(2)*this%nc(3)*d]) call insert_knot_A_5_1(& this%degree(1),& this%knot1,& Xc,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xc_new) Xc_new = reshape(Xc_new,[(n_new+1)*this%nc(2)*this%nc(3),d]) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), Xc=Xc_new) end do end if elseif (dir == 2) then! direction 2 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(2)-1,this%degree(2),Xth(i),this%knot2) ! if (this%knot2(k+1) == Xth(i)) then if (abs(this%knot2(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot2, Xth(i)) else s = 0 end if d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d+1], order=[2,1,3,4]) Xcw = reshape(Xc4,[this%nc(2),this%nc(1)*this%nc(3)*(d+1)]) call insert_knot_A_5_1(& this%degree(2),& this%knot2,& Xcw,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xcw_new) Xc4 = reshape(Xcw_new, [n_new+1,this%nc(1),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(1),n_new+1,this%nc(3),d+1], order=[2,1,3,4]) Xcw_new = reshape(Xc4,[this%nc(1)*(n_new+1)*this%nc(3),d+1]) allocate(Xc_new(1:this%nc(1)*(n_new+1)*this%nc(3),1:d)) allocate(Wc_new(1:this%nc(1)*(n_new+1)*this%nc(3))) do j = 1, this%nc(1)*(n_new+1)*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), 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(2)-1,this%degree(2),Xth(i),this%knot2) ! if (this%knot2(k+1) == Xth(i)) then if (abs(this%knot2(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot2, Xth(i)) else s = 0 end if d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d], order=[2,1,3,4]) Xc = reshape(Xc4,[this%nc(2),this%nc(1)*this%nc(3)*d]) call insert_knot_A_5_1(& this%degree(2),& this%knot2,& Xc,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xc_new) Xc4 = reshape(Xc_new, [n_new+1,this%nc(1),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(1),n_new+1,this%nc(3),d], order=[2,1,3,4]) Xc_new = reshape(Xc4,[this%nc(1)*(n_new+1)*this%nc(3),d]) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), Xc=Xc_new) end do end if elseif (dir == 3) then! direction 3 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(3)-1,this%degree(3),Xth(i),this%knot3) ! if (this%knot3(k+1) == Xth(i)) then if (abs(this%knot3(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot3, Xth(i)) else s = 0 end if d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d+1], order=[3,2,1,4]) Xcw = reshape(Xc4,[this%nc(3),this%nc(2)*this%nc(1)*(d+1)]) call insert_knot_A_5_1(& this%degree(3),& this%knot3,& Xcw,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xcw_new) Xc4 = reshape(Xcw_new, [n_new+1,this%nc(2),this%nc(1),d+1]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),n_new+1,d+1], order=[3,2,1,4]) Xcw_new = reshape(Xc4,[this%nc(1)*this%nc(2)*(n_new+1),d+1]) allocate(Xc_new(1:this%nc(1)*this%nc(2)*(n_new+1),1:d)) allocate(Wc_new(1:this%nc(1)*this%nc(2)*(n_new+1))) do j = 1, this%nc(1)*this%nc(2)*(n_new+1) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=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(3)-1,this%degree(3),Xth(i),this%knot3) ! if (this%knot3(k+1) == Xth(i)) then if (abs(this%knot3(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot3, Xth(i)) else s = 0 end if d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d], order=[3,2,1,4]) Xc = reshape(Xc4,[this%nc(3),this%nc(2)*this%nc(1)*d]) call insert_knot_A_5_1(& this%degree(3),& this%knot3,& Xc,& Xth(i),& k,& s,& r(i),& n_new,& knot_new,& Xc_new) Xc4 = reshape(Xc_new, [n_new+1,this%nc(2),this%nc(1),d]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),n_new+1,d], order=[3,2,1,4]) Xc_new = reshape(Xc4, [this%nc(1)*this%nc(2)*(n_new+1),d]) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=knot_new, Xc=Xc_new) end do end if else error stop 'Invalid direction.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine elevate_degree(this, dir, t) class(nurbs_volume), intent(inout) :: this integer, intent(in) :: dir integer, intent(in) :: t real(rk), allocatable :: Xc(:,:), Xcw(:,:), Xcw_new(:,:), Xc_new(:,:), Wc_new(:), knot_new(:) integer :: nc_new, d, j real(rk), allocatable:: Xc4(:,:,:,:) if (dir == 1) then ! direction 1 if (allocated(this%Wc)) then ! NURBS d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xcw = reshape(Xcw,[this%nc(1),this%nc(2)*this%nc(3)*(d+1)],order=[1,2]) call elevate_degree_A_5_9(t, this%knot1, this%degree(1), Xcw, nc_new, knot_new, Xcw_new) Xcw_new = reshape(Xcw_new,[nc_new*this%nc(2)*this%nc(3),d+1],order=[1,2]) allocate(Xc_new(1:nc_new*this%nc(2)*this%nc(3),1:d)) allocate(Wc_new(1:nc_new*this%nc(2)*this%nc(3))) do j = 1, nc_new*this%nc(2)*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), Xc=Xc_new, Wc=Wc_new) deallocate(Xcw, Xcw_new, Xc_new, Wc_new) else ! B-Spline d = size(this%Xc,2) Xc = reshape(this%Xc,[this%nc(1),this%nc(2)*this%nc(3)*d],order=[1,2]) call elevate_degree_A_5_9(t, this%knot1, this%degree(1), Xc, nc_new, knot_new, Xc_new) Xc_new = reshape(Xc_new,[nc_new*this%nc(2)*this%nc(3),d],order=[1,2]) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), Xc=Xc_new) end if elseif (dir == 2) then ! direction 2 if (allocated(this%Wc)) then ! NURBS d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d+1], order=[2,1,3,4]) Xcw = reshape(Xc4,[this%nc(2),this%nc(1)*this%nc(3)*(d+1)]) call elevate_degree_A_5_9(t, this%knot2, this%degree(2), Xcw, nc_new, knot_new, Xcw_new) Xc4 = reshape(Xcw_new, [nc_new,this%nc(1),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(1),nc_new,this%nc(3),d+1], order=[2,1,3,4]) Xcw_new = reshape(Xc4,[this%nc(1)*nc_new*this%nc(3),d+1]) allocate(Xc_new(1:this%nc(1)*nc_new*this%nc(3),1:d)) allocate(Wc_new(1:this%nc(1)*nc_new*this%nc(3))) do j = 1, this%nc(1)*nc_new*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), Xc=Xc_new, Wc=Wc_new) deallocate(Xcw, Xcw_new, Xc_new, Wc_new) else ! B-Spline d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d], order=[2,1,3,4]) Xc = reshape(Xc4,[this%nc(2),this%nc(1)*this%nc(3)*d]) call elevate_degree_A_5_9(t, this%knot2, this%degree(2), Xc, nc_new, knot_new, Xc_new) Xc4 = reshape(Xc_new, [nc_new,this%nc(1),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(1),nc_new,this%nc(3),d], order=[2,1,3,4]) Xc_new = reshape(Xc4,[this%nc(1)*nc_new*this%nc(3),d]) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), Xc=Xc_new) end if elseif (dir == 3) then ! direction 3 if (allocated(this%Wc)) then ! NURBS d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d+1], order=[3,2,1,4]) Xcw = reshape(Xc4,[this%nc(3),this%nc(2)*this%nc(1)*(d+1)]) call elevate_degree_A_5_9(t, this%knot3, this%degree(3), Xcw, nc_new, knot_new, Xcw_new) Xc4 = reshape(Xcw_new, [nc_new,this%nc(2),this%nc(1),d+1]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),nc_new,d+1], order=[3,2,1,4]) Xcw_new = reshape(Xc4,[this%nc(1)*this%nc(2)*nc_new,d+1]) allocate(Xc_new(1:this%nc(1)*this%nc(2)*nc_new,1:d)) allocate(Wc_new(1:this%nc(1)*this%nc(2)*nc_new)) do j = 1, this%nc(1)*this%nc(2)*nc_new Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=knot_new, Xc=Xc_new, Wc=Wc_new) deallocate(Xcw, Xcw_new, Xc_new, Wc_new) else ! B-Spline d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d], order=[3,2,1,4]) Xc = reshape(Xc4,[this%nc(3),this%nc(2)*this%nc(1)*d]) call elevate_degree_A_5_9(t, this%knot3, this%degree(3), Xc, nc_new, knot_new, Xc_new) Xc4 = reshape(Xc_new, [nc_new,this%nc(2),this%nc(1),d]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),nc_new,d], order=[3,2,1,4]) Xc_new = reshape(Xc4,[this%nc(1)*this%nc(2)*nc_new,d]) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=knot_new, Xc=Xc_new) end if else error stop 'Invalid direction.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function is_rational(this) result(r) class(nurbs_volume), intent(in) :: this logical :: r r = .false. if (allocated(this%Wc)) then ! if (any(this%Wc /= this%Wc(1))) then if (any(abs(this%Wc - this%Wc(1)) > 2.0_rk*epsilon(0.0_rk))) 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_volume), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn_Xc_vis)) then if (size(this%elemConn_Xc_vis,1) /= size(elemConn,1) .or. size(this%elemConn_Xc_vis,2) /= size(elemConn,2)) then deallocate(this%elemConn_Xc_vis) end if end if 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_volume), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn_Xg_vis)) then if (size(this%elemConn_Xg_vis,1) /= size(elemConn,1) .or. size(this%elemConn_Xg_vis,2) /= size(elemConn,2)) then deallocate(this%elemConn_Xg_vis) end if end if this%elemConn_Xg_vis = elemConn end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_elem(this, elemConn) class(nurbs_volume), intent(inout) :: this integer, intent(in), contiguous :: elemConn(:,:) if (allocated(this%elemConn)) then if (size(this%elemConn,1) /= size(elemConn,1) .or. size(this%elemConn,2) /= size(elemConn,2)) then deallocate(this%elemConn) end if end if this%elemConn = elemConn end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function get_elem_Xc_vis(this) result(elemConn) class(nurbs_volume), 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_volume), 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_volume), intent(in) :: this integer, allocatable :: elemConn(:,:) elemConn = this%elemConn end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_hexahedron(this, L, nc, Wc) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: L(:) integer, intent(in), contiguous :: nc(:) real(rk), intent(in), contiguous, optional :: Wc(:) if (present(Wc)) then call this%set(nc, hexahedron_Xc(L, nc), Wc) else call this%set(nc, hexahedron_Xc(L, nc)) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine put_to_nurbs(this, X, elemConn) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: X(:,:) integer, intent(in), contiguous :: elemConn(:,:) integer :: i real(rk), allocatable :: Tgc1(:), Tgc2(:), Tgc3(:), Tgc(:) real(rk), allocatable :: Xt(:,:) real(rk) :: min_X1, max_X1, min_X2, max_X2, min_X3, max_X3 ! Assuming knot vectors are in the range [0,1] ! Normalize the X coordinates to the range [0,1] allocate(Xt(size(X,1), size(X,2))) min_X1 = minval(X(:,1)) max_X1 = maxval(X(:,1)) min_X2 = minval(X(:,2)) max_X2 = maxval(X(:,2)) min_X3 = minval(X(:,3)) max_X3 = maxval(X(:,3)) Xt(:,1) = (X(:,1) - min_X1) / (max_X1 - min_X1) Xt(:,2) = (X(:,2) - min_X2) / (max_X2 - min_X2) Xt(:,3) = (X(:,3) - min_X3) / (max_X3 - min_X3) allocate(this%Xg(size(Xt,1), size(this%Xc,2))) allocate(Tgc(this%nc(1)*this%nc(2)*this%nc(3))) if (allocated(this%Wc)) then ! NURBS volume do i = 1, size(Xt, 1) Tgc1 = basis_bspline(Xt(i,1), this%knot1, this%nc(1), this%degree(1)) Tgc2 = basis_bspline(Xt(i,2), this%knot2, this%nc(2), this%degree(2)) Tgc3 = basis_bspline(Xt(i,3), this%knot3, this%nc(3), this%degree(3)) Tgc = kron(Tgc3, kron(Tgc2, Tgc1)) Tgc = Tgc*(this%Wc/(dot_product(Tgc,this%Wc))) this%Xg(i,:) = matmul(Tgc,this%Xc) end do else ! B-Spline volume do i = 1, size(Xt, 1) Tgc1 = basis_bspline(Xt(i,1), this%knot1, this%nc(1), this%degree(1)) Tgc2 = basis_bspline(Xt(i,2), this%knot2, this%nc(2), this%degree(2)) Tgc3 = basis_bspline(Xt(i,3), this%knot3, this%nc(3), this%degree(3)) Tgc = kron(Tgc3, kron(Tgc2, Tgc1)) this%Xg(i,:) = matmul(Tgc,this%Xc) end do end if call this%set_elem_Xg_vis(elemConn) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine remove_knots(this, dir ,Xth,r) class(nurbs_volume), intent(inout) :: this integer, intent(in) :: dir real(rk), intent(in), contiguous :: Xth(:) integer, intent(in), contiguous :: r(:) integer :: k, i, s, d, j, nc_new, t real(rk), allocatable :: Xc(:,:), Xcw(:,:), Xcw_new(:,:), Xc_new(:,:), Wc_new(:), knot_new(:) real(rk), allocatable :: Xc4(:,:,:,:) if (dir == 1) then ! direction 1 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(1)-1,this%degree(1),Xth(i),this%knot1) ! if (this%knot1(k+1) == Xth(i)) then if (abs(this%knot1(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot1, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xcw = reshape(Xcw,[this%nc(1),this%nc(2)*this%nc(3)*(d+1)],order=[1,2]) call remove_knots_A_5_8(& this%degree(1),& this%knot1,& 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) Xcw_new = reshape(Xcw_new,[(nc_new)*this%nc(2)*this%nc(3),d+1],order=[1,2]) allocate(Xc_new(1:(nc_new)*this%nc(2)*this%nc(3),1:d)) allocate(Wc_new(1:(nc_new)*this%nc(2)*this%nc(3))) do j = 1, (nc_new)*this%nc(2)*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), Xc=Xc_new, Wc=Wc_new) deallocate(Xcw_new, Xc_new, Wc_new) end if end do else ! B-Spline do i = 1, size(Xth) k = findspan(this%nc(1)-1,this%degree(1),Xth(i),this%knot1) ! if (this%knot1(k+1) == Xth(i)) then if (abs(this%knot1(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot1, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) Xc = reshape(this%Xc,[this%nc(1),this%nc(2)*this%nc(3)*d]) call remove_knots_A_5_8(& this%degree(1),& this%knot1,& Xc,& Xth(i),& k,& s,& r(i),& t,& knot_new,& Xc_new) if (allocated(Xc)) deallocate(Xc) if (t == 0) then ! no change else nc_new = size(Xcw_new,1) Xc_new = reshape(Xc_new,[(nc_new)*this%nc(2)*this%nc(3),d]) call this%set(knot1=knot_new, knot2=this%get_knot(2), knot3=this%get_knot(3), Xc=Xc_new) end if end do end if elseif (dir == 2) then! direction 2 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(2)-1,this%degree(2),Xth(i),this%knot2) ! if (this%knot2(k+1) == Xth(i)) then if (abs(this%knot2(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot2, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d+1], order=[2,1,3,4]) Xcw = reshape(Xc4,[this%nc(2),this%nc(1)*this%nc(3)*(d+1)]) call remove_knots_A_5_8(& this%degree(2),& this%knot2,& 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) Xc4 = reshape(Xcw_new, [nc_new,this%nc(1),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(1),nc_new,this%nc(3),d+1], order=[2,1,3,4]) Xcw_new = reshape(Xc4,[this%nc(1)*(nc_new)*this%nc(3),d+1]) allocate(Xc_new(1:this%nc(1)*(nc_new)*this%nc(3),1:d)) allocate(Wc_new(1:this%nc(1)*(nc_new)*this%nc(3))) do j = 1, this%nc(1)*(nc_new)*this%nc(3) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), Xc=Xc_new, Wc=Wc_new) deallocate(Xcw_new, Xc_new, Wc_new) end if end do else ! B-Spline do i = 1, size(Xth) k = findspan(this%nc(2)-1,this%degree(2),Xth(i),this%knot2) ! if (this%knot2(k+1) == Xth(i)) then if (abs(this%knot2(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot2, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(2),this%nc(1),this%nc(3),d], order=[2,1,3,4]) Xc = reshape(Xc4, [this%nc(2),this%nc(1)*this%nc(3)*d]) call remove_knots_A_5_8(& this%degree(2),& this%knot2,& Xc,& Xth(i),& k,& s,& r(i),& t,& knot_new,& Xc_new) if (allocated(Xc)) deallocate(Xc) if (t == 0) then ! no change else nc_new = size(Xcw_new,1) Xc4 = reshape(Xc_new, [nc_new,this%nc(1),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(1),nc_new,this%nc(3),d], order=[2,1,3,4]) Xc_new = reshape(Xc4, [this%nc(1)*(nc_new)*this%nc(3),d]) call this%set(knot1=this%get_knot(1), knot2=knot_new, knot3=this%get_knot(3), Xc=Xc_new) end if end do end if elseif (dir == 3) then! direction 3 if (allocated(this%Wc)) then ! NURBS do i = 1, size(Xth) k = findspan(this%nc(3)-1,this%degree(3),Xth(i),this%knot3) ! if (this%knot3(k+1) == Xth(i)) then if (abs(this%knot3(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot3, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) allocate(Xcw(size(this%Xc,1),d+1)) do j = 1, size(this%Xc,1) Xcw(j,1:d) = this%Xc(j,1:d)*this%Wc(j) end do Xcw(:,d+1) = this%Wc(:) Xc4 = reshape(Xcw, [this%nc(1),this%nc(2),this%nc(3),d+1]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d+1], order=[3,2,1,4]) Xcw = reshape(Xc4, [this%nc(3),this%nc(2)*this%nc(1)*(d+1)]) call remove_knots_A_5_8(& this%degree(3),& this%knot3,& 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) Xc4 = reshape(Xcw_new, [nc_new,this%nc(2),this%nc(1),d+1]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),nc_new,d+1], order=[3,2,1,4]) Xcw_new = reshape(Xc4, [this%nc(1)*this%nc(2)*(nc_new),d+1]) allocate(Xc_new(1:this%nc(1)*this%nc(2)*(nc_new),1:d)) allocate(Wc_new(1:this%nc(1)*this%nc(2)*(nc_new))) do j = 1, this%nc(1)*this%nc(2)*(nc_new) Xc_new(j,1:d) = Xcw_new(j,1:d)/Xcw_new(j,d+1) end do Wc_new(:) = Xcw_new(:,d+1) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=knot_new, Xc=Xc_new, Wc=Wc_new) deallocate(Xcw_new, Xc_new, Wc_new) end if end do else ! B-Spline do i = 1, size(Xth) k = findspan(this%nc(3)-1,this%degree(3),Xth(i),this%knot3) ! if (this%knot3(k+1) == Xth(i)) then if (abs(this%knot3(k+1) - Xth(i)) < 2.0_rk*epsilon(0.0_rk)) then s = compute_multiplicity(this%knot3, Xth(i)) else s = 0 end if k = k + 1 d = size(this%Xc,2) Xc4 = reshape(this%Xc, [this%nc(1),this%nc(2),this%nc(3),d]) Xc4 = reshape(Xc4, [this%nc(3),this%nc(2),this%nc(1),d], order=[3,2,1,4]) Xc = reshape(Xc4, [this%nc(3),this%nc(2)*this%nc(1)*d]) call remove_knots_A_5_8(& this%degree(3),& this%knot3,& Xc,& Xth(i),& k,& s,& r(i),& t,& knot_new,& Xc_new) if (allocated(Xc)) deallocate(Xc) if (t == 0) then ! no change else nc_new = size(Xcw_new,1) Xc4 = reshape(Xc_new, [nc_new,this%nc(2),this%nc(1),d]) Xc4 = reshape(Xc4, [this%nc(1),this%nc(2),nc_new,d], order=[3,2,1,4]) Xc_new = reshape(Xc4, [this%nc(1)*this%nc(2)*(nc_new),d]) call this%set(knot1=this%get_knot(1), knot2=this%get_knot(2), knot3=knot_new, Xc=Xc_new) end if end do end if else error stop 'Invalid direction.' end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elem(this) result(elemConn) class(nurbs_volume), intent(in) :: this integer, allocatable :: elemConn(:,:) call elemConn_Cn(this%nc(1), this%nc(2), this%nc(3),& this%degree(1),this%degree(2),this%degree(3),& unique(this%knot1),unique(this%knot2),unique(this%knot3),& this%get_multiplicity(1),this%get_multiplicity(2),this%get_multiplicity(3),& elemConn) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine rotate_Xc(this, alpha, beta, theta) class(nurbs_volume), intent(inout) :: this real(rk), intent(in) :: alpha, beta, theta integer :: i do i = 1, this%nc(1)*this%nc(2)*this%nc(3) 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_volume), intent(inout) :: this real(rk), intent(in) :: alpha, beta, theta integer :: i do i = 1, this%ng(1)*this%ng(2)*this%ng(3) 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_volume), intent(inout) :: this real(rk), intent(in) :: vec(:) integer :: i do i = 1, this%nc(1)*this%nc(2)*this%nc(3) 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_volume), intent(inout) :: this real(rk), intent(in) :: vec(:) integer :: i do i = 1, this%ng(1)*this%ng(2)*this%ng(3) 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_volume), 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)"//achar(10)//& "p.deep_clean()"//achar(10)//& "del p" call execute_command_line('python -c "'//trim(adjustl(pyvista_script))//'"') end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_ring(this, center, radius1, radius2, length) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius1, radius2, length real(rk), allocatable :: Xc(:,:), Wc(:), knot1(:), knot2(:), knot3(:) integer :: i ! Define control points for ring allocate(Xc(28, 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] Xc(1:7,1:2) = Xc(1:7,1:2) * radius1 Xc(8,:) = [ 1.0_rk, 0.0_rk, 0.0_rk] Xc(9,:) = [ 1.0_rk, sqrt(3.0_rk), 0.0_rk] Xc(10,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(11,:)= [-2.0_rk, 0.0_rk, 0.0_rk] Xc(12,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(13,:)= [ 1.0_rk, -sqrt(3.0_rk), 0.0_rk] Xc(14,:)= [ 1.0_rk, 0.0_rk, 0.0_rk] Xc(8:14,1:2) = Xc(8:14,1:2) * radius2 Xc(15,:)= [ 1.0_rk, 0.0_rk, length] Xc(16,:)= [ 1.0_rk, sqrt(3.0_rk), length] Xc(17,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, length] Xc(18,:)= [-2.0_rk, 0.0_rk, length] Xc(19,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, length] Xc(20,:)= [ 1.0_rk, -sqrt(3.0_rk), length] Xc(21,:)= [ 1.0_rk, 0.0_rk, length] Xc(15:21,1:2) = Xc(15:21,1:2) * radius1 Xc(22,:)= [ 1.0_rk, 0.0_rk, length] Xc(23,:)= [ 1.0_rk, sqrt(3.0_rk), length] Xc(24,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, length] Xc(25,:)= [-2.0_rk, 0.0_rk, length] Xc(26,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, length] Xc(27,:)= [ 1.0_rk, -sqrt(3.0_rk), length] Xc(28,:)= [ 1.0_rk, 0.0_rk, length] Xc(22:28,1:2) = Xc(22:28,1:2) * radius2 ! Translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) 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,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk] ! Define knot vector knot1 = [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] knot2 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] knot3 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot1, knot2, knot3, Xc, Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_C(this, center, radius1, radius2, length) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius1, radius2, length real(rk), allocatable :: Xc(:,:), Wc(:), knot1(:), knot2(:), knot3(:) integer :: i ! Define control points for C-shape allocate(Xc(20, 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(1:5,1:2) = Xc(1:5,1:2) * radius1 Xc(6,:)= [ 1.0_rk, 0.0_rk, 0.0_rk] Xc(7,:)= [ 1.0_rk, sqrt(3.0_rk), 0.0_rk] Xc(8,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(9,:)= [-2.0_rk, 0.0_rk, 0.0_rk] Xc(10,:)=[-0.5_rk, -sqrt(3.0_rk)/2.0_rk, 0.0_rk] Xc(6:10,1:2) = Xc(6:10,1:2) * radius2 Xc(11,:)= [ 1.0_rk, 0.0_rk, length] Xc(12,:)= [ 1.0_rk, sqrt(3.0_rk), length] Xc(13,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, length] Xc(14,:)= [-2.0_rk, 0.0_rk, length] Xc(15,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, length] Xc(11:15,1:2) = Xc(11:15,1:2) * radius1 Xc(16,:)= [ 1.0_rk, 0.0_rk, length] Xc(17,:)= [ 1.0_rk, sqrt(3.0_rk), length] Xc(18,:)= [-0.5_rk, sqrt(3.0_rk)/2.0_rk, length] Xc(19,:)= [-2.0_rk, 0.0_rk, length] Xc(20,:)= [-0.5_rk, -sqrt(3.0_rk)/2.0_rk, length] Xc(16:20,1:2) = Xc(16:20,1:2) * radius2 ! Translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) end do ! Define weights for the control points Wc = [1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk,& 1.0_rk, 0.5_rk, 1.0_rk, 0.5_rk, 1.0_rk] ! Define knot vector knot1 = [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] knot2 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] knot3 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot1, knot2, knot3, Xc, Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine set_half_ring(this, center, radius1, radius2, length) class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: center(:) real(rk), intent(in) :: radius1, radius2, length real(rk), allocatable :: Xc(:,:), Wc(:), knot1(:), knot2(:), knot3(:) integer :: i ! Define control points for half ring allocate(Xc(20, 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] Xc(1:5,1:2) = Xc(1:5,1:2) * radius1 Xc(6,:) = [ 0.5_rk, 0.0_rk, 0.0_rk] Xc(7,:) = [ 0.5_rk, 0.5_rk, 0.0_rk] Xc(8,:) = [ 0.0_rk, 0.5_rk, 0.0_rk] Xc(9,:) = [-0.5_rk, 0.5_rk, 0.0_rk] Xc(10,:) = [-0.5_rk, 0.0_rk, 0.0_rk] Xc(6:10,1:2) = Xc(6:10,1:2) * radius2 Xc(11,:) = [ 0.5_rk, 0.0_rk, length] Xc(12,:) = [ 0.5_rk, 0.5_rk, length] Xc(13,:) = [ 0.0_rk, 0.5_rk, length] Xc(14,:) = [-0.5_rk, 0.5_rk, length] Xc(15,:) = [-0.5_rk, 0.0_rk, length] Xc(11:15,1:2) = Xc(11:15,1:2) * radius1 Xc(16,:) = [ 0.5_rk, 0.0_rk, length] Xc(17,:) = [ 0.5_rk, 0.5_rk, length] Xc(18,:) = [ 0.0_rk, 0.5_rk, length] Xc(19,:) = [-0.5_rk, 0.5_rk, length] Xc(20,:) = [-0.5_rk, 0.0_rk, length] Xc(16:20,1:2) = Xc(16:20,1:2) * radius2 ! Translate the control points do i = 1, size(Xc, 1) Xc(i,:) = center + Xc(i,:) 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,& 1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk,& 1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk, 1.0_rk/sqrt(2.0_rk), 1.0_rk,& 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 knot1 = [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] knot2 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] knot3 = [0.0_rk, 0.0_rk, 1.0_rk, 1.0_rk] ! Set knot vector, control points, and weights call this%set(knot1, knot2, knot3, 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_volume), intent(in) :: this real(rk), intent(in) :: point_Xg(:) real(rk), intent(out), allocatable, optional :: nearest_Xg(:) real(rk), intent(out), allocatable, optional :: nearest_Xt(:) integer, intent(out), optional :: id integer :: id_ real(rk), allocatable :: distances(:) allocate(distances(this%ng(1)*this%ng(2)*this%ng(3))) distances = nearest_point_help_3d(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_volume), intent(inout) :: this real(rk), intent(in) :: point_Xg(:) real(rk), intent(in) :: tol integer, intent(in) :: maxit real(rk), intent(out) :: nearest_Xt(3) real(rk), allocatable, intent(out), optional :: nearest_Xg(:) real(rk):: obj, grad(3), hess(3,3), dk(3), alphak, tau, beta, lower_bounds(3), upper_bounds(3) real(rk), allocatable :: Xg(:), xk(:), xkn(:), Tgc(:), dTgc(:,:), d2Tgc(:,:) integer :: k, l logical :: convergenz type(nurbs_volume) :: copy_this alphak = 0.0_rk dk = 0.0_rk k = 0 ! lower and upper bounds lower_bounds = [minval(this%knot1), minval(this%knot2), minval(this%knot3)] upper_bounds = [maxval(this%knot1), maxval(this%knot2), maxval(this%knot3)] ! guess initial point copy_this = this call copy_this%create(50,50,50) 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(1) < minval(this%knot1)) then xk(1) = minval(this%knot1) else if (xk(1) > maxval(this%knot1)) then xk(1) = maxval(this%knot1) end if if (xk(2) < minval(this%knot2)) then xk(2) = minval(this%knot2) else if (xk(2) > maxval(this%knot2)) then xk(2) = maxval(this%knot2) end if if (xk(3) < minval(this%knot3)) then xk(3) = minval(this%knot3) else if (xk(3) > maxval(this%knot3)) then xk(3) = maxval(this%knot3) end if xkn = xk convergenz = .false. allocate(Xg(size(this%Xc,2))) ! allocate(dTgc(size(this%Xc,1), 2)) ! allocate(d2Tgc(size(this%Xc,1), 2)) 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(1) = dot_product((Xg-point_Xg)/obj, matmul(dTgc(:,1),this%Xc)) grad(2) = dot_product((Xg-point_Xg)/obj, matmul(dTgc(:,2),this%Xc)) grad(3) = dot_product((Xg-point_Xg)/obj, matmul(dTgc(:,3),this%Xc)) hess(1,1) = ( dot_product(matmul(dTgc(:,1),this%Xc), matmul(dTgc(:,1),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(1:this%nc(1)*this%nc(2)*this%nc(3) ,1),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,1), this%Xc))*grad(1) ) / obj**2 hess(2,1) = ( dot_product(matmul(dTgc(:,1),this%Xc), matmul(dTgc(:,2),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(this%nc(1)*this%nc(2)*this%nc(3)+1:2*this%nc(1)*this%nc(2)*this%nc(3) ,1),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,2), this%Xc))*grad(1) ) / obj**2 hess(3,1) = ( dot_product(matmul(dTgc(:,1),this%Xc), matmul(dTgc(:,3),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(2*this%nc(1)*this%nc(2)*this%nc(3)+1:3*this%nc(1)*this%nc(2)*this%nc(3) ,1),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,3), this%Xc))*grad(1) ) / obj**2 hess(1,2) = ( dot_product(matmul(dTgc(:,2),this%Xc), matmul(dTgc(:,1),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(1:this%nc(1)*this%nc(2)*this%nc(3) ,2),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,1), this%Xc))*grad(2) ) / obj**2 hess(2,2) = ( dot_product(matmul(dTgc(:,2),this%Xc), matmul(dTgc(:,2),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(this%nc(1)*this%nc(2)*this%nc(3)+1:2*this%nc(1)*this%nc(2)*this%nc(3) ,2),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,2), this%Xc))*grad(2) ) / obj**2 hess(3,2) = ( dot_product(matmul(dTgc(:,2),this%Xc), matmul(dTgc(:,3),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(2*this%nc(1)*this%nc(2)*this%nc(3)+1:3*this%nc(1)*this%nc(2)*this%nc(3) ,2),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,3), this%Xc))*grad(2) ) / obj**2 hess(1,3) = ( dot_product(matmul(dTgc(:,3),this%Xc), matmul(dTgc(:,1),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(1:this%nc(1)*this%nc(2)*this%nc(3) ,3),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,1), this%Xc))*grad(3) ) / obj**2 hess(2,3) = ( dot_product(matmul(dTgc(:,3),this%Xc), matmul(dTgc(:,2),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(this%nc(1)*this%nc(2)*this%nc(3)+1:2*this%nc(1)*this%nc(2)*this%nc(3) ,3),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,2), this%Xc))*grad(3) ) / obj**2 hess(3,3) = ( dot_product(matmul(dTgc(:,3),this%Xc), matmul(dTgc(:,3),this%Xc)) + dot_product((Xg-point_Xg), & matmul(d2Tgc(2*this%nc(1)*this%nc(2)*this%nc(3)+1:3*this%nc(1)*this%nc(2)*this%nc(3) ,3),this%Xc)) ) /obj & - ( dot_product(Xg-point_Xg, matmul(dTgc(:,3), this%Xc))*grad(3) ) / obj**2 ! debug print '(i3,1x,3e20.10,1x,e20.10)', k, xk, norm2(grad) if (norm2(grad) <= tol .or. (k>0 .and. norm2(xk-xkn) <= tol)) then convergenz = .true. nearest_Xt = xk if (present(nearest_Xg)) nearest_Xg = this%cmp_Xg(nearest_Xt) else dk = - matmul(inv(hess), grad) ! 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*dot_product(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 function cmp_elemFace(this, elem, face) result(elemConn) class(nurbs_volume), intent(in) :: this integer, intent(in) :: elem integer, intent(in) :: face integer, allocatable :: elemConn(:) integer :: n(3), ii, jj, k !> number of nodes in each direction n = this%degree + 1 select case(face) case(1) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn(elem, 1 : n(1)*n(2)) case(2) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn(elem, n(1)*n(2)*n(3)-n(1)*n(2)+1 : n(1)*n(2)*n(3)) case(3) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn(elem, n(1)*n(2)*jj + ii - n(1)*n(2)) end do end do case(4) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn(elem, n(1)*n(2)*jj + ii - n(1)) end do end do case(5) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn(elem, n(1)*ii - n(1) + 1) end do case(6) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn(elem, n(1)*ii) end do end select end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elemFace_Xc_vis(this, elem, face) result(elemConn) class(nurbs_volume), intent(in) :: this integer, intent(in) :: elem integer, intent(in) :: face integer, allocatable :: elemConn(:) integer :: n(3), ii, jj, k !> number of nodes in each direction n = [2,2,2] select case(face) case(1) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn_Xc_vis(elem, 1 : n(1)*n(2)) case(2) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn_Xc_vis(elem, n(1)*n(2)*n(3)-n(1)*n(2)+1 : n(1)*n(2)*n(3)) case(3) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn_Xc_vis(elem, n(1)*n(2)*jj + ii - n(1)*n(2)) end do end do case(4) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn_Xc_vis(elem, n(1)*n(2)*jj + ii - n(1)) end do end do case(5) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn_Xc_vis(elem, n(1)*ii - n(1) + 1) end do case(6) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn_Xc_vis(elem, n(1)*ii) end do end select end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_elemFace_Xg_vis(this, elem, face) result(elemConn) class(nurbs_volume), intent(in) :: this integer, intent(in) :: elem integer, intent(in) :: face integer, allocatable :: elemConn(:) integer :: n(3), ii, jj, k !> number of nodes in each direction n = [2,2,2] select case(face) case(1) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn_Xg_vis(elem, 1 : n(1)*n(2)) case(2) allocate(elemConn(n(1)*n(2))) elemConn = this%elemConn_Xg_vis(elem, n(1)*n(2)*n(3)-n(1)*n(2)+1 : n(1)*n(2)*n(3)) case(3) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn_Xg_vis(elem, n(1)*n(2)*jj + ii - n(1)*n(2)) end do end do case(4) allocate(elemConn(n(1)*n(3))) k = 0 do jj = 1, n(3) do ii = 1, n(1) k = k+1 elemConn(k) = this%elemConn_Xg_vis(elem, n(1)*n(2)*jj + ii - n(1)) end do end do case(5) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn_Xg_vis(elem, n(1)*ii - n(1) + 1) end do case(6) allocate(elemConn(n(2)*n(3))) do ii = 1, n(2)*n(3) elemConn(ii) = this%elemConn_Xg_vis(elem, n(1)*ii) end do end select end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_degreeFace(this, face) result(degree) class(nurbs_volume), intent(in) :: this integer, intent(in) :: face integer :: degree(3) select case (face) case(1) degree = [this%degree(1), this%degree(2), 0] case(2) degree = [this%degree(1), this%degree(2), 0] case(3) degree = [this%degree(1), 0, this%degree(3)] case(4) degree = [this%degree(1), 0, this%degree(3)] case(5) degree = [0, this%degree(2), this%degree(3)] case(6) degree = [0, this%degree(2), this%degree(3)] case default error stop 'Invalid face number' end select end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine ansatz(this, ie, ig, Tgc, dTgc_dXg, dV) class(nurbs_volume), intent(inout) :: this integer, intent(in) :: ie, ig real(rk), intent(out) :: dV real(rk), allocatable, intent(out) :: Tgc(:), dTgc_dXg(:,:) real(rk), allocatable :: Xth(:,:), Xth_e(:,:), Xth_eT(:,:), Xc_eT(:,:), Xth1(:), Xth2(:), Xth3(:), Xksi(:,:), Wksi(:) integer, allocatable :: elem_th(:,:), elem_c(:,:), elem_ce(:) type(nurbs_volume) :: th, th_e real(rk), allocatable :: dTtth_dXksi(:,:), Ttth(:), dTgc_dXt(:,:), Xt(:), dXt_dXksi(:,:), dXg_dXt(:,:) 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], [0.0_rk, 1.0_rk], [0.0_rk, 1.0_rk], this%degree, Xksi, Wksi) Xth1 = unique(this%knot1) Xth2 = unique(this%knot2) Xth3 = unique(this%knot3) call ndgrid(Xth1, Xth2, Xth3, Xth) call th%set([0.0_rk,Xth1,1.0_rk], [0.0_rk,Xth2,1.0_rk], [0.0_rk,Xth3,1.0_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], [0.0_rk,0.0_rk,1.0_rk,1.0_rk], [0.0_rk,0.0_rk,1.0_rk,1.0_rk], Xth_e) Xth_eT = transpose(Xth_e) elem_ce = elem_c(ie,:) Xc_eT = transpose(this%Xc(elem_ce,:)) call th_e%derivative(Xksi(ig,:), dTtth_dXksi, Ttth) Xt = matmul(Xth_eT, Ttth) dXt_dXksi = matmul(Xth_eT, dTtth_dXksi) call this%derivative(Xt, dTgc_dXt, Tgc, elem_ce) dXg_dXt = matmul(Xc_eT, dTgc_dXt) dTgc_dXg = matmul(dTgc_dXt, inv(dXg_dXt)) dXg_dXksi = matmul(dXg_dXt, dXt_dXksi) det_dXg_dXksi = det(dXg_dXksi) dV = det_dXg_dXksi*Wksi(ig) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine cmp_volume(this, volume) class(nurbs_volume), intent(inout) :: this real(rk), intent(out) :: volume real(rk), allocatable :: Tgc(:), dTgc_dXg(:,:) integer :: ie, ig real(rk) :: dV, dV_ig volume = 0.0_rk #if defined(__NVCOMPILER) do ie = 1, size(this%cmp_elem(),1) #else do concurrent (ie = 1:size(this%cmp_elem(),1)) reduce(+:volume) #endif dV = 0.0_rk do ig = 1, size(this%cmp_elem(),2) call this%ansatz(ie, ig, Tgc, dTgc_dXg, dV_ig) dV = dV + dV_ig end do volume = volume + dV end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function cmp_Tgc_3d(Xti, knot1, knot2, knot3, nc, degree, Wc) result(Tgc) real(rk), intent(in), contiguous :: Xti(:) real(rk), intent(in), contiguous :: knot1(:) real(rk), intent(in), contiguous :: knot2(:) real(rk), intent(in), contiguous :: knot3(:) integer, intent(in) :: degree(3), nc(3) real(rk), intent(in), contiguous :: Wc(:) real(rk) :: Tgc(nc(1)*nc(2)*nc(3)) real(rk) :: tmp integer :: i Tgc = kron(basis_bspline(Xti(3), knot3, nc(3), degree(3)),& kron(& basis_bspline(Xti(2), knot2, nc(2), degree(2)),& basis_bspline(Xti(1), knot1, nc(1), degree(1)))) tmp = dot_product(Tgc, Wc) do concurrent (i = 1: nc(1)*nc(2)*nc(3)) Tgc(i) = (Tgc(i) * Wc(i)) / tmp end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Xg_nurbs_3d(Xt, knot1, knot2, knot3, degree, nc, ng, Xc, Wc) result(Xg) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Xg(:,:) integer :: i allocate(Xg(ng(1)*ng(2)*ng(3), size(Xc,2))) #if defined(__NVCOMPILER) do i = 1, ng(1)*ng(2)*ng(3) #else do concurrent (i = 1: ng(1)*ng(2)*ng(3)) #endif Xg(i,:) = matmul(cmp_Tgc_3d(Xt(i,:), knot1, knot2, knot3, nc, degree, Wc), Xc) end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Xg_nurbs_3d_1point(Xt, knot1, knot2, knot3, degree, nc, Xc, Wc) result(Xg) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Xg(:) real(rk), allocatable :: Tgc(:) allocate(Xg(size(Xc,2))) allocate(Tgc(nc(1)*nc(2)*nc(3))) Tgc = kron(basis_bspline(Xt(3), knot3, nc(3), degree(3)),& kron(& basis_bspline(Xt(2), knot2, nc(2), degree(2)),& basis_bspline(Xt(1), knot1, nc(1), degree(1)))) Tgc = Tgc*(Wc/(dot_product(Tgc,Wc))) Xg = matmul(Tgc, Xc) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Xg_bspline_3d(Xt, knot1, knot2, knot3, degree, nc, ng, Xc) result(Xg) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), allocatable :: Xg(:,:) integer :: i allocate(Xg(ng(1)*ng(2)*ng(3), size(Xc,2))) #if defined(__NVCOMPILER) do i = 1, ng(1)*ng(2)*ng(3) #else do concurrent (i = 1: ng(1)*ng(2)*ng(3)) #endif Xg(i,:) = matmul(kron(basis_bspline(Xt(i,3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(i,2), knot2, nc(2), degree(2)),& basis_bspline(Xt(i,1), knot1, nc(1), degree(1)))),& Xc) end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Xg_bspline_3d_1point(Xt, knot1, knot2, knot3, degree, nc, Xc) result(Xg) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) real(rk), intent(in), contiguous :: Xc(:,:) real(rk), allocatable :: Xg(:) allocate(Xg(size(Xc,2))) Xg = matmul(kron(basis_bspline(Xt(3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(2), knot2, nc(2), degree(2)),& basis_bspline(Xt(1), knot1, nc(1), degree(1)))),& Xc) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_dTgc_nurbs_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng, Wc, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable, intent(out) :: dTgc(:,:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) real(rk), allocatable :: dBi(:,:), Bi(:) integer :: i allocate(dTgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) allocate(Bi(nc(1)*nc(2)*nc(3)), dBi(nc(1)*nc(2)*nc(3), 3)) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif call basis_bspline_der(Xt(i,1), knot1, nc(1), degree(1), dB1, B1) call basis_bspline_der(Xt(i,2), knot2, nc(2), degree(2), dB2, B2) call basis_bspline_der(Xt(i,3), knot3, nc(3), degree(3), dB3, B3) Bi = kron( B3, kron( B2, B1)) Tgc(i,:) = Bi*(Wc/(dot_product(Bi,Wc))) dBi(:,1) = kron(kron(B3,B2),dB1) dBi(:,2) = kron(kron(B3,dB2),B1) dBi(:,3) = kron(kron(dB3,B2),B1) dTgc(i,:,1) = ( dBi(:,1)*Wc - Tgc(i,:)*dot_product(dBi(:,1),Wc) ) / dot_product(Bi,Wc) dTgc(i,:,2) = ( dBi(:,2)*Wc - Tgc(i,:)*dot_product(dBi(:,2),Wc) ) / dot_product(Bi,Wc) dTgc(i,:,3) = ( dBi(:,3)*Wc - Tgc(i,:)*dot_product(dBi(:,3),Wc) ) / dot_product(Bi,Wc) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_dTgc_nurbs_3d_scalar(Xt, knot1, knot2, knot3, degree, nc, Wc, dTgc, Tgc, elem) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) 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) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) real(rk), allocatable :: dBi(:,:), Bi(:) call basis_bspline_der(Xt(1), knot1, nc(1), degree(1), dB1, B1) call basis_bspline_der(Xt(2), knot2, nc(2), degree(2), dB2, B2) call basis_bspline_der(Xt(3), knot3, nc(3), degree(3), dB3, B3) if (.not. present(elem)) then allocate(dTgc(nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(nc(1)*nc(2)*nc(3))) allocate(dBi(nc(1)*nc(2)*nc(3), 3), Bi(nc(1)*nc(2)*nc(3))) Bi = kron( B3, kron( B2, B1)) Tgc = Bi*(Wc/(dot_product(Bi,Wc))) dBi(:,1) = kron(kron(B3,B2),dB1) dBi(:,2) = kron(kron(B3,dB2),B1) dBi(:,3) = kron(kron(dB3,B2),B1) dTgc(:,1) = ( dBi(:,1)*Wc - Tgc*dot_product(dBi(:,1),Wc) ) / dot_product(Bi,Wc) dTgc(:,2) = ( dBi(:,2)*Wc - Tgc*dot_product(dBi(:,2),Wc) ) / dot_product(Bi,Wc) dTgc(:,3) = ( dBi(:,3)*Wc - Tgc*dot_product(dBi(:,3),Wc) ) / dot_product(Bi,Wc) else allocate(dTgc(size(elem), 3)) allocate(Tgc(size(elem))) allocate(dBi(size(elem), 3), Bi(size(elem))) associate(Biall => kron( B3, kron( B2, B1))) Bi = Biall(elem) Tgc = Bi*(Wc(elem)/(dot_product(Bi,Wc(elem)))) end associate associate(dB1all => kron(kron(B3,B2),dB1), dB2all => kron(kron(B3,dB2),B1), dB3all => kron(kron(dB3,B2),B1)) dBi(:,1) = dB1all(elem) dBi(:,2) = dB2all(elem) dBi(:,3) = dB3all(elem) end associate dTgc(:,1) = ( dBi(:,1)*Wc(elem) - Tgc*dot_product(dBi(:,1),Wc(elem)) ) / dot_product(Bi,Wc(elem)) dTgc(:,2) = ( dBi(:,2)*Wc(elem) - Tgc*dot_product(dBi(:,2),Wc(elem)) ) / dot_product(Bi,Wc(elem)) dTgc(:,3) = ( dBi(:,3)*Wc(elem) - Tgc*dot_product(dBi(:,3),Wc(elem)) ) / dot_product(Bi,Wc(elem)) end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_dTgc_bspline_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), allocatable, intent(out) :: dTgc(:,:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) integer :: i allocate(dTgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif call basis_bspline_der(Xt(i,1), knot1, nc(1), degree(1), dB1, B1) call basis_bspline_der(Xt(i,2), knot2, nc(2), degree(2), dB2, B2) call basis_bspline_der(Xt(i,3), knot3, nc(3), degree(3), dB3, B3) Tgc(i,:) = kron(B3, kron(B2, B1)) dTgc(i,:,1) = kron(kron(B3,B2),dB1) dTgc(i,:,2) = kron(kron(B3,dB2),B1) dTgc(i,:,3) = kron(kron(dB3,B2),B1) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_dTgc_bspline_3d_scalar(Xt, knot1, knot2, knot3, degree, nc, dTgc, Tgc, elem) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in), optional :: elem(:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) call basis_bspline_der(Xt(1), knot1, nc(1), degree(1), dB1, B1) call basis_bspline_der(Xt(2), knot2, nc(2), degree(2), dB2, B2) call basis_bspline_der(Xt(3), knot3, nc(3), degree(3), dB3, B3) if (.not. present(elem)) then allocate(dTgc(nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(nc(1)*nc(2)*nc(3))) Tgc = kron(B3, kron(B2, B1)) dTgc(:,1) = kron(kron(B3,B2),dB1) dTgc(:,2) = kron(kron(B3,dB2),B1) dTgc(:,3) = kron(kron(dB3,B2),B1) else allocate(dTgc(size(elem), 3)) allocate(Tgc(size(elem))) associate(B => kron(B3, kron(B2, B1))) Tgc = B(elem) end associate associate(dB1 => kron(kron(B3,B2),dB1), dB2 => kron(kron(B3,dB2),B1), dB3 => kron(kron(dB3,B2),B1)) dTgc(:,1) = dB1(elem) dTgc(:,2) = dB2(elem) dTgc(:,3) = dB3(elem) end associate end if end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_d2Tgc_nurbs_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng, Wc, d2Tgc, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) 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) :: d2B1(nc(1)), d2B2(nc(2)), d2B3(nc(3)) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) real(rk), allocatable :: Tgci(:), dTgci(:) real(rk), allocatable :: d2Bi(:,:), dBi(:,:), Bi(:) integer :: i allocate(Bi(nc(1)*nc(2)*nc(3)), dBi(nc(1)*nc(2)*nc(3), 3), d2Bi(3*nc(1)*nc(2)*nc(3), 3)) allocate(Tgci(nc(1)*nc(2)*nc(3)), dTgci(nc(1)*nc(2)*nc(3))) allocate(d2Tgc(ng(1)*ng(2)*ng(3), 3*nc(1)*nc(2)*nc(3), 3)) allocate(dTgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif call basis_bspline_2der(Xt(i,1), knot1, nc(1), degree(1), d2B1, dB1, B1) call basis_bspline_2der(Xt(i,2), knot2, nc(2), degree(2), d2B2, dB2, B2) call basis_bspline_2der(Xt(i,3), knot3, nc(3), degree(3), d2B3, dB3, B3) Bi = kron(B3, kron(B2, B1)) Tgc(i,:) = Bi*(Wc/(dot_product(Bi,Wc))) dBi(:,1) = kron(kron(B3,B2),dB1) dBi(:,2) = kron(kron(B3,dB2),B1) dBi(:,3) = kron(kron(dB3,B2),B1) dTgc(i,:,1) = ( dBi(:,1)*Wc - Tgc(i,:)*dot_product(dBi(:,1),Wc) ) / dot_product(Bi,Wc) dTgc(i,:,2) = ( dBi(:,2)*Wc - Tgc(i,:)*dot_product(dBi(:,2),Wc) ) / dot_product(Bi,Wc) dTgc(i,:,3) = ( dBi(:,3)*Wc - Tgc(i,:)*dot_product(dBi(:,3),Wc) ) / dot_product(Bi,Wc) d2Bi(1:nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,B2),d2B1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,dB2),dB1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = kron(kron(dB3,B2),dB1) d2Bi(1:nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,dB2),dB1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,d2B2),B1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = kron(kron(dB3,dB2),B1) d2Bi(1:nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,B2),dB1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,dB2),B1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = kron(kron(d2B3,B2),B1) d2Tgc(i, 1:nc(1)*nc(2)*nc(3) ,1) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,1)*Wc & - 2.0_rk*dTgc(i, :,1)*dot_product(dBi(:,1),Wc) & - Tgc(i,:)*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(i, nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1)*Wc & - dTgc(i, :,1)*dot_product(dBi(:,2),Wc) - dTgc(i, :,2)*dot_product(dBi(:,1),Wc) & - Tgc(i,:)*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(i, 2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1)*Wc & - dTgc(i, :,1)*dot_product(dBi(:,3),Wc) - dTgc(i, :,3)*dot_product(dBi(:,1),Wc) & - Tgc(i,:)*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(i, 1:nc(1)*nc(2)*nc(3) ,2) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,2)*Wc & - dTgc(i, :,1)*dot_product(dBi(:,2),Wc) - dTgc(i, :,2)*dot_product(dBi(:,1),Wc) & - Tgc(i,:)*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(i, nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2)*Wc & - 2.0_rk*dTgc(i, :,2)*dot_product(dBi(:,2),Wc) & - Tgc(i,:)*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(i, 2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2)*Wc & - dTgc(i, :,2)*dot_product(dBi(:,3),Wc) - dTgc(i, :,3)*dot_product(dBi(:,2),Wc) & - Tgc(i,:)*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(i, 1:nc(1)*nc(2)*nc(3) ,3) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,3)*Wc & - dTgc(i, :,1)*dot_product(dBi(:,3),Wc) - dTgc(i, :,3)*dot_product(dBi(:,1),Wc) & - Tgc(i,:)*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) d2Tgc(i, nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3)*Wc & - dTgc(i, :,2)*dot_product(dBi(:,3),Wc) - dTgc(i, :,3)*dot_product(dBi(:,2),Wc) & - Tgc(i,:)*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) d2Tgc(i, 2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3)*Wc & - 2.0_rk*dTgc(i, :,3)*dot_product(dBi(:,3),Wc) & - Tgc(i,:)*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_d2Tgc_nurbs_3d_scalar(Xt, knot1, knot2, knot3, degree, nc, Wc, d2Tgc, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) 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) :: d2B1(nc(1)), d2B2(nc(2)), d2B3(nc(3)) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) real(rk), allocatable :: d2Bi(:,:), dBi(:,:), Bi(:) allocate(Bi(nc(1)*nc(2)*nc(3)), dBi(nc(1)*nc(2)*nc(3), 3), d2Bi(3*nc(1)*nc(2)*nc(3), 3)) allocate(d2Tgc(3*nc(1)*nc(2)*nc(3), 3)) allocate(dTgc(nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(nc(1)*nc(2)*nc(3))) call basis_bspline_2der(Xt(1), knot1, nc(1), degree(1), d2B1, dB1, B1) call basis_bspline_2der(Xt(2), knot2, nc(2), degree(2), d2B2, dB2, B2) call basis_bspline_2der(Xt(3), knot3, nc(3), degree(3), d2B3, dB3, B3) Bi = kron(B3, kron(B2, B1)) Tgc = Bi*(Wc/(dot_product(Bi,Wc))) dBi(:,1) = kron(kron(B3,B2),dB1) dBi(:,2) = kron(kron(B3,dB2),B1) dBi(:,3) = kron(kron(dB3,B2),B1) dTgc(:,1) = ( dBi(:,1)*Wc - Tgc*dot_product(dBi(:,1),Wc) ) / dot_product(Bi,Wc) dTgc(:,2) = ( dBi(:,2)*Wc - Tgc*dot_product(dBi(:,2),Wc) ) / dot_product(Bi,Wc) dTgc(:,3) = ( dBi(:,3)*Wc - Tgc*dot_product(dBi(:,3),Wc) ) / dot_product(Bi,Wc) d2Bi(1:nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,B2),d2B1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,dB2),dB1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = kron(kron(dB3,B2),dB1) d2Bi(1:nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,dB2),dB1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,d2B2),B1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = kron(kron(dB3,dB2),B1) d2Bi(1:nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,B2),dB1) d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,dB2),B1) d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = kron(kron(d2B3,B2),B1) d2Tgc(1:nc(1)*nc(2)*nc(3) ,1) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,1)*Wc & - 2.0_rk*dTgc(:,1)*dot_product(dBi(:,1),Wc) & - Tgc*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1)*Wc & - dTgc(:,1)*dot_product(dBi(:,2),Wc) - dTgc(:,2)*dot_product(dBi(:,1),Wc) & - Tgc*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1)*Wc & - dTgc(:,1)*dot_product(dBi(:,3),Wc) - dTgc(:,3)*dot_product(dBi(:,1),Wc) & - Tgc*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1),Wc)) / dot_product(Bi,Wc) d2Tgc(1:nc(1)*nc(2)*nc(3) ,2) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,2)*Wc & - dTgc(:,1)*dot_product(dBi(:,2),Wc) - dTgc(:,2)*dot_product(dBi(:,1),Wc) & - Tgc*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2)*Wc & - 2.0_rk*dTgc(:,2)*dot_product(dBi(:,2),Wc) & - Tgc*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2)*Wc & - dTgc(:,2)*dot_product(dBi(:,3),Wc) - dTgc(:,3)*dot_product(dBi(:,2),Wc) & - Tgc*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2),Wc)) / dot_product(Bi,Wc) d2Tgc(1:nc(1)*nc(2)*nc(3) ,3) = (d2Bi(1:nc(1)*nc(2)*nc(3) ,3)*Wc & - dTgc(:,1)*dot_product(dBi(:,3),Wc) - dTgc(:,3)*dot_product(dBi(:,1),Wc) & - Tgc*dot_product(d2Bi(1:nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = (d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3)*Wc & - dTgc(:,2)*dot_product(dBi(:,3),Wc) - dTgc(:,3)*dot_product(dBi(:,2),Wc) & - Tgc*dot_product(d2Bi(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = (d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3)*Wc & - 2.0_rk*dTgc(:,3)*dot_product(dBi(:,3),Wc) & - Tgc*dot_product(d2Bi(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3),Wc)) / dot_product(Bi,Wc) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_d2Tgc_bspline_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng, d2Tgc, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), allocatable, intent(out) :: d2Tgc(:,:,:) real(rk), allocatable, intent(out) :: dTgc(:,:,:) real(rk), allocatable, intent(out) :: Tgc(:,:) integer :: i real(rk) :: d2B1(nc(1)), d2B2(nc(2)), d2B3(nc(3)) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) allocate(d2Tgc(ng(1)*ng(2)*ng(3), 3*nc(1)*nc(2)*nc(3), 3)) allocate(dTgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif call basis_bspline_2der(Xt(i,1), knot1, nc(1), degree(1), d2B1, dB1, B1) call basis_bspline_2der(Xt(i,2), knot2, nc(2), degree(2), d2B2, dB2, B2) call basis_bspline_2der(Xt(i,3), knot3, nc(3), degree(3), d2B3, dB3, B3) Tgc(i,:) = kron(B3, kron(B2, B1)) dTgc(i,:,1) = kron(kron(B3,B2),dB1) dTgc(i,:,2) = kron(kron(B3,dB2),B1) dTgc(i,:,3) = kron(kron(dB3,B2),B1) d2Tgc(i,1:nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,B2),d2B1) d2Tgc(i,nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,dB2),dB1) d2Tgc(i,2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = kron(kron(dB3,B2),dB1) d2Tgc(i,1:nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,dB2),dB1) d2Tgc(i,nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,d2B2),B1) d2Tgc(i,2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = kron(kron(dB3,dB2),B1) d2Tgc(i,1:nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,B2),dB1) d2Tgc(i,nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,dB2),B1) d2Tgc(i,2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = kron(kron(d2B3,B2),B1) end do end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine compute_d2Tgc_bspline_3d_scalar(Xt, knot1, knot2, knot3, degree, nc, d2Tgc, dTgc, Tgc) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) real(rk), allocatable, intent(out) :: d2Tgc(:,:) real(rk), allocatable, intent(out) :: dTgc(:,:) real(rk), allocatable, intent(out) :: Tgc(:) real(rk) :: d2B1(nc(1)), d2B2(nc(2)), d2B3(nc(3)) real(rk) :: dB1(nc(1)), dB2(nc(2)), dB3(nc(3)) real(rk) :: B1(nc(1)), B2(nc(2)), B3(nc(3)) allocate(d2Tgc(3*nc(1)*nc(2)*nc(3), 3)) allocate(dTgc(nc(1)*nc(2)*nc(3), 3)) allocate(Tgc(nc(1)*nc(2)*nc(3))) call basis_bspline_2der(Xt(1), knot1, nc(1), degree(1), d2B1, dB1, B1) call basis_bspline_2der(Xt(2), knot2, nc(2), degree(2), d2B2, dB2, B2) call basis_bspline_2der(Xt(3), knot3, nc(3), degree(3), d2B3, dB3, B3) Tgc = kron(B3, kron(B2, B1)) dTgc(:,1) = kron(kron(B3,B2),dB1) dTgc(:,2) = kron(kron(B3,dB2),B1) dTgc(:,3) = kron(kron(dB3,B2),B1) d2Tgc(1:nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,B2),d2B1) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,1) = kron(kron(B3,dB2),dB1) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,1) = kron(kron(dB3,B2),dB1) d2Tgc(1:nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,dB2),dB1) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,2) = kron(kron(B3,d2B2),B1) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,2) = kron(kron(dB3,dB2),B1) d2Tgc(1:nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,B2),dB1) d2Tgc(nc(1)*nc(2)*nc(3)+1:2*nc(1)*nc(2)*nc(3) ,3) = kron(kron(dB3,dB2),B1) d2Tgc(2*nc(1)*nc(2)*nc(3)+1:3*nc(1)*nc(2)*nc(3) ,3) = kron(kron(d2B3,B2),B1) end subroutine !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Tgc_nurbs_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng, Wc) result(Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Tgc(:,:) real(rk), allocatable :: Tgci(:) integer :: i allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) allocate(Tgci(nc(1)*nc(2)*nc(3))) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif Tgci = kron(basis_bspline(Xt(i,3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(i,2), knot2, nc(2), degree(2)),& basis_bspline(Xt(i,1), knot1, nc(1), degree(1)))) Tgc(i,:) = Tgci*(Wc/(dot_product(Tgci,Wc))) end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Tgc_nurbs_3d_scalar(Xt, knot1, knot2, knot3, degree, nc, Wc) result(Tgc) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) real(rk), intent(in), contiguous :: Wc(:) real(rk), allocatable :: Tgc(:) allocate(Tgc(nc(1)*nc(2)*nc(3))) Tgc = kron(basis_bspline(Xt(3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(2), knot2, nc(2), degree(2)),& basis_bspline(Xt(1), knot1, nc(1), degree(1)))) Tgc = Tgc*(Wc/(dot_product(Tgc,Wc))) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Tgc_bspline_3d_vector(Xt, knot1, knot2, knot3, degree, nc, ng) result(Tgc) real(rk), intent(in), contiguous :: Xt(:,:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) integer, intent(in) :: ng(3) real(rk), allocatable :: Tgc(:,:) integer :: i allocate(Tgc(ng(1)*ng(2)*ng(3), nc(1)*nc(2)*nc(3))) #if defined(__NVCOMPILER) do i = 1, size(Xt, 1) #else do concurrent (i = 1: size(Xt, 1)) #endif Tgc(i,:) = kron(basis_bspline(Xt(i,3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(i,2), knot2, nc(2), degree(2)),& basis_bspline(Xt(i,1), knot1, nc(1), degree(1)))) end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function compute_Tgc_bspline_3d_scalar(Xt, knot1, knot2, knot3, degree, nc) result(Tgc) real(rk), intent(in), contiguous :: Xt(:) real(rk), intent(in), contiguous :: knot1(:), knot2(:), knot3(:) integer, intent(in) :: degree(3) integer, intent(in) :: nc(3) real(rk), allocatable :: Tgc(:) allocate(Tgc(nc(1)*nc(2)*nc(3))) Tgc= kron(basis_bspline(Xt(3), knot3, nc(3), degree(3)), kron(& basis_bspline(Xt(2), knot2, nc(2), degree(2)),& basis_bspline(Xt(1), knot1, nc(1), degree(1)))) end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure function nearest_point_help_3d(ng, Xg, point_Xg) result(distances) integer, intent(in) :: ng(3) real(rk), intent(in), contiguous :: Xg(:,:) real(rk), intent(in), contiguous :: point_Xg(:) real(rk), allocatable :: distances(:) integer :: i allocate(distances(ng(1)*ng(2)*ng(3))) #if defined(__NVCOMPILER) do i = 1, ng(1)*ng(2)*ng(3) #else do concurrent (i = 1: ng(1)*ng(2)*ng(3)) #endif distances(i) = norm2(Xg(i,:) - point_Xg) end do end function !=============================================================================== !=============================================================================== !> author: Seyed Ali Ghasemi !> license: BSD 3-Clause pure subroutine lsq_fit_bspline(this, Xt, Xdata, ndata) use forcad_interface, only: solve class(nurbs_volume), intent(inout) :: this real(rk), intent(in), contiguous :: Xt(:,:), Xdata(:,:) integer, intent(in) :: ndata(3) real(rk), allocatable :: T(:,:), Tt(:,:) integer :: i, n if (this%nc(1) > ndata(1)) error stop "Error: in the first direction, number of control points exceeds number of data points." if (this%nc(2) > ndata(2)) error stop "Error: in the second direction, number of control points exceeds number of data points." if (this%nc(3) > ndata(3)) error stop "Error: in the third direction, number of control points exceeds number of data points." n = ndata(1)*ndata(2)*ndata(3) allocate(T(n, this%nc(1)*this%nc(2)*this%nc(3))) #if defined(__NVCOMPILER) || (defined(__GFORTRAN__) && (__GNUC__ < 15 || (__GNUC__ == 15 && __GNUC_MINOR__ < 1))) do i = 1, n #else do concurrent (i = 1: n) #endif T(i,:) = kron(& basis_bspline(Xt(i,3), this%knot3, this%nc(3), this%degree(3)), kron(& basis_bspline(Xt(i,2), this%knot2, this%nc(2), this%degree(2)),& basis_bspline(Xt(i,1), this%knot1, this%nc(1), this%degree(1)))) end do Tt = transpose(T) this%Xc = solve(matmul(Tt, T), matmul(Tt, Xdata)) end subroutine !=============================================================================== end module forcad_nurbs_volume