nurbs_volume – ForCAD

type, public :: nurbs_volume

Components

Type	Visibility	Attributes		Name
real(kind=rk),	private,	allocatable	::	Wc(:)	Weights for the control points (1D array: [nc(1)nc(2)nc(3)])
real(kind=rk),	private,	allocatable	::	Xc(:,:)	Control points (2D array: [nc(1)nc(2)nc(3), dim])
real(kind=rk),	private,	allocatable	::	Xg(:,:)	Geometry points (2D array: [ng(1)ng(2)ng(3), dim])
real(kind=rk),	private,	allocatable	::	Xt(:,:)	Evaluation parameter values (2D array: [ng(1)ng(2)ng(3), dim]
real(kind=rk),	private,	allocatable	::	Xt1(:)	Evaluation parameter values in the first direction (1D array: [ng(1)])
real(kind=rk),	private,	allocatable	::	Xt2(:)	Evaluation parameter values in the second direction (1D array: [ng(2)])
real(kind=rk),	private,	allocatable	::	Xt3(:)	Evaluation parameter values in the third direction (1D array: [ng(3)])
integer,	private		::	degree(3)	Degree (order) of the volume
integer,	private,	allocatable	::	elemConn(:,:)	IGA element connectivity
integer,	private,	allocatable	::	elemConn_Xc_vis(:,:)	Connectivity for visualization of control points
integer,	private,	allocatable	::	elemConn_Xg_vis(:,:)	Connectivity for visualization of geometry points
real(kind=rk),	private,	allocatable	::	knot1(:)	Knot vector in the first direction (1D array)
real(kind=rk),	private,	allocatable	::	knot2(:)	Knot vector in the second direction (1D array)
real(kind=rk),	private,	allocatable	::	knot3(:)	Knot vector in the third direction (1D array)
integer,	private		::	nc(3)	Number of control points in each direction
integer,	private		::	ng(3)	Number of geometry points in each direction

Type-Bound Procedures

procedure, public :: ansatz

Compute the shape functions, derivative of shape functions and dV

private pure subroutine ansatz(this, ie, ig, Tgc, dTgc_dXg, dV)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
integer,	intent(in)		::	ie
integer,	intent(in)		::	ig
real(kind=rk),	intent(out),	allocatable	::	Tgc(:)
real(kind=rk),	intent(out),	allocatable	::	dTgc_dXg(:,:)
real(kind=rk),	intent(out)		::	dV

generic, public :: basis => basis_vector, basis_scalar

Compute the basis functions of the NURBS volume

private pure subroutine basis_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	Tgc(:,:)

private pure subroutine basis_scalar(this, Xt, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	Xt(:)
real(kind=rk),	intent(out),	allocatable	::	Tgc(:)

procedure, public :: cmp_Xg

Compute geometry points

private pure function cmp_Xg(this, Xt) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xt(:)

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

procedure, public :: cmp_degree

Compute degree of the NURBS volume

private pure subroutine cmp_degree(this, dir)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	dir

procedure, public :: cmp_degreeFace

Compute degrees of the faces

private pure function cmp_degreeFace(this, face) result(degree)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	face

Return Value integer, (3)

procedure, public :: cmp_elem

Generate IGA element connectivity

private pure function cmp_elem(this) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_elemFace

Compute faces of the IGA elements

private pure function cmp_elemFace(this, elem, face) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

number of nodes in each direction

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	elem
integer,	intent(in)	::	face

Return Value integer, allocatable, (:)

procedure, public :: cmp_elemFace_Xc_vis

Compute faces of the control points

private pure function cmp_elemFace_Xc_vis(this, elem, face) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

number of nodes in each direction

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	elem
integer,	intent(in)	::	face

Return Value integer, allocatable, (:)

procedure, public :: cmp_elemFace_Xg_vis

Compute faces of the geometry points

private pure function cmp_elemFace_Xg_vis(this, elem, face) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

number of nodes in each direction

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	elem
integer,	intent(in)	::	face

Return Value integer, allocatable, (:)

procedure, public :: cmp_elem_Xc_vis

Generate connectivity for control points

private pure function cmp_elem_Xc_vis(this, p) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in),	optional,	contiguous	::	p(:)

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_elem_Xg_vis

Generate connectivity for geometry points

private pure function cmp_elem_Xg_vis(this, p) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in),	optional,	contiguous	::	p(:)

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_nc

Compute number of required control points

private pure subroutine cmp_nc(this, dir)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	dir

procedure, public :: cmp_volume

Compute the volume of the NURBS volume

private pure subroutine cmp_volume(this, volume)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(out)			::	volume

procedure, public :: create

Generate geometry points

private pure subroutine create(this, res1, res2, res3, Xt1, Xt2, Xt3, Xt)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt(:,:)

generic, public :: derivative => derivative_vector, derivative_scalar

Compute the derivative of the NURBS volume

private pure subroutine derivative_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	dTgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:,:)

private pure subroutine derivative_scalar(this, Xt, dTgc, Tgc, elem)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xt(:)
real(kind=rk),	intent(out),		allocatable	::	dTgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:)
integer,	intent(in),	optional		::	elem(:)

generic, public :: derivative2 => derivative2_vector, derivative2_scalar

Compute the second derivative of the NURBS volume

private pure subroutine derivative2_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, d2Tgc, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	d2Tgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	dTgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:,:)

private pure subroutine derivative2_scalar(this, Xt, d2Tgc, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xt(:)
real(kind=rk),	intent(out),		allocatable	::	d2Tgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	dTgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:)

procedure, public :: elevate_degree

Elevate the degree of the NURBS volume

private pure subroutine elevate_degree(this, dir, t)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
integer,	intent(in)	::	dir
integer,	intent(in)	::	t

procedure, public :: export_Xc

Export control points to VTK file

private impure subroutine export_Xc(this, filename)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
character(len=*),	intent(in)			::	filename

procedure, public :: export_Xg

Export geometry points to VTK file

private impure subroutine export_Xg(this, filename)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
character(len=*),	intent(in)			::	filename

procedure, public :: finalize

Finalize the NURBS volume object

private pure subroutine finalize(this)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this

generic, public :: get_Wc => get_Wc_all, get_Wci

Get weights

private pure function get_Wc_all(this) result(Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

private pure function get_Wci(this, n) result(Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

Return Value real(kind=rk)

generic, public :: get_Xc => get_Xc_all, get_Xci, get_Xcid

Get control points

private pure function get_Xc_all(this) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

private pure function get_Xci(this, n) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

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

private pure function get_Xcid(this, n, dir) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	n
integer,	intent(in)	::	dir

Return Value real(kind=rk)

generic, public :: get_Xg => get_Xg_all, get_Xgi, get_Xgid

Get geometry points

private pure function get_Xg_all(this) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

private pure function get_Xgi(this, n) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

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

private pure function get_Xgid(this, n, dir) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	n
integer,	intent(in)	::	dir

Return Value real(kind=rk)

procedure, public :: get_Xt

Get parameter values

private pure function get_Xt(this, dir) result(Xt)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

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

procedure, public :: get_continuity

Compute and return the continuity of the NURBS volume

private pure function get_continuity(this, dir) result(c)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

Return Value integer, allocatable, (:)

generic, public :: get_degree => get_degree_all, get_degree_dir

Get degree of the NURBS volume

private pure function get_degree_all(this) result(degree)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, (3)

private pure function get_degree_dir(this, dir) result(degree)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

Return Value integer

procedure, public :: get_elem

Get IGA element connectivity

private pure function get_elem(this) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, allocatable, (:,:)

procedure, public :: get_elem_Xc_vis

Get connectivity for control points

private pure function get_elem_Xc_vis(this) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, allocatable, (:,:)

procedure, public :: get_elem_Xg_vis

Get connectivity for geometry points

private pure function get_elem_Xg_vis(this) result(elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, allocatable, (:,:)

generic, public :: get_knot => get_knoti, get_knot_all

Get knot vector

private pure function get_knoti(this, dir, i) result(knot)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	dir
integer,	intent(in)	::	i

Return Value real(kind=rk)

private pure function get_knot_all(this, dir) result(knot)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

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

procedure, public :: get_multiplicity

Compute and return the multiplicity of the knots

private pure function get_multiplicity(this, dir) result(m)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

Return Value integer, allocatable, (:)

generic, public :: get_nc => get_nc_all, get_nc_dir

Get number of control points

private pure function get_nc_all(this) result(nc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, (3)

private pure function get_nc_dir(this, dir) result(nc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

Return Value integer

procedure, public :: get_ng

Get number of geometry points

private pure function get_ng(this) result(ng)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, (3)

procedure, public :: insert_knots

Insert knots into the knot vector

private pure subroutine insert_knots(this, dir, Xth, r)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
integer,	intent(in)		::	dir
real(kind=rk),	intent(in),	contiguous	::	Xth(:)
integer,	intent(in),	contiguous	::	r(:)

procedure, public :: is_rational

Check if the NURBS volume is rational

private pure function is_rational(this) result(r)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value logical

procedure, public :: modify_Wc

Modify weights

private pure subroutine modify_Wc(this, W, num)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
real(kind=rk),	intent(in)	::	W
integer,	intent(in)	::	num

procedure, public :: modify_Xc

Modify control points

private pure subroutine modify_Xc(this, X, num, dir)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
real(kind=rk),	intent(in)	::	X
integer,	intent(in)	::	num
integer,	intent(in)	::	dir

procedure, public :: nearest_point

Find the nearest point on the NURBS volume (Approximation)

private pure subroutine nearest_point(this, point_Xg, nearest_Xg, nearest_Xt, id)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
real(kind=rk),	intent(in)			::	point_Xg(:)
real(kind=rk),	intent(out),	optional,	allocatable	::	nearest_Xg(:)
real(kind=rk),	intent(out),	optional,	allocatable	::	nearest_Xt(:)
integer,	intent(out),	optional		::	id

procedure, public :: nearest_point2

Find the nearest point on the NURBS volume (Minimization - Newton's method)

private impure subroutine nearest_point2(this, point_Xg, tol, maxit, nearest_Xt, nearest_Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in)			::	point_Xg(:)
real(kind=rk),	intent(in)			::	tol
integer,	intent(in)			::	maxit
real(kind=rk),	intent(out)			::	nearest_Xt(3)
real(kind=rk),	intent(out),	optional,	allocatable	::	nearest_Xg(:)

procedure, public :: put_to_nurbs

Put a shape to a NURBS volume

private pure subroutine put_to_nurbs(this, X, elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	X(:,:)
integer,	intent(in),	contiguous	::	elemConn(:,:)

procedure, public :: remove_knots

Remove knots from the knot vector

private pure subroutine remove_knots(this, dir, Xth, r)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
integer,	intent(in)		::	dir
real(kind=rk),	intent(in),	contiguous	::	Xth(:)
integer,	intent(in),	contiguous	::	r(:)

procedure, public :: rotate_Xc

Rotate control points

private pure subroutine rotate_Xc(this, alpha, beta, theta)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
real(kind=rk),	intent(in)	::	alpha
real(kind=rk),	intent(in)	::	beta
real(kind=rk),	intent(in)	::	theta

procedure, public :: rotate_Xg

Rotate geometry points

private pure subroutine rotate_Xg(this, alpha, beta, theta)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
real(kind=rk),	intent(in)	::	alpha
real(kind=rk),	intent(in)	::	beta
real(kind=rk),	intent(in)	::	theta

generic, public :: set => set1, set2, set3, set4

Set NURBS volume

private pure subroutine set1(this, knot1, knot2, knot3, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set control points and weights for the NURBS volume object.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	knot1(:)
real(kind=rk),	intent(in),		contiguous	::	knot2(:)
real(kind=rk),	intent(in),		contiguous	::	knot3(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

private pure subroutine set2(this, Xth_dir1, Xth_dir2, Xth_dir3, degree, continuity1, continuity2, continuity3, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set control points and weights for the NURBS volume object.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xth_dir1(:)
real(kind=rk),	intent(in),		contiguous	::	Xth_dir2(:)
real(kind=rk),	intent(in),		contiguous	::	Xth_dir3(:)
integer,	intent(in),		contiguous	::	degree(:)
integer,	intent(in),		contiguous	::	continuity1(:)
integer,	intent(in),		contiguous	::	continuity2(:)
integer,	intent(in),		contiguous	::	continuity3(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

private pure subroutine set3(this, nc, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set Bezier or Rational Bezier volume using control points and weights.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	nc(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

private pure subroutine set4(this, degree, nc, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	degree(:)
integer,	intent(in),		contiguous	::	nc(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set1

Set knot vectors, control points and weights for the NURBS volume object

private pure subroutine set1(this, knot1, knot2, knot3, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set control points and weights for the NURBS volume object.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	knot1(:)
real(kind=rk),	intent(in),		contiguous	::	knot2(:)
real(kind=rk),	intent(in),		contiguous	::	knot3(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set2

Set NURBS volume using nodes of parameter space, degree, continuity, control points and weights

private pure subroutine set2(this, Xth_dir1, Xth_dir2, Xth_dir3, degree, continuity1, continuity2, continuity3, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set control points and weights for the NURBS volume object.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xth_dir1(:)
real(kind=rk),	intent(in),		contiguous	::	Xth_dir2(:)
real(kind=rk),	intent(in),		contiguous	::	Xth_dir3(:)
integer,	intent(in),		contiguous	::	degree(:)
integer,	intent(in),		contiguous	::	continuity1(:)
integer,	intent(in),		contiguous	::	continuity2(:)
integer,	intent(in),		contiguous	::	continuity3(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set3

Set Bezier or Rational Bezier volume using control points and weights

private pure subroutine set3(this, nc, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Set Bezier or Rational Bezier volume using control points and weights.

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	nc(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set4

Set NURBS volume using degree, number of control points, control points and weights

private pure subroutine set4(this, degree, nc, Xc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	degree(:)
integer,	intent(in),		contiguous	::	nc(:)
real(kind=rk),	intent(in),		contiguous	::	Xc(:,:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set_C

Set a C-shape

private pure subroutine set_C(this, center, radius1, radius2, length)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	center(:)
real(kind=rk),	intent(in)		::	radius1
real(kind=rk),	intent(in)		::	radius2
real(kind=rk),	intent(in)		::	length

procedure, public :: set_elem

Set IGA element connectivity

private pure subroutine set_elem(this, elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	elemConn(:,:)

procedure, public :: set_elem_Xc_vis

Set connectivity for control points

private pure subroutine set_elem_Xc_vis(this, elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	elemConn(:,:)

procedure, public :: set_elem_Xg_vis

Set connectivity for geometry points

private pure subroutine set_elem_Xg_vis(this, elemConn)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),		contiguous	::	elemConn(:,:)

procedure, public :: set_half_ring

Set a half ring

private pure subroutine set_half_ring(this, center, radius1, radius2, length)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	center(:)
real(kind=rk),	intent(in)		::	radius1
real(kind=rk),	intent(in)		::	radius2
real(kind=rk),	intent(in)		::	length

procedure, public :: set_hexahedron

Set a hexahedron

private pure subroutine set_hexahedron(this, L, nc, Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	L(:)
integer,	intent(in),		contiguous	::	nc(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Wc(:)

procedure, public :: set_ring

Set a ring

private pure subroutine set_ring(this, center, radius1, radius2, length)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	center(:)
real(kind=rk),	intent(in)		::	radius1
real(kind=rk),	intent(in)		::	radius2
real(kind=rk),	intent(in)		::	length

procedure, public :: show

Show the NURBS object using PyVista

private impure subroutine show(this, vtkfile_Xc, vtkfile_Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(inout)	::	this
character(len=*),	intent(in)	::	vtkfile_Xc
character(len=*),	intent(in)	::	vtkfile_Xg

procedure, public :: translate_Xc

Translate control points

private pure subroutine translate_Xc(this, vec)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in)			::	vec(:)

procedure, public :: translate_Xg

Translate geometry points

private pure subroutine translate_Xg(this, vec)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in)			::	vec(:)

procedure, private :: basis_scalar

Compute the basis functions of the NURBS volume

private pure subroutine basis_scalar(this, Xt, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Attributes		Name
class(nurbs_volume),	intent(inout)		::	this
real(kind=rk),	intent(in),	contiguous	::	Xt(:)
real(kind=rk),	intent(out),	allocatable	::	Tgc(:)

procedure, private :: basis_vector

Compute the basis functions of the NURBS volume

private pure subroutine basis_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	Tgc(:,:)

procedure, private :: derivative2_scalar

Compute the second derivative of the NURBS volume

private pure subroutine derivative2_scalar(this, Xt, d2Tgc, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xt(:)
real(kind=rk),	intent(out),		allocatable	::	d2Tgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	dTgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:)

procedure, private :: derivative2_vector

Compute the second derivative of the NURBS volume

private pure subroutine derivative2_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, d2Tgc, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	d2Tgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	dTgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:,:)

procedure, private :: derivative_scalar

Compute the derivative of the NURBS volume

private pure subroutine derivative_scalar(this, Xt, dTgc, Tgc, elem)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
real(kind=rk),	intent(in),		contiguous	::	Xt(:)
real(kind=rk),	intent(out),		allocatable	::	dTgc(:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:)
integer,	intent(in),	optional		::	elem(:)

procedure, private :: derivative_vector

Compute the derivative of the NURBS volume

private pure subroutine derivative_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, dTgc, Tgc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(inout)			::	this
integer,	intent(in),	optional		::	res1
integer,	intent(in),	optional		::	res2
integer,	intent(in),	optional		::	res3
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt1(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt2(:)
real(kind=rk),	intent(in),	optional,	contiguous	::	Xt3(:)
real(kind=rk),	intent(out),		allocatable	::	dTgc(:,:,:)
real(kind=rk),	intent(out),	optional,	allocatable	::	Tgc(:,:)

procedure, private :: get_Wc_all

Get all weights

private pure function get_Wc_all(this) result(Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

procedure, private :: get_Wci

Get i-th weight

private pure function get_Wci(this, n) result(Wc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

Return Value real(kind=rk)

procedure, private :: get_Xc_all

Get all control points

private pure function get_Xc_all(this) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

procedure, private :: get_Xci

Get i-th control point

private pure function get_Xci(this, n) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

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

procedure, private :: get_Xcid

Get i-th control point in a specific direction

private pure function get_Xcid(this, n, dir) result(Xc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	n
integer,	intent(in)	::	dir

Return Value real(kind=rk)

procedure, private :: get_Xg_all

Get all geometry points

private pure function get_Xg_all(this) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

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

procedure, private :: get_Xgi

Get i-th geometry point

private pure function get_Xgi(this, n) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	n

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

procedure, private :: get_Xgid

Get i-th geometry point in a specific direction

private pure function get_Xgid(this, n, dir) result(Xg)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	n
integer,	intent(in)	::	dir

Return Value real(kind=rk)

procedure, private :: get_degree_all

Get degree of the NURBS volume in all directions

private pure function get_degree_all(this) result(degree)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, (3)

procedure, private :: get_degree_dir

Get degree of the NURBS volume in a specific direction

private pure function get_degree_dir(this, dir) result(degree)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

Return Value integer

procedure, private :: get_knot_all

Get all knot vectors

private pure function get_knot_all(this, dir) result(knot)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

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

procedure, private :: get_knoti

Get i-th knot value

private pure function get_knoti(this, dir, i) result(knot)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent		Name
class(nurbs_volume),	intent(in)	::	this
integer,	intent(in)	::	dir
integer,	intent(in)	::	i

Return Value real(kind=rk)

procedure, private :: get_nc_all

Get number of control points in all directions

private pure function get_nc_all(this) result(nc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this

Return Value integer, (3)

procedure, private :: get_nc_dir

Get number of control points in a specific direction

private pure function get_nc_dir(this, dir) result(nc)

Author: Seyed Ali Ghasemi
License: BSD 3-Clause

Arguments

Type	Intent	Optional	Attributes		Name
class(nurbs_volume),	intent(in)			::	this
integer,	intent(in)			::	dir

nurbs_volume Derived Type

Contents

Variables

Type-Bound Procedures

type, public :: nurbs_volume

Components

Type-Bound Procedures

procedure, public :: ansatz

private pure subroutine ansatz(this, ie, ig, Tgc, dTgc_dXg, dV)

Arguments

generic, public :: basis => basis_vector, basis_scalar

private pure subroutine basis_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, Tgc)

Arguments

private pure subroutine basis_scalar(this, Xt, Tgc)

Arguments

procedure, public :: cmp_Xg

private pure function cmp_Xg(this, Xt) result(Xg)

Arguments

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

procedure, public :: cmp_degree

private pure subroutine cmp_degree(this, dir)

Arguments

procedure, public :: cmp_degreeFace

private pure function cmp_degreeFace(this, face) result(degree)

Arguments

Return Value integer, (3)

procedure, public :: cmp_elem

private pure function cmp_elem(this) result(elemConn)

Arguments

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_elemFace

private pure function cmp_elemFace(this, elem, face) result(elemConn)

Arguments

Return Value integer, allocatable, (:)

procedure, public :: cmp_elemFace_Xc_vis

private pure function cmp_elemFace_Xc_vis(this, elem, face) result(elemConn)

Arguments

Return Value integer, allocatable, (:)

procedure, public :: cmp_elemFace_Xg_vis

private pure function cmp_elemFace_Xg_vis(this, elem, face) result(elemConn)

Arguments

Return Value integer, allocatable, (:)

procedure, public :: cmp_elem_Xc_vis

private pure function cmp_elem_Xc_vis(this, p) result(elemConn)

Arguments

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_elem_Xg_vis

private pure function cmp_elem_Xg_vis(this, p) result(elemConn)

Arguments

Return Value integer, allocatable, (:,:)

procedure, public :: cmp_nc

private pure subroutine cmp_nc(this, dir)

Arguments

procedure, public :: cmp_volume

private pure subroutine cmp_volume(this, volume)

Arguments

procedure, public :: create

private pure subroutine create(this, res1, res2, res3, Xt1, Xt2, Xt3, Xt)

Arguments

generic, public :: derivative => derivative_vector, derivative_scalar

private pure subroutine derivative_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, dTgc, Tgc)

Arguments

private pure subroutine derivative_scalar(this, Xt, dTgc, Tgc, elem)

Arguments

generic, public :: derivative2 => derivative2_vector, derivative2_scalar

private pure subroutine derivative2_vector(this, res1, res2, res3, Xt1, Xt2, Xt3, d2Tgc, dTgc, Tgc)

Arguments

private pure subroutine derivative2_scalar(this, Xt, d2Tgc, dTgc, Tgc)

Arguments

procedure, public :: elevate_degree

private pure subroutine elevate_degree(this, dir, t)

Arguments

procedure, public :: export_Xc

private impure subroutine export_Xc(this, filename)

Arguments

procedure, public :: export_Xg

private impure subroutine export_Xg(this, filename)

Arguments

procedure, public :: finalize

private pure subroutine finalize(this)