fitpack_parametric_surfaces Module Reference

OOP wrapper for parametric surface fitting in \( \mathbb{R}^d \). More...

Data Types
interface	fitpack_parametric_surface
	Bicubic parametric surface fitter in \( \mathbb{R}^d \). More...

Functions/Subroutines
type(fitpack_parametric_surface) function	new_from_points (u, v, z, periodic_bc, ierr)
	Construct a parametric surface from gridded data and perform a default fit.
integer function	new_fit (this, u, v, z, smoothing, periodic_bc)
	Load new data and perform a fresh parametric surface fit.
elemental subroutine	destroy (this)
	Destroy a parametric surface object and release all allocated memory.
subroutine	new_points (this, u, v, z, periodic_bc)
	Load new gridded data and allocate workspace for parametric surface fitting.
pure subroutine	allocate_knot_storage (this, knots)
real(fp_real) function, dimension(this%idim)	surf_eval_one (this, u, v, ierr)
	Evaluate the parametric surface at a single \( (u, v) \) point.
real(fp_real) function, dimension(size(v), size(u), this%idim)	surf_eval_grid (this, u, v, ierr)
	Evaluate the parametric surface on a rectangular parameter grid.
integer function	interpolating_curve (this, reset_knots)
	Fit an interpolating parametric surface ( \( s = 0 \)).
integer function	surface_fit_least_squares (this, u_knots, v_knots, smoothing, reset_knots)
	Fit a least-squares parametric surface with current or user-supplied knots.
integer function	surf_fit_automatic_knots (this, smoothing, periodic, keep_knots)
	Fit a smoothing parametric surface with automatic knot placement.
elemental integer(fp_size) function	parsurf_comm_size (this)
	Return the communication buffer size for the parametric surface.
pure subroutine	parsurf_comm_pack (this, buffer)
	Pack parametric surface data into a communication buffer.
pure subroutine	parsurf_comm_expand (this, buffer)
	Expand parametric surface data from a communication buffer.

Detailed Description

OOP wrapper for parametric surface fitting in \( \mathbb{R}^d \).

Provides fitpack_parametric_surface, a derived type for fitting bicubic parametric tensor-product spline surfaces through gridded data in \( d \)-dimensional space. The surface maps parameter pairs \( (u, v) \) to points \( \mathbf{s}(u, v) = (s_1(u,v), \ldots, s_d(u,v)) \), with optional periodicity in either or both parameter directions.

See also

Dierckx, Ch. 10, §10.2 (pp. 241–254); parsur, surev

Function/Subroutine Documentation

allocate_knot_storage()

pure subroutine fitpack_parametric_surfaces::allocate_knot_storage ( class(fitpack_parametric_surface), intent(inout) this, integer, dimension(2), intent(in) knots )

private

destroy()

elemental subroutine fitpack_parametric_surfaces::destroy ( class(fitpack_parametric_surface), intent(inout) this )

private

Destroy a parametric surface object and release all allocated memory.

interpolating_curve()

integer function fitpack_parametric_surfaces::interpolating_curve ( class(fitpack_parametric_surface), intent(inout) this, logical, intent(in), optional reset_knots )

private

Fit an interpolating parametric surface ( \( s = 0 \)).

See also

parsur

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new_fit()

integer function fitpack_parametric_surfaces::new_fit ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), dimension(:,:,:), intent(in) z, real(fp_real), intent(in), optional smoothing, logical, dimension(2), intent(in), optional periodic_bc )

private

Load new data and perform a fresh parametric surface fit.

See also

parsur

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new_from_points()

type(fitpack_parametric_surface) function fitpack_parametric_surfaces::new_from_points ( real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), dimension(:,:,:), intent(in) z, logical, dimension(2), intent(in), optional periodic_bc, integer, intent(out), optional ierr )

private

Construct a parametric surface from gridded data and perform a default fit.

Parameters

[in]	u	Parameter grid in the u direction.
[in]	v	Parameter grid in the v direction.
[in]	z	Data values z(j,i,l) for component l at (u(i),v(j)).
[in]	periodic_BC	Optional periodicity flags [u_periodic, v_periodic].
[out]	ierr	Optional error flag.

Returns

Fitted parametric surface object.

See also

parsur

new_points()

subroutine fitpack_parametric_surfaces::new_points ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), dimension(:,:,:), intent(in) z, logical, dimension(2), intent(in), optional periodic_bc )

private

Load new gridded data and allocate workspace for parametric surface fitting.

See also

parsur

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parsurf_comm_expand()

pure subroutine fitpack_parametric_surfaces::parsurf_comm_expand ( class(fitpack_parametric_surface), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand parametric surface data from a communication buffer.

parsurf_comm_pack()

pure subroutine fitpack_parametric_surfaces::parsurf_comm_pack ( class(fitpack_parametric_surface), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack parametric surface data into a communication buffer.

parsurf_comm_size()

elemental integer(fp_size) function fitpack_parametric_surfaces::parsurf_comm_size ( class(fitpack_parametric_surface), intent(in) this )

private

Return the communication buffer size for the parametric surface.

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surf_eval_grid()

real(fp_real) function, dimension(size(v),size(u),this%idim) fitpack_parametric_surfaces::surf_eval_grid ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, integer, intent(out), optional ierr )

private

Evaluate the parametric surface on a rectangular parameter grid.

Returns f(j,i,l) = \( s_l(u_i, v_j) \).

See also

surev

surf_eval_one()

real(fp_real) function, dimension(this%idim) fitpack_parametric_surfaces::surf_eval_one ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), intent(in) u, real(fp_real), intent(in) v, integer, intent(out), optional ierr )

private

Evaluate the parametric surface at a single \( (u, v) \) point.

Returns

Point \( \mathbf{s}(u, v) \in \mathbb{R}^d \).

See also

surev

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surf_fit_automatic_knots()

integer function fitpack_parametric_surfaces::surf_fit_automatic_knots ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, dimension(2), intent(in), optional periodic, logical, intent(in), optional keep_knots )

private

Fit a smoothing parametric surface with automatic knot placement.

See also

parsur

Ensure we start with new knots (unless caller wants to keep them)

surface_fit_least_squares()

integer function fitpack_parametric_surfaces::surface_fit_least_squares ( class(fitpack_parametric_surface), intent(inout) this, real(fp_real), dimension(:), intent(in), optional u_knots, real(fp_real), dimension(:), intent(in), optional v_knots, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional reset_knots )

private

Fit a least-squares parametric surface with current or user-supplied knots.

Optional u_knots and v_knots set interior knots directly. If omitted, the current knot vectors are used.

See also

parsur

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