fitpack_parametric_curves Module Reference

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

Data Types
type	fitpack_closed_curve
	Closed (periodic) parametric curve fitter. More...
type	fitpack_constrained_curve
	Parametric curve fitter with derivative constraints at the endpoints. More...
interface	fitpack_parametric_curve
	Open parametric curve fitter in \( \mathbb{R}^d \). More...

Functions/Subroutines
type(fitpack_parametric_curve) function	new_from_points (x, u, w, ierr)
	Construct a parametric curve from data points and perform a default fit.
integer function	new_fit (this, x, u, w, smoothing, order)
	Load new data points and perform a fresh fit.
elemental subroutine	destroy (this)
	Destroy a parametric curve object and release all allocated memory.
elemental subroutine	con_destroy (this)
	Destroy a constrained parametric curve, including endpoint constraints.
subroutine	new_points (this, x, u, w)
	Load new data points into the parametric curve and allocate workspace.
elemental subroutine	clean_constraints (this)
	Remove all endpoint derivative constraints.
subroutine	set_constraints (this, ddx_begin, ddx_end, ierr)
	Set or reset endpoint derivative constraints for a constrained parametric curve.
real(fp_real) function, dimension(this%idim)	curve_eval_one (this, u, ierr)
	Evaluate the parametric curve at a single parameter value.
real(fp_real) function, dimension(this%idim, size(u))	curve_eval_many (this, u, ierr)
	Evaluate the parametric curve at multiple parameter values.
integer function	interpolating_curve (this, order, reset_knots)
	Fit an interpolating parametric spline ( \( s = 0 \)) through the data points.
integer function	parcur_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares parametric spline with fixed knots.
integer function	curve_fit_automatic_knots (this, smoothing, order, keep_knots)
	Fit a smoothing parametric spline with automatic knot placement.
real(fp_real) function, dimension(this%idim)	curve_derivative (this, u, order, ierr)
	Evaluate the k-th derivative of the parametric curve at a single parameter value.
real(fp_real) function, dimension(this%idim, 0:this%order)	curve_all_derivatives (this, u, ierr)
	Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).
subroutine	set_default_parameters (this)
	Compute default parameter values from cumulative chord lengths.
real(fp_real) function, dimension(this%idim, size(u))	curve_derivatives (this, u, order, ierr)
	Evaluate the k-th derivative at multiple parameter values.
elemental integer(fp_size) function	parcur_comm_size (this)
	Return the communication buffer size for the parametric curve.
pure subroutine	parcur_comm_pack (this, buffer)
	Pack parametric curve data into a communication buffer.
pure subroutine	parcur_comm_expand (this, buffer)
	Expand parametric curve data from a communication buffer.
elemental integer(fp_size) function	concur_comm_size (this)
	Return the communication buffer size for the constrained curve.
pure subroutine	concur_comm_pack (this, buffer)
	Pack constrained curve data into a communication buffer.
pure subroutine	concur_comm_expand (this, buffer)
	Expand constrained curve data from a communication buffer.

Variables
integer, parameter	max_k = 5

Detailed Description

OOP wrappers for parametric curve fitting in \( \mathbb{R}^d \).

Provides three types for fitting parametric curves through data points in \( d \)-dimensional space ( \( d \geq 1 \)):

• fitpack_parametric_curve — open parametric spline (parcur)
• fitpack_closed_curve — closed (periodic) parametric spline (clocur)
• fitpack_constrained_curve — parametric spline with derivative constraints at endpoints (concur)

Each component \( s_j(u) \) of the curve is represented as a B-spline of degree \( k \) over a common knot vector, with the parameter \( u \) either user-supplied or automatically computed from cumulative chord lengths.

See also

Dierckx, Ch. 9 (pp. 199–228); parcur, clocur, concur

Function/Subroutine Documentation

clean_constraints()

elemental subroutine fitpack_parametric_curves::clean_constraints ( class(fitpack_constrained_curve), intent(inout) this )

private

Remove all endpoint derivative constraints.

con_destroy()

elemental subroutine fitpack_parametric_curves::con_destroy ( class(fitpack_constrained_curve), intent(inout) this )

private

Destroy a constrained parametric curve, including endpoint constraints.

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concur_comm_expand()

pure subroutine fitpack_parametric_curves::concur_comm_expand ( class(fitpack_constrained_curve), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand constrained curve data from a communication buffer.

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concur_comm_pack()

pure subroutine fitpack_parametric_curves::concur_comm_pack ( class(fitpack_constrained_curve), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack constrained curve data into a communication buffer.

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concur_comm_size()

elemental integer(fp_size) function fitpack_parametric_curves::concur_comm_size ( class(fitpack_constrained_curve), intent(in) this )

private

Return the communication buffer size for the constrained curve.

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curve_all_derivatives()

real(fp_real) function, dimension(this%idim,0:this%order) fitpack_parametric_curves::curve_all_derivatives ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), intent(in) u, integer, intent(out), optional ierr )

private

Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

Returns

Array \( (d \times (k+1)) \) of derivatives at u.

See also

cualde

curve_derivative()

real(fp_real) function, dimension(this%idim) fitpack_parametric_curves::curve_derivative ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), intent(in) u, integer, intent(in) order, integer, intent(out), optional ierr )

private

Evaluate the k-th derivative of the parametric curve at a single parameter value.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns

Derivative vector \( \mathbf{s}^{(\text{order})}(u) \in \mathbb{R}^d \).

See also

cualde

curve_derivatives()

real(fp_real) function, dimension(this%idim,size(u)) fitpack_parametric_curves::curve_derivatives ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), dimension(:), intent(in) u, integer, intent(in) order, integer, intent(out), optional ierr )

private

Evaluate the k-th derivative at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[in]	order	Derivative order.
[out]	ierr	Optional error flag.

Returns

Array \( (d \times m) \) of derivative vectors.

See also

cualde

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curve_eval_many()

real(fp_real) function, dimension(this%idim,size(u)) fitpack_parametric_curves::curve_eval_many ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), dimension(:), intent(in) u, integer, intent(out), optional ierr )

private

Evaluate the parametric curve at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[out]	ierr	Optional error flag.

Returns

Points \( \mathbf{s}(u_i) \) as columns of a \( d \times m \) array.

See also

curev

curve_eval_one()

real(fp_real) function, dimension(this%idim) fitpack_parametric_curves::curve_eval_one ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), intent(in) u, integer, intent(out), optional ierr )

private

Evaluate the parametric curve at a single parameter value.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

Returns

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

See also

curev

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curve_fit_automatic_knots()

integer function fitpack_parametric_curves::curve_fit_automatic_knots ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), intent(in), optional smoothing, integer(fp_size), intent(in), optional order, logical, intent(in), optional keep_knots )

private

Fit a smoothing parametric spline with automatic knot placement.

Dispatches to parcur (open), clocur (closed), or concur (constrained) depending on the dynamic type.

See also

parcur, clocur, concur

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

destroy()

elemental subroutine fitpack_parametric_curves::destroy ( class(fitpack_parametric_curve), intent(inout) this )

private

Destroy a parametric curve object and release all allocated memory.

interpolating_curve()

integer function fitpack_parametric_curves::interpolating_curve ( class(fitpack_parametric_curve), intent(inout) this, integer(fp_size), intent(in), optional order, logical, intent(in), optional reset_knots )

private

Fit an interpolating parametric spline ( \( s = 0 \)) through the data points.

See also

parcur, clocur, concur

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new_fit()

integer function fitpack_parametric_curves::new_fit ( class(fitpack_parametric_curve), intent(inout) this, real (fp_real), dimension(:,:), intent(in) x, real (fp_real), dimension(size(x,2)), intent(in), optional u, real (fp_real), dimension(size(x,2)), intent(in), optional w, real (fp_real), intent(in), optional smoothing, integer(fp_size), intent(in), optional order )

private

Load new data points and perform a fresh fit.

See also

parcur, clocur, concur

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new_from_points()

type(fitpack_parametric_curve) function fitpack_parametric_curves::new_from_points ( real(fp_real), dimension(:,:), intent(in) x, real(fp_real), dimension(size(x,2)), intent(in), optional u, real(fp_real), dimension(size(x,2)), intent(in), optional w, integer, intent(out), optional ierr )

private

Construct a parametric curve from data points and perform a default fit.

Parameters

[in]	x	Data points \( (d \times m) \): each column is a point in \( \mathbb{R}^d \).
[in]	u	Optional parameter values (must be strictly increasing). If omitted, computed from cumulative chord lengths.
[in]	w	Optional positive weights, one per data point.
[out]	ierr	Optional error flag.

Returns

Fitted parametric curve object.

See also

parcur

new_points()

subroutine fitpack_parametric_curves::new_points ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), dimension(:,:), intent(in) x, real(fp_real), dimension(size(x,2)), intent(in), optional u, real(fp_real), dimension(size(x,2)), intent(in), optional w )

private

Load new data points into the parametric curve and allocate workspace.

Parameters

[in,out]	this	The parametric curve (destroyed and reinitialized).
[in]	x	Data points \( (d \times m) \): each column is a point.
[in]	u	Optional parameter values. If omitted, computed from chord lengths.
[in]	w	Optional positive weights.

See also

parcur, clocur, concur

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parcur_comm_expand()

pure subroutine fitpack_parametric_curves::parcur_comm_expand ( class(fitpack_parametric_curve), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand parametric curve data from a communication buffer.

parcur_comm_pack()

pure subroutine fitpack_parametric_curves::parcur_comm_pack ( class(fitpack_parametric_curve), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack parametric curve data into a communication buffer.

parcur_comm_size()

elemental integer(fp_size) function fitpack_parametric_curves::parcur_comm_size ( class(fitpack_parametric_curve), intent(in) this )

private

Return the communication buffer size for the parametric curve.

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parcur_fit_least_squares()

integer function fitpack_parametric_curves::parcur_fit_least_squares ( class(fitpack_parametric_curve), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional reset_knots )

private

Fit a least-squares parametric spline with fixed knots.

See also

parcur, clocur, concur

set_constraints()

subroutine fitpack_parametric_curves::set_constraints ( class(fitpack_constrained_curve), intent(inout) this, real(fp_real), dimension(:,0:), intent(in), optional ddx_begin, real(fp_real), dimension (:,0:), intent(in), optional ddx_end, integer, intent(out), optional ierr )

private

Set or reset endpoint derivative constraints for a constrained parametric curve.

Resets all constraints, then applies the supplied left and/or right boundary conditions. Omitting ddx_begin or ddx_end removes constraints at that endpoint.

Parameters

[in,out]	this	The constrained curve object.
[in]	ddx_begin	Left endpoint constraints: column 0 = function value, column \( \ell \) = \( \ell \)-th derivative ( \( d \times (ib) \)).
[in]	ddx_end	Right endpoint constraints (same layout as ddx_begin).
[out]	ierr	Error flag (optional).

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set_default_parameters()

subroutine fitpack_parametric_curves::set_default_parameters ( class(fitpack_parametric_curve), intent(inout) this )

private

Compute default parameter values from cumulative chord lengths.

Sets \( u_i \) to normalized cumulative Euclidean distances between consecutive data points, so that \( u_1 = 0 \) and \( u_m = 1 \).

Variable Documentation

max_k

integer, parameter fitpack_parametric_curves::max_k = 5

private