Splines

#include <Splines.hh>

Inheritance diagram for Splines::SplineSurf:

Public Member Functions
	SplineSurf (string const &name="Spline")
virtual	~SplineSurf ()
void	clear ()
virtual void	write_to_stream (ostream_type &s) const =0
virtual char const *	type_name () const =0
virtual string	info () const
void	info (ostream_type &stream) const
void	dump_data (ostream_type &s) const
Open/Close
bool	is_x_closed () const
void	make_x_closed ()
void	make_x_opened ()
bool	is_y_closed () const
void	make_y_closed ()
void	make_y_opened ()
bool	is_x_bounded () const
void	make_x_unbounded ()
void	make_x_bounded ()
bool	is_y_bounded () const
void	make_y_unbounded ()
void	make_y_bounded ()
Info
string const &	name () const
integer	num_point_x () const
integer	num_point_y () const
real_type	x_node (integer i) const
real_type	y_node (integer i) const
real_type	z_node (integer i, integer j) const
real_type	x_min () const
real_type	x_max () const
real_type	y_min () const
real_type	y_max () const
real_type	z_min () const
real_type	z_max () const
Build Spline
void	build (real_type const x[], integer incx, real_type const y[], integer incy, real_type const z[], integer ldZ, integer nx, integer ny, bool fortran_storage=false, bool transposed=false)
void	build (vector< real_type > const &x, vector< real_type > const &y, vector< real_type > const &z, bool fortran_storage=false, bool transposed=false)
void	build (real_type const z[], integer ldZ, integer nx, integer ny, bool fortran_storage=false, bool transposed=false)
void	build (vector< real_type > const &z, integer nx, integer ny, bool fortran_storage=false, bool transposed=false)
void	setup (GenericContainer const &gc)
void	build (GenericContainer const &gc)
Evaluate
virtual real_type	eval (real_type x, real_type y) const =0
virtual void	D (real_type x, real_type y, real_type d[3]) const =0
virtual real_type	Dx (real_type x, real_type y) const =0
virtual real_type	Dy (real_type x, real_type y) const =0
virtual void	DD (real_type x, real_type y, real_type dd[6]) const =0
virtual real_type	Dxx (real_type x, real_type y) const =0
virtual real_type	Dxy (real_type x, real_type y) const =0
virtual real_type	Dyy (real_type x, real_type y) const =0
real_type	operator() (real_type x, real_type y) const
real_type	eval_D_1 (real_type x, real_type y) const
real_type	eval_D_2 (real_type x, real_type y) const
real_type	eval_D_1_1 (real_type x, real_type y) const
real_type	eval_D_1_2 (real_type x, real_type y) const
real_type	eval_D_2_2 (real_type x, real_type y) const

Detailed Description

Spline Management Class

Constructor & Destructor Documentation

SplineSurf()

Splines::SplineSurf::SplineSurf ( string const & name = "Spline" )

inline

Spline constructor

~SplineSurf()

virtual Splines::SplineSurf::~SplineSurf ( )

virtual

Spline destructor

Member Function Documentation

build() [1/5]

void Splines::SplineSurf::build ( GenericContainer const & gc )

inline

Build a spline using data in GenericContainer

build() [2/5]

void Splines::SplineSurf::build	(	real_type const	x[],
		integer	incx,
		real_type const	y[],
		integer	incy,
		real_type const	z[],
		integer	ldZ,
		integer	nx,
		integer	ny,
		bool	fortran_storage = false,
		bool	transposed = false )

Build surface spline

Parameters

x	vector of x-coordinates
incx	access elements as x[0], x[incx], x[2*incx],...
y	vector of y-coordinates
incy	access elements as y[0], y[incy], y[2*incy],...
z	matrix of z-values. Elements are stored by row Z(i,j) = z[i*ny+j] as C-matrix
ldZ	leading dimension of z
nx	number of points in x direction
ny	number of points in y direction
fortran_storage	if true elements are stored by column i.e. Z(i,j) = z[i+j*nx] as Fortran-matrix
transposed	if true matrix Z is stored transposed

Build a spline surface with data

• x the vector of x-nodes (size nx)
• y the vector of y-nodes (size ny)
• z the matrix of z-values, \( z_{ij} = f(x_i,y_j) \)

         +----------+
         |          |  internally data is stored by column
index j  ny  zij    |  zij = data[ i*ny + j ]
         |          |
         +--- nx ---+
           index i

• fortran_storage is true if matrix z is stored by column
• transposed is true means that data are stored transposed

build() [3/5]

void Splines::SplineSurf::build	(	real_type const	z[],
		integer	ldZ,
		integer	nx,
		integer	ny,
		bool	fortran_storage = false,
		bool	transposed = false )

Build a spline surface with data

• z the matrix of z-values, \( z_{ij} = f(x_i,y_j) \)
• ldZ leading dimension of matriz z
• nx number of nodes in x-direction
• ny number of nodes in y-direction

nodes are equispaced in x and y directions.

         +----------+
         |          |  internally data is stored by column
index j  ny  zij    |  zij = data[ i*ny + j ]
         |          |
         +--- nx ---+
           index i

• fortran_storage is true if matrix z is stored by column
• transposed is true means that data are stored transposed

build() [4/5]

void Splines::SplineSurf::build ( vector< real_type > const & x, vector< real_type > const & y, vector< real_type > const & z, bool fortran_storage = false, bool transposed = false )

inline

Build surface spline

Parameters

x	vector of x-coordinates, nx = x.size()
y	vector of y-coordinates, ny = y.size()
z	matrix of z-values. Elements are stored by row Z(i,j) = z[i*ny+j] as C-matrix
fortran_storage	if true elements are stored by column i.e. Z(i,j) = z[i+j*nx] as Fortran-matrix
transposed	if true matrix Z is stored transposed

build() [5/5]

void Splines::SplineSurf::build ( vector< real_type > const & z, integer nx, integer ny, bool fortran_storage = false, bool transposed = false )

inline

Build surface spline

Parameters

z	matrix of z-values. Elements are stored by row Z(i,j) = z[i*ny+j] as C-matrix. ldZ leading dimension of the matrix is ny for C-storage and nx for Fortran storage.
nx	x-dimension
ny	y-dimension
fortran_storage	if true elements are stored by column i.e. Z(i,j) = z[i+j*nx] as Fortran-matrix
transposed	if true matrix Z is stored transposed

clear()

void Splines::SplineSurf::clear

(

)

Cancel the support points, empty the spline.

D()

virtual void Splines::SplineSurf::D ( real_type x, real_type y, real_type d[3] ) const

pure virtual

Value and first derivatives at point \( (x,y) \):

• d[0] value of the spline \( S(x,y) \)
• d[1] derivative respect to \( x \) of the spline: \( S_x(x,y) \)
• d[2] derivative respect to \( y \) of the spline: \( S_y(x,y) \)

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

DD()

virtual void Splines::SplineSurf::DD ( real_type x, real_type y, real_type dd[6] ) const

pure virtual

Value, first and second derivatives at point \( (x,y) \):

• dd[0] value of the spline \( S(x,y) \)
• dd[1] derivative respect to \( x \) of the spline: \( S_x(x,y) \)
• dd[2] derivative respect to \( y \) of the spline: \( S_y(x,y) \)
• dd[3] second derivative respect to \( x \) of the spline: \( S_{xx}(x,y) \)
• dd[4] mixed second derivative: \( S_{xy}(x,y) \)
• dd[5] second derivative respect to \( y \) of the spline: \( S_{yy}(x,y) \)

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

dump_data()

void Splines::SplineSurf::dump_data

(

ostream_type &

s

)

const

Print stored data x, y, and matrix z.

Dx()

virtual real_type Splines::SplineSurf::Dx ( real_type x, real_type y ) const

pure virtual

First derivatives respect to \( x \) at point \( (x,y) \) of the spline: \( S_x(x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

Dxx()

virtual real_type Splines::SplineSurf::Dxx ( real_type x, real_type y ) const

pure virtual

Second derivatives respect to \( x \) at point \( (x,y) \) of the spline: \( S_{xx}(x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

Dxy()

virtual real_type Splines::SplineSurf::Dxy ( real_type x, real_type y ) const

pure virtual

Mixed second derivatives: \( S_{xy}(x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

Dy()

virtual real_type Splines::SplineSurf::Dy ( real_type x, real_type y ) const

pure virtual

First derivatives respect to \( y \) at point \( (x,y) \) of the spline: \( S_y(x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

Dyy()

virtual real_type Splines::SplineSurf::Dyy ( real_type x, real_type y ) const

pure virtual

Second derivatives respect to \( y \) at point \( (x,y) \) of the spline: \( S_{yy}(x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

eval()

virtual real_type Splines::SplineSurf::eval ( real_type x, real_type y ) const

pure virtual

Evaluate spline value at point \( (x,y) \).

Implemented in Splines::BiCubicSplineBase, Splines::BilinearSpline, and Splines::BiQuinticSplineBase.

eval_D_1()

real_type Splines::SplineSurf::eval_D_1 ( real_type x, real_type y ) const

inline

Alias for Dx(x,y)

eval_D_1_1()

real_type Splines::SplineSurf::eval_D_1_1 ( real_type x, real_type y ) const

inline

Alias for Dxx(x,y)

eval_D_1_2()

real_type Splines::SplineSurf::eval_D_1_2 ( real_type x, real_type y ) const

inline

Alias for Dxy(x,y)

eval_D_2()

real_type Splines::SplineSurf::eval_D_2 ( real_type x, real_type y ) const

inline

Alias for Dy(x,y)

eval_D_2_2()

real_type Splines::SplineSurf::eval_D_2_2 ( real_type x, real_type y ) const

inline

Alias for Dyy(x,y)

info() [1/2]

virtual string Splines::SplineSurf::info ( ) const

virtual

String information of the kind and order of the spline

info() [2/2]

void Splines::SplineSurf::info ( ostream_type & stream ) const

inline

Print information of the kind and order of the spline

is_x_bounded()

bool Splines::SplineSurf::is_x_bounded ( ) const

inline

Return true if the parameter x assumed bounded. If false the spline is estrapolated for x values outside the range.

is_x_closed()

bool Splines::SplineSurf::is_x_closed ( ) const

inline

Return true if the surface is assumed closed in the x direction.

is_y_bounded()

bool Splines::SplineSurf::is_y_bounded ( ) const

inline

Return true if the parameter y assumed bounded. If false the spline is extrapolated for y values outside the range.

is_y_closed()

bool Splines::SplineSurf::is_y_closed ( ) const

inline

Return true if the surface is assumed closed in the y direction.

make_x_bounded()

void Splines::SplineSurf::make_x_bounded ( )

inline

Make the spline surface bounded in the x direction.

make_x_closed()

void Splines::SplineSurf::make_x_closed ( )

inline

Setup the surface as closed in the x direction.

make_x_opened()

void Splines::SplineSurf::make_x_opened ( )

inline

Setup the surface as open in the x direction.

make_x_unbounded()

void Splines::SplineSurf::make_x_unbounded ( )

inline

Make the spline surface unbounded in the x direction.

make_y_bounded()

void Splines::SplineSurf::make_y_bounded ( )

inline

Make the spline surface bounded in the x direction.

make_y_closed()

void Splines::SplineSurf::make_y_closed ( )

inline

Setup the surface as closed in the y direction.

make_y_opened()

void Splines::SplineSurf::make_y_opened ( )

inline

Setup the surface as open in the y direction.

make_y_unbounded()

void Splines::SplineSurf::make_y_unbounded ( )

inline

Make the spline surface unbounded in the y direction

name()

string const & Splines::SplineSurf::name ( ) const

inline

Returns

string with the name of the spline

num_point_x()

integer Splines::SplineSurf::num_point_x ( ) const

inline

Return the number of support points of the spline along x direction.

num_point_y()

integer Splines::SplineSurf::num_point_y ( ) const

inline

Return the number of support points of the spline along y direction.

operator()()

real_type Splines::SplineSurf::operator() ( real_type x, real_type y ) const

inline

Evaluate spline value at point \( (x,y) \).

setup()

void Splines::SplineSurf::setup

(

GenericContainer const &

gc

)

Build spline using data in gc

Setup a spline surface using a GenericContainer

• gc("fortran_storage") if true zdata is stored by column, otherwise by rows
• gc("transposed") if true zdata is stored transposed
• gc("xdata") vector of mesh point in x direction
• gc("ydata") vector of mesh point in y direction
• gc("zdata") may be
  • matrix of size nx x ny (ny x nx if data is transposed)
  • vector of size nx x ny stiring the data.
• nx number of nodes in x-direction the size of vector in x direction
• ny number of nodes in y-direction the size of vector in y direction

nodes are equispaced in x and y directions.

         +----------+
         |          |  internally data is stored by column
index j  ny  zij    |  zij = data[ i*ny + j ]
         |          |
         +--- nx ---+
           index i

• fortran_storage is true if matrix z is stored by column
• transposed is true means that data are stored transposed

type_name()

virtual char const * Splines::SplineSurf::type_name ( ) const

pure virtual

Return spline type as a string pointer.

Implemented in Splines::Akima2Dspline, Splines::BiCubicSpline, Splines::BilinearSpline, and Splines::BiQuinticSpline.

write_to_stream()

virtual void Splines::SplineSurf::write_to_stream ( ostream_type & s ) const

pure virtual

Print spline coefficients.

Implemented in Splines::Akima2Dspline, Splines::BiCubicSpline, Splines::BilinearSpline, and Splines::BiQuinticSpline.

x_max()

real_type Splines::SplineSurf::x_max ( ) const

inline

Return x-maximum spline value.

x_min()

real_type Splines::SplineSurf::x_min ( ) const

inline

Return x-minumum spline value.

x_node()

real_type Splines::SplineSurf::x_node ( integer i ) const

inline

Return the i-th node of the spline (x component).

y_max()

real_type Splines::SplineSurf::y_max ( ) const

inline

Return y-maximum spline value.

y_min()

real_type Splines::SplineSurf::y_min ( ) const

inline

Return y-minumum spline value.

y_node()

real_type Splines::SplineSurf::y_node ( integer i ) const

inline

Return the i-th node of the spline (y component).

z_max()

real_type Splines::SplineSurf::z_max ( ) const

inline

Return z-maximum spline value.

z_min()

real_type Splines::SplineSurf::z_min ( ) const

inline

Return z-minumum spline value.

z_node()

real_type Splines::SplineSurf::z_node ( integer i, integer j ) const

inline

Return the i-th node of the spline (y component).

---

The documentation for this class was generated from the following files:

• /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Splines/src/Splines.hh
• /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Splines/src/SplinesBivariate.cc