Splines

#include <Splines2D.hxx>

Public Member Functions
void	clear ()
void	write_to_stream (ostream_type &s) const
char const *	type_name () const
string	info () const
void	info (ostream_type &stream) const
void	dump_data (ostream_type &stream) const
Constructors
	Spline2D (string const &name="Spline2D")
virtual	~Spline2D ()
void	build (SplineType2D tp, 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 (SplineType2D tp, vector< real_type > const &x, vector< real_type > const &y, vector< real_type > const &z, bool fortran_storage=false, bool transposed=false)
void	build (SplineType2D tp, real_type const z[], integer ldZ, integer nx, integer ny, bool fortran_storage=false, bool transposed=false)
void	build (SplineType2D tp, 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)
Open/Close/Bound
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
Get bounds
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
Evaluate
real_type	operator() (real_type x, real_type y) const
real_type	eval (real_type x, real_type y) const
First derivatives:
void	D (real_type x, real_type y, real_type d[3]) const
real_type	Dx (real_type x, real_type y) const
real_type	Dy (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
Second derivatives:
void	DD (real_type x, real_type y, real_type dd[6]) const
real_type	Dxx (real_type x, real_type y) const
real_type	Dxy (real_type x, real_type y) const
real_type	Dyy (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

Bi-quintic spline base class

Constructor & Destructor Documentation

Spline2D()

Splines::Spline2D::Spline2D ( string const & name = "Spline2D" )

inline

Build an empty spline of Spline2D type

Parameters

name	the name of the spline

~Spline2D()

virtual Splines::Spline2D::~Spline2D ( )

inlinevirtual

Spline destructor.

Member Function Documentation

build() [1/5]

void Splines::Spline2D::build ( GenericContainer const & gc )

inline

Build a spline using data in GenericContainer

build() [2/5]

void Splines::Spline2D::build ( SplineType2D tp, 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 )

inline

Build surface spline

Parameters

tp	spline type
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[incx], y[2*incx],...
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() [3/5]

void Splines::Spline2D::build ( SplineType2D tp, real_type const z[], integer ldZ, integer nx, integer ny, bool fortran_storage = false, bool transposed = false )

inline

Build surface spline

Parameters

tp	spline type
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. Elements are stored by row Z(i,j) = z[i*ldZ+j] as C-matrix
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

build() [4/5]

void Splines::Spline2D::build ( SplineType2D tp, 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

tp	spline type
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::Spline2D::build ( SplineType2D tp, vector< real_type > const & z, integer nx, integer ny, bool fortran_storage = false, bool transposed = false )

inline

Build surface spline

Parameters

tp	spline type
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::Spline2D::clear ( )

inline

Cancel the support points, empty the spline.

D()

void Splines::Spline2D::D ( real_type x, real_type y, real_type d[3] ) const

inline

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: \( S_y(x,y) \)

DD()

void Splines::Spline2D::DD ( real_type x, real_type y, real_type dd[6] ) const

inline

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: \( S_{yy}(x,y) \)

dump_data()

void Splines::Spline2D::dump_data ( ostream_type & stream ) const

inline

Dump spline values on the streams

Dx()

real_type Splines::Spline2D::Dx ( real_type x, real_type y ) const

inline

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

Dxx()

real_type Splines::Spline2D::Dxx ( real_type x, real_type y ) const

inline

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

Dxy()

real_type Splines::Spline2D::Dxy ( real_type x, real_type y ) const

inline

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

Dy()

real_type Splines::Spline2D::Dy ( real_type x, real_type y ) const

inline

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

Dyy()

real_type Splines::Spline2D::Dyy ( real_type x, real_type y ) const

inline

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

eval()

real_type Splines::Spline2D::eval ( real_type x, real_type y ) const

inline

Evaluate spline value at (x,y).

eval_D_1()

real_type Splines::Spline2D::eval_D_1 ( real_type x, real_type y ) const

inline

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

eval_D_1_1()

real_type Splines::Spline2D::eval_D_1_1 ( real_type x, real_type y ) const

inline

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

eval_D_1_2()

real_type Splines::Spline2D::eval_D_1_2 ( real_type x, real_type y ) const

inline

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

eval_D_2()

real_type Splines::Spline2D::eval_D_2 ( real_type x, real_type y ) const

inline

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

eval_D_2_2()

real_type Splines::Spline2D::eval_D_2_2 ( real_type x, real_type y ) const

inline

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

info() [1/2]

string Splines::Spline2D::info ( ) const

inline

String information of the kind and order of the spline

info() [2/2]

void Splines::Spline2D::info ( ostream_type & stream ) const

inline

Print information of the kind and order of the spline

is_x_bounded()

bool Splines::Spline2D::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::Spline2D::is_x_closed ( ) const

inline

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

is_y_bounded()

bool Splines::Spline2D::is_y_bounded ( ) const

inline

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

is_y_closed()

bool Splines::Spline2D::is_y_closed ( ) const

inline

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

make_x_bounded()

void Splines::Spline2D::make_x_bounded ( )

inline

Make the spline surface bounded in the x direction.

make_x_closed()

void Splines::Spline2D::make_x_closed ( )

inline

Setup the surface as closed in the x direction.

make_x_opened()

void Splines::Spline2D::make_x_opened ( )

inline

Setup the surface as open in the x direction.

make_x_unbounded()

void Splines::Spline2D::make_x_unbounded ( )

inline

Make the spline surface unbounded in the x direction.

make_y_bounded()

void Splines::Spline2D::make_y_bounded ( )

inline

Make the spline surface bounded in the y direction

make_y_closed()

void Splines::Spline2D::make_y_closed ( )

inline

Setup the surface as closed in the y direction.

make_y_opened()

void Splines::Spline2D::make_y_opened ( )

inline

Setup the surface as open in the y direction.

make_y_unbounded()

void Splines::Spline2D::make_y_unbounded ( )

inline

Make the spline surface unbounded in the y direction

name()

string const & Splines::Spline2D::name ( ) const

inline

Returns

string with the name of the spline

num_point_x()

integer Splines::Spline2D::num_point_x ( ) const

inline

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

num_point_y()

integer Splines::Spline2D::num_point_y ( ) const

inline

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

operator()()

real_type Splines::Spline2D::operator() ( real_type x, real_type y ) const

inline

Evaluate spline value at (x,y).

setup()

void Splines::Spline2D::setup

(

GenericContainer const &

gc

)

Build spline surface using gc

• gc("spline_type")
  • "bilinear" build a bilinear spline surface
  • "bicubic" build a spline surface with cubic spline
  • "biquintic" build a spline surface with quintic spline
  • "Akima" or "akima "build a spline surface with cubic spline using Akima algorithm to avoid obscillation

type_name()

char const * Splines::Spline2D::type_name ( ) const

inline

Return spline typename

write_to_stream()

void Splines::Spline2D::write_to_stream ( ostream_type & s ) const

inline

Print spline coefficients.

x_max()

real_type Splines::Spline2D::x_max ( ) const

inline

Return x-maximum spline value.

x_min()

real_type Splines::Spline2D::x_min ( ) const

inline

Return x-minumum spline value.

x_node()

real_type Splines::Spline2D::x_node ( integer i ) const

inline

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

y_max()

real_type Splines::Spline2D::y_max ( ) const

inline

Return y-maximum spline value

y_min()

real_type Splines::Spline2D::y_min ( ) const

inline

Return y-minumum spline value.

y_node()

real_type Splines::Spline2D::y_node ( integer i ) const

inline

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

z_max()

real_type Splines::Spline2D::z_max ( ) const

inline

Return z-maximum spline value

z_min()

real_type Splines::Spline2D::z_min ( ) const

inline

Return z-minumum spline value

z_node()

real_type Splines::Spline2D::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/Splines2D.hxx
• /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Splines/src/Splines2D.cc