Splines

Inheritance diagram for Spline2D:

Public Member Functions
function	Spline2D (in name, in varargin)
function	build (in self, in x, in y, in z)
function	eval (in self, in x, in y)
function	eval_Dx (in self, in x, in y)
function	eval_Dy (in self, in x, in y)
function	eval_Dxx (in self, in x, in y)
function	eval_Dxy (in self, in x, in y)
function	eval_Dyy (in self, in x, in y)
function	make_x_opened (in self)
function	is_x_closed (in self)
function	make_x_bounded (in self)
function	make_x_unbounded (in self)
function	is_x_bounded (in self)
function	make_y_opened (in self)
function	is_y_closed (in self)
function	make_y_bounded (in self)
function	make_y_unbounded (in self)
function	is_y_bounded (in self)

Protected Member Functions
function	copyElement (in self)

Detailed Description

MATLAB class wrapper for the underlying C++ class.

The construction of the 2D spline is done as follows

• instantiate the spline object

spl = Spline2D( kind, X, Y, ZZ );
% or
spl = Spline2D( kind );
spl.build( X, Y, ZZ );

kind is a string and can be any of

kind	meaning
'bilinear'	piecewise linear in X e Y direction
'cubic'	piecewise cubic in X e Y direction
'akima'	piecewise cubic with Akima non oscillatory construction
'biquintic'	piecewise quintic in X e Y direction

Evaluation is simple

Z = spl.eval( X, Y );

where X and Y are scalar or vector or matrix of the same size. the result Z is scalar or vector or matrix of the same size of the inputs.

example of usage

X = -2:0.01:2;
Y = -2:0.01:2;
[XX,YY] = ndgrid(X,Y);
ZZ  = peaks(XX,YY);
spl = Spline2D('bicubic',X,Y,ZZ);
 
surf(XX,YY,ZZ), view(145,-2), set(gca,'Fontsize',16);
 
X = -2:0.1:2;
Y = -2:0.1:2;
[XX,YY] = ndgrid(X,Y);
 
ZZ = spl.eval(XX,YY);

'

Constructor & Destructor Documentation

Spline2D()

function Spline2D::Spline2D	(	in	name,
		in	varargin )

Build a spline given a table of point and type:

spl = Spline2D( kind );          % initialize
spl = Spline2D( kind, X, Y, Z ); % initialize and build

Member Function Documentation

build()

function Spline2D::build	(	in	self,
		in	x,
		in	y,
		in	z )

Build a spline given a table of point and type:

spl.build( X, Y, Z );

X and Y are vector Z is a matrix nx x ny

copyElement()

function Spline2D::copyElement ( in self )

protected

Make a deep copy of a curve object

Usage

B = A.copy();

where A is the curve object to be copied.

eval()

function Spline2D::eval	(	in	self,
		in	x,
		in	y )

Evaluate spline (and its derivatives) at (x,y)

P = spl.eval( x, y );
[P,Px,Py] = spl.eval( x, y );
[P,Px,Py,Pxx,Pxy,Pyy] = spl.eval( x, y );

x and y are salar or vector or matrix of the same size

eval_Dx()

function Spline2D::eval_Dx	(	in	self,
		in	x,
		in	y )

Evaluate spline x derivative at (x,y)

Dx = spl.eval_Dx( x, y );

x and y are salar or vector or matrix of the same size

eval_Dxx()

function Spline2D::eval_Dxx	(	in	self,
		in	x,
		in	y )

Evaluate spline x second derivative at (x,y)

Dxx = spl.eval_Dxx( x, y );

x and y are salar or vector or matrix of the same size

eval_Dxy()

function Spline2D::eval_Dxy	(	in	self,
		in	x,
		in	y )

Evaluate spline xy second derivative at (x,y)

Dxy = spl.eval_Dxy( x, y );

x and y are salar or vector or matrix of the same size

eval_Dy()

function Spline2D::eval_Dy	(	in	self,
		in	x,
		in	y )

Evaluate spline y derivative at (x,y)

Dy = spl.eval_Dy( x, y );

x and y are salar or vector or matrix of the same size

eval_Dyy()

function Spline2D::eval_Dyy	(	in	self,
		in	x,
		in	y )

Evaluate spline y second derivative at (x,y)

Dyy = spl.eval_Dyy( x, y );

x and y are salar or vector or matrix of the same size

is_x_bounded()

function Spline2D::is_x_bounded

(

in

self

)

Check if spline is computable only in the x-range where is defined. Return true if can be computed only in the range.

ok = spl.is_x_bounded();

is_x_closed()

function Spline2D::is_x_closed

(

in

self

)

Return true if spline surface is of closed type in x-direction

ok = spl.is_x_closed();

is_y_bounded()

function Spline2D::is_y_bounded

(

in

self

)

Check if spline is computable only in the y-range where is defined. Return true if can be computed only in the range.

ok = spl.is_y_bounded();

is_y_closed()

function Spline2D::is_y_closed

(

in

self

)

Return true if spline surface is of closed type in y-direction

ok = spl.is_y_closed();

make_x_bounded()

function Spline2D::make_x_bounded

(

in

self

)

Make spline surface computable only in the x-range where is defined. If x is outside range an error is produced.

spl.make_x_bounded();

make_x_opened()

function Spline2D::make_x_opened

(

in

self

)

    Set spline surface as closed in `x direction

/ / {matlab} / spl.make_x_closed(); / / public: function make_x_closed(in self );

/ / Set spline surface as opened in x direction @iverbatim {matlab} spl.make_x_opened(); `

make_x_unbounded()

function Spline2D::make_x_unbounded

(

in

self

)

Make spline surface computable outside the x-range is defined. If x is outside range value is extrapolated.

spl.make_x_unbounded();

make_y_bounded()

function Spline2D::make_y_bounded

(

in

self

)

Make spline surface computable only in the y-range where is defined. If y is outside range an error is produced.

spl.make_y_bounded();

make_y_opened()

function Spline2D::make_y_opened

(

in

self

)

    Set spline surface as closed in `y direction

/ / {matlab} / spl.make_y_closed(); / / public: function make_y_closed(in self );

/ / Set spline surface as opened in y direction @iverbatim {matlab} spl.make_y_opened(); `

make_y_unbounded()

function Spline2D::make_y_unbounded

(

in

self

)

Make spline surface computable outside the y-range is defined. If y is outside range value is extrapolated.

spl.make_y_unbounded();

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

• /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Splines/toolbox/lib/Spline2D.m