Representation of a tension function. More...

#include <tension_function.hpp>

Inheritance diagram for ecl::TensionFunction:

Public Member Functions
double	dderivative (const double &tau, const double &x) const
	Generates the 2nd derivative for a certain tension at the specified point.
double	derivative (const double &tau, const double &x) const
	Generates the derivative for a certain tension at the specified point.
double	operator() (const double &tau, const double &x) const
	Calculates the value for a certain tension at the specified point.
	TensionFunction ()
	Default constructor.
template<typename Derived >
	TensionFunction (const BluePrint< Derived > &blueprint)
	Blueprint constructor.
virtual	~TensionFunction ()
Private Attributes
double	x_0
double	x_f
double	y_0
double	y_f
double	z_0
double	z_f
Friends
class	blueprints::TensionSecondDerivativeInterpolation
template<typename OutputStream >
OutputStream &	operator<< (OutputStream &ostream, const TensionFunction &function)
	Streaming output insertion operator for tension functions.

Detailed Description

Representation of a tension function.

This is a hyperbolic function often used in spline interpolations that parameterises the 'tension' of a curve interpolation between points. At low tension it behaves like a cubic polynomial, while at high tension, it tends towards a piecewise smooth series of linear functions.

Theoretical Notes:

Tension functions are derived from the following constraints on an interval [x_i, x_i+1]:

  f'''' - tau^2 f'' = 0
  f(x_i)     = y_i
  f(x_i+1)   = y_i+1
  f''(x_i)   = z_i
  f''(x_i+1) = z_i+1

This yields a C2 continuous function with hyperbolic terms (not a polynomial) that ranges from looking like a cubic interpolation at low tensions (tau -> 0) and a linearly blended interpolation at high tensions.

Definition at line 110 of file tension_function.hpp.

Constructor & Destructor Documentation

ecl::TensionFunction::TensionFunction ( ) [inline]

Default constructor.

Don't really need this, but things like vectors and array containers need it so they can reserve the appropriate storage.

Definition at line 121 of file tension_function.hpp.

virtual ecl::TensionFunction::~TensionFunction ( ) [inline, virtual]

Definition at line 122 of file tension_function.hpp.

template<typename Derived >

ecl::TensionFunction::TensionFunction ( const BluePrint< Derived > & blueprint ) [inline]

Blueprint constructor.

Constructor that allows automatic generation from an existing blueprint. This can be used simply in the following manner for any static element belonging to the BluePrintFactory.

 TensionFunction f = TensionFunction::Interpolation(2.0,0.0,0.0,3.0,1.0,0.0);

Since this is not explicit, it will also allow assignment.

 TensionFunction f;
 f = TensionFunction::Interpolation(2.0,0.0,0.0,3.0,1.0,0.0);

This will emit a compile time failure if the template argument does not conform to the blueprints concept (refer to ecl_concepts' documentation).

Parameters:

blueprint : the blue print to use to generate this instance.

See also:: ecl::utilities::BluePrintFactory<TensionFunction>.

Definition at line 146 of file tension_function.hpp.

Member Function Documentation

double ecl::TensionFunction::dderivative	(	const double &	tau,
		const double &	x
	)		const

Generates the 2nd derivative for a certain tension at the specified point.

Calculates the value of the 2nd derivative for a certain tension at the specified point.

Parameters:

tau	: the tension parameter.
x	: the point at which you wish to calculate the value for.

Returns:: double : the value of the 2nd derivative at x for tension tau.

Definition at line 37 of file lib/tension_function.cpp.

double ecl::TensionFunction::derivative	(	const double &	tau,
		const double &	x
	)		const

Generates the derivative for a certain tension at the specified point.

Calculates the value of the derivative for a certain tension at the specified point.

Parameters:

tau	: the tension parameter.
x	: the point at which you wish to calculate the value for.

Returns:: double : the value of the derivative at x for tension tau.

Definition at line 26 of file lib/tension_function.cpp.

double ecl::TensionFunction::operator()	(	const double &	tau,
		const double &	x
	)		const

Calculates the value for a certain tension at the specified point.

Parameters:

tau	: the tension parameter.
x	: the point at which you wish to calculate the value for.

Returns:: double : the value of the function at x for tension tau.

Definition at line 45 of file lib/tension_function.cpp.

Friends And Related Function Documentation

friend class blueprints::TensionSecondDerivativeInterpolation [friend]

Definition at line 195 of file tension_function.hpp.

template<typename OutputStream >

OutputStream& operator<<	(	OutputStream &	ostream,
		const TensionFunction &	function
	)		`[friend]`

Streaming output insertion operator for tension functions.

Template Parameters:

OutputStream : the type of stream being used.

Parameters:

ostream	: the output stream being used.
function	: the tension function.

Returns:: OutputStream : the output stream.

Definition at line 223 of file tension_function.hpp.

Member Data Documentation

double ecl::TensionFunction::x_0 [private]

Definition at line 203 of file tension_function.hpp.

double ecl::TensionFunction::x_f [private]

Definition at line 203 of file tension_function.hpp.

double ecl::TensionFunction::y_0 [private]

Definition at line 204 of file tension_function.hpp.

double ecl::TensionFunction::y_f [private]

Definition at line 204 of file tension_function.hpp.

double ecl::TensionFunction::z_0 [private]

Definition at line 202 of file tension_function.hpp.

double ecl::TensionFunction::z_f [private]

Definition at line 202 of file tension_function.hpp.

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

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation