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. More...

double	derivative (const double &tau, const double &x) const
	Generates the derivative for a certain tension at the specified point. More...

double	operator() (const double &tau, const double &x) const
	Calculates the value for a certain tension at the specified point. More...

	TensionFunction ()
	Default constructor. More...

template<typename Derived >
	TensionFunction (const BluePrint< Derived > &blueprint)
	Blueprint constructor. More...

virtual	~TensionFunction ()

Public Member Functions inherited from ecl::BluePrintFactory< TensionFunction >
virtual	~BluePrintFactory ()

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. More...

Additional Inherited Members
Static Public Member Functions inherited from ecl::BluePrintFactory< TensionFunction >
static blueprints::TensionSecondDerivativeInterpolation	Interpolation (const double x_i, const double y_i, const double yddot_i, const double x_f, const double y_f, const double yddot_f)
	Blueprint for interpolating a tension function between two end points using second derivatives. More...

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 ( )

inlinevirtual

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

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation