Public Member Functions | Private Attributes | Friends
ecl::TensionFunction Class Reference

Representation of a tension function. More...

#include <tension_function.hpp>

Inheritance diagram for ecl::TensionFunction:
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List of all members.

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

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.

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

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.

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:


ecl_geometry
Author(s): Daniel Stonier
autogenerated on Thu Jun 6 2019 21:17:53