Representation of a tension function. More...
#include <tension_function.hpp>
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. | |
| template<typename Derived > | |
| TensionFunction (const BluePrint< Derived > &blueprint) | |
| Blueprint constructor. | |
| TensionFunction () | |
| Default 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. | |
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.
| 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.
| 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).
| blueprint | : the blue print to use to generate this instance. |
Definition at line 146 of file tension_function.hpp.
| 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.
| tau | : the tension parameter. | |
| x | : the point at which you wish to calculate the value for. |
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.
| tau | : the tension parameter. | |
| x | : the point at which you wish to calculate the value for. |
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.
| tau | : the tension parameter. | |
| x | : the point at which you wish to calculate the value for. |
Definition at line 45 of file lib/tension_function.cpp.
friend class blueprints::TensionSecondDerivativeInterpolation [friend] |
Definition at line 195 of file tension_function.hpp.
| OutputStream& operator<< | ( | OutputStream & | ostream, | |
| const TensionFunction & | function | |||
| ) | [friend] |
Streaming output insertion operator for tension functions.
Streaming output insertion operator for tension functions.
| OutputStream | : the type of stream being used. |
| ostream | : the output stream being used. | |
| function | : the tension function. |
Definition at line 223 of file tension_function.hpp.
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.
