PiecewiseScalarField3< ScalarField3T, ScalarT > Class Template Reference
The PiecewiseScalarField3 class constructs a scalar field F in R^3 as a union of scalar fields Pn, defined over regions Rn i.e. piecewise. More...
#include <gz/math/PiecewiseScalarField3.hh>
Classes | |
| struct | Piece |
| A scalar field P in R^3 and the region R in which it is defined. More... | |
Public Member Functions | |
| PiecewiseScalarField3 ()=default | |
| Constructor. More... | |
| PiecewiseScalarField3 (const std::vector< Piece > &_pieces) | |
| Constructor. More... | |
| ScalarT | Evaluate (const Vector3< ScalarT > &_p) const |
Evaluate the piecewise scalar field at _p More... | |
| ScalarT | Minimum () const |
| Compute the piecewise scalar field minimum. More... | |
| ScalarT | Minimum (Vector3< ScalarT > &_pMin) const |
| Compute the piecewise scalar field minimum Note that, since this method computes the minimum for each region independently, it implicitly assumes continuity in the boundaries between regions, if any. More... | |
| ScalarT | operator() (const Vector3< ScalarT > &_p) const |
| Call operator overload. More... | |
Static Public Member Functions | |
| static PiecewiseScalarField3 | Throughout (ScalarField3T _field) |
Define piecewise scalar field as _field throughout R^3 space. More... | |
Detailed Description
template<typename ScalarField3T, typename ScalarT>
class gz::math::PiecewiseScalarField3< ScalarField3T, ScalarT >
The PiecewiseScalarField3 class constructs a scalar field F in R^3 as a union of scalar fields Pn, defined over regions Rn i.e. piecewise.
- Template Parameters
-
ScalarField3T a callable type taking a single Vector3<ScalarT> value as argument and returning a ScalarT value. Additionally: - for PiecewiseScalarField3 to have a stream operator overload, ScalarField3T must support stream operator overload;
- for PiecewiseScalarField3::Minimum to be callable, ScalarField3T must implement a ScalarT Minimum(const Region3<ScalarT> &, Vector3<ScalarT> &) method that computes its minimum in the given region and returns an argument value that yields said minimum.
ScalarT a numeric type for which std::numeric_limits<> traits have been specialized.
Example
#include <iostream>
#include <gz/math/AdditivelySeparableScalarField3.hh>
#include <gz/math/PiecewiseScalarField3.hh>
#include <gz/math/Polynomial3.hh>
int main(int argc, char **argv)
{
const double kConstant = 1.;
const gz::math::Polynomial3d xPoly(
gz::math::Vector4d(0., 1., 0., 1.));
const gz::math::Polynomial3d yPoly(
gz::math::Vector4d(1., 0., 1., 0.));
const gz::math::Polynomial3d zPoly(
gz::math::Vector4d(1., 0., 0., -1.));
using AdditivelySeparableScalarField3dT =
using PiecewiseScalarField3dT =
AdditivelySeparableScalarField3dT>;
const PiecewiseScalarField3dT scalarField({
{gz::math::Region3d( // x < 0 halfspace
-gz::math::INF_D, 0.),
AdditivelySeparableScalarField3dT(
kConstant, xPoly, yPoly, zPoly)},
{gz::math::Region3d( // x >= 0 halfspace
0., gz::math::INF_D),
AdditivelySeparableScalarField3dT(
-kConstant, xPoly, yPoly, zPoly)}});
// A printable piecewise scalar field.
std::cout << "A piecewise scalar field in R^3 is made up of "
<< "several pieces e.g. P(x, y, z) = "
<< scalarField << std::endl;
// A piecewise scalar field can be evaluated.
std::cout << "Evaluating P(x, y, z) at (1, 0, 0) yields "
<< scalarField(gz::math::Vector3d::UnitX)
<< std::endl;
std::cout << "Evaluating P(x, y, z) at (-1, 0, 0) yields "
<< scalarField(-gz::math::Vector3d::UnitX)
<< std::endl;
// A piecewise scalar field can be queried for its minimum
// (provided the underlying scalar function allows it).
std::cout << "The global minimum of P(x, y, z) is "
<< scalarField.Minimum() << std::endl;
}
Constructor & Destructor Documentation
◆ PiecewiseScalarField3() [1/2]
|
default |
Constructor.
◆ PiecewiseScalarField3() [2/2]
|
inlineexplicit |
Constructor.
- Parameters
-
[in] _pieces scalar fields Pn and the regions Rn in which these are defined. Regions should not overlap.
References std::endl().
Member Function Documentation
◆ Evaluate()
|
inline |
Evaluate the piecewise scalar field at _p
- Parameters
-
[in] _p piecewise scalar field argument
- Returns
- the result of evaluating
F(_p), or NaN if the scalar field is not defined at_p
References std::find_if(), and numeric_limits::quiet_NaN().
Referenced by PiecewiseScalarField3< ScalarField3T, ScalarT >::operator()().
◆ Minimum() [1/2]
|
inline |
Compute the piecewise scalar field minimum.
- Returns
- the scalar field minimum, or NaN if the scalar field is not defined anywhere (i.e. default constructed)
◆ Minimum() [2/2]
|
inline |
Compute the piecewise scalar field minimum Note that, since this method computes the minimum for each region independently, it implicitly assumes continuity in the boundaries between regions, if any.
- Parameters
-
[out] _pMin scalar field argument that yields the minimum, or NaN if the scalar field is not defined anywhere (i.e. default constructed)
- Returns
- the scalar field minimum, or NaN if the scalar field is not defined anywhere (i.e. default constructed)
References numeric_limits::infinity(), and numeric_limits::quiet_NaN().
◆ operator()()
|
inline |
Call operator overload.
- Parameters
-
[in] _p piecewise scalar field argument
- Returns
- the result of evaluating
F(_p), or NaN if the scalar field is not defined at_p
References PiecewiseScalarField3< ScalarField3T, ScalarT >::Evaluate().
◆ Throughout()
|
inlinestatic |
Define piecewise scalar field as _field throughout R^3 space.
- Parameters
-
[in] _field a scalar field in R^3
- Returns
_fieldas a piecewise scalar field
References std::move().
The documentation for this class was generated from the following file: