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 <ignition/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 ignition::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 =
      gz::math::AdditivelySeparableScalarField3d<
        gz::math::Polynomial3d>;
  using PiecewiseScalarField3dT =
      gz::math::PiecewiseScalarField3d<
        AdditivelySeparableScalarField3dT>;
  const PiecewiseScalarField3dT scalarField({
      {gz::math::Region3d(  // x < 0 halfspace
          gz::math::Intervald::Open(
              -gz::math::INF_D, 0.),
          gz::math::Intervald::Unbounded,
          gz::math::Intervald::Unbounded),
       AdditivelySeparableScalarField3dT(
           kConstant, xPoly, yPoly, zPoly)},
      {gz::math::Region3d(  // x >= 0 halfspace
          gz::math::Intervald::LeftClosed(
              0., gz::math::INF_D),
          gz::math::Intervald::Unbounded,
          gz::math::Intervald::Unbounded),
       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]

PiecewiseScalarField3 ( )

default

Constructor.

PiecewiseScalarField3() [2/2]

PiecewiseScalarField3 ( const std::vector< Piece > &  _pieces )

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()

ScalarT Evaluate ( const Vector3< ScalarT > &  _p ) const

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]

ScalarT Minimum ( ) const

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]

ScalarT Minimum ( Vector3< ScalarT > &  _pMin ) const

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()()

ScalarT operator() ( const Vector3< ScalarT > &  _p ) const

inline

Call operator overload.

See also

PiecewiseScalarField3::Evaluate()

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()

static PiecewiseScalarField3 Throughout ( ScalarField3T  _field )

inlinestatic

Define piecewise scalar field as _field throughout R^3 space.

Parameters

[in]

_field

a scalar field in R^3

Returns

_field as a piecewise scalar field

References std::move().

---

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

• gz/math/PiecewiseScalarField3.hh