Reference documentation for deal.II version 9.4.1
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Public Types | Public Member Functions | Public Attributes | Static Public Attributes | Private Member Functions | Private Attributes | List of all members
Functions::SignedDistance::Ellipsoid< dim > Class Template Reference

#include <deal.II/base/function_signed_distance.h>

Inheritance diagram for Functions::SignedDistance::Ellipsoid< dim >:
[legend]

Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type
 

Public Member Functions

 Ellipsoid (const Point< dim > &center, const std::array< double, dim > &radii, const double tolerance=1e-14, const unsigned int max_iter=10)
 
double value (const Point< dim > &point, const unsigned int component=0) const override
 
Tensor< 1, dim > gradient (const Point< dim > &, const unsigned int component=0) const override
 
virtual void vector_value (const Point< dim > &p, Vector< RangeNumberType > &values) const
 
virtual void value_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
 
virtual void vector_value_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const
 
virtual void vector_values (const std::vector< Point< dim > > &points, std::vector< std::vector< RangeNumberType > > &values) const
 
virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients) const
 
virtual void gradient_list (const std::vector< Point< dim > > &points, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients, const unsigned int component=0) const
 
virtual void vector_gradients (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const
 
virtual void vector_gradient_list (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const
 
virtual RangeNumberType laplacian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_laplacian (const Point< dim > &p, Vector< RangeNumberType > &values) const
 
virtual void laplacian_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
 
virtual void vector_laplacian_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const
 
virtual SymmetricTensor< 2, dim, RangeNumberType > hessian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &values) const
 
virtual void hessian_list (const std::vector< Point< dim > > &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &values, const unsigned int component=0) const
 
virtual void vector_hessian_list (const std::vector< Point< dim > > &points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType > > > &values) const
 
virtual std::size_t memory_consumption () const
 
Number get_time () const
 
virtual void set_time (const Number new_time)
 
virtual void advance_time (const Number delta_t)
 

Public Attributes

const unsigned int n_components
 

Static Public Attributes

static constexpr unsigned int dimension = dim
 

Private Member Functions

double evaluate_ellipsoid (const Point< dim > &point) const
 
Point< dim > compute_closest_point_ellipse (const Point< dim > &point) const
 
Tensor< 1, dim, double > compute_analyical_normal_vector_on_ellipse (const Point< dim > &point) const
 
double compute_signed_distance_ellipse (const Point< dim > &point) const
 
Tensor< 1, 2, double > compute_analyical_normal_vector_on_ellipse (const Point< 2 > &point) const
 
double compute_signed_distance_ellipse (const Point< 2 > &point) const
 

Private Attributes

const Point< dim > center
 
const std::array< double, dim > radii
 
const double tolerance
 
const unsigned int max_iter
 
Number time
 

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

std::atomic< unsigned intcounter
 
std::map< std::string, unsigned intcounter_map
 
std::vector< std::atomic< bool > * > validity_pointers
 
const std::type_info * object_info
 
void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 
void check_no_subscribers () const noexcept
 
using map_value_type = decltype(counter_map)::value_type
 
using map_iterator = decltype(counter_map)::iterator
 
static std::mutex mutex
 
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Detailed Description

template<int dim>
class Functions::SignedDistance::Ellipsoid< dim >

Signed-distance level set function to an ellipsoid defined by:

\[ \sum_{i=1}^{dim} \frac{(x_i - c_i)^2}{R_i^2} = 1 \]

Here, \(c_i\) are the coordinates of the center of the ellipsoid and \(R_i\) are the elliptic radii. This function is zero on the ellipsoid, negative inside the ellipsoid and positive outside the ellipsoid.

Definition at line 144 of file function_signed_distance.h.

Member Typedef Documentation

◆ time_type

template<int dim, typename RangeNumberType = double>
using Function< dim, RangeNumberType >::time_type = typename FunctionTime< typename numbers::NumberTraits<RangeNumberType>::real_type>::time_type
inherited

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

Constructor & Destructor Documentation

◆ Ellipsoid()

template<int dim>
Functions::SignedDistance::Ellipsoid< dim >::Ellipsoid ( const Point< dim > &  center,
const std::array< double, dim > &  radii,
const double  tolerance = 1e-14,
const unsigned int  max_iter = 10 
)

Constructor, takes the center and radii of the ellipsoid.

Parameters
centerCenter of the ellipsoid.
radiiArray of radii of the ellipsoid.
toleranceTolerance of the distance computation.
max_iterMax. number of iteration of the distance computation algorithm.

Definition at line 134 of file function_signed_distance.cc.

Member Function Documentation

◆ value()

template<int dim>
double Functions::SignedDistance::Ellipsoid< dim >::value ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
overridevirtual

Return the value of the function at the given point. Unless there is only one component (i.e. the function is scalar), you should state the component you want to have evaluated; it defaults to zero, i.e. the first component.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 151 of file function_signed_distance.cc.

◆ gradient()

template<int dim>
Tensor< 1, dim > Functions::SignedDistance::Ellipsoid< dim >::gradient ( const Point< dim > &  point,
const unsigned int  component = 0 
) const
overridevirtual

Calculates the gradient of the signed distance function via the normal of the closest point on the ellipsoid.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 171 of file function_signed_distance.cc.

◆ evaluate_ellipsoid()

template<int dim>
double Functions::SignedDistance::Ellipsoid< dim >::evaluate_ellipsoid ( const Point< dim > &  point) const
private

Evaluates the ellipsoid function:

\[ f(\vec{x}) = \sum_{i=1}^{dim} \frac{(x_i - c_i)^2}{R_i^2} - 1 \]

Definition at line 200 of file function_signed_distance.cc.

◆ compute_closest_point_ellipse()

template<int dim>
Point< dim > Functions::SignedDistance::Ellipsoid< dim >::compute_closest_point_ellipse ( const Point< dim > &  point) const
private

Computes the closest point on the given ellipse for an arbitrary point.

Definition at line 212 of file function_signed_distance.cc.

◆ compute_analyical_normal_vector_on_ellipse() [1/2]

template<int dim>
Tensor< 1, dim, double > Functions::SignedDistance::Ellipsoid< dim >::compute_analyical_normal_vector_on_ellipse ( const Point< dim > &  point) const
private

Computes the analytical normal vector of a origin centred ellipse at a given point according to:

/ \ / b x a y \ | n_x , n_y | = | --— , --— | \ / \ a b /

Parameters
point[x, y]
Returns
[n_x , n_y]

Definition at line 284 of file function_signed_distance.cc.

◆ compute_signed_distance_ellipse() [1/2]

template<int dim>
double Functions::SignedDistance::Ellipsoid< dim >::compute_signed_distance_ellipse ( const Point< dim > &  point) const
private

Compute the signed distance to a 2D ellipsoid i.e. ellipse.

Definition at line 309 of file function_signed_distance.cc.

◆ compute_analyical_normal_vector_on_ellipse() [2/2]

Tensor< 1, 2, double > Functions::SignedDistance::Ellipsoid< 2 >::compute_analyical_normal_vector_on_ellipse ( const Point< 2 > &  point) const
private

Definition at line 295 of file function_signed_distance.cc.

◆ compute_signed_distance_ellipse() [2/2]

double Functions::SignedDistance::Ellipsoid< 2 >::compute_signed_distance_ellipse ( const Point< 2 > &  point) const
private

Definition at line 319 of file function_signed_distance.cc.

◆ vector_value()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_value ( const Point< dim > &  p,
Vector< RangeNumberType > &  values 
) const
virtualinherited

◆ value_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::value_list ( const std::vector< Point< dim > > &  points,
std::vector< RangeNumberType > &  values,
const unsigned int  component = 0 
) const
virtualinherited

Set values to the point values of the specified component of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array.

By default, this function repeatedly calls value() for each point separately, to fill the output array.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_value_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_value_list ( const std::vector< Point< dim > > &  points,
std::vector< Vector< RangeNumberType > > &  values 
) const
virtualinherited

Set values to the point values of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array, and that all elements be vectors with the same number of components as this function has.

By default, this function repeatedly calls vector_value() for each point separately, to fill the output array.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_values()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_values ( const std::vector< Point< dim > > &  points,
std::vector< std::vector< RangeNumberType > > &  values 
) const
virtualinherited

For each component of the function, fill a vector of values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

◆ vector_gradient()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradient ( const Point< dim > &  p,
std::vector< Tensor< 1, dim, RangeNumberType > > &  gradients 
) const
virtualinherited

Return the gradient of all components of the function at the given point.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ gradient_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::gradient_list ( const std::vector< Point< dim > > &  points,
std::vector< Tensor< 1, dim, RangeNumberType > > &  gradients,
const unsigned int  component = 0 
) const
virtualinherited

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.

◆ vector_gradients()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradients ( const std::vector< Point< dim > > &  points,
std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &  gradients 
) const
virtualinherited

For each component of the function, fill a vector of gradient values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

◆ vector_gradient_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_gradient_list ( const std::vector< Point< dim > > &  points,
std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &  gradients 
) const
virtualinherited

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.

◆ laplacian()

template<int dim, typename RangeNumberType = double>
virtual RangeNumberType Function< dim, RangeNumberType >::laplacian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_laplacian()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_laplacian ( const Point< dim > &  p,
Vector< RangeNumberType > &  values 
) const
virtualinherited

Compute the Laplacian of all components at point p and store them in values.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ laplacian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::laplacian_list ( const std::vector< Point< dim > > &  points,
std::vector< RangeNumberType > &  values,
const unsigned int  component = 0 
) const
virtualinherited

Compute the Laplacian of one component at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ vector_laplacian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_laplacian_list ( const std::vector< Point< dim > > &  points,
std::vector< Vector< RangeNumberType > > &  values 
) const
virtualinherited

Compute the Laplacians of all components at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

◆ hessian()

template<int dim, typename RangeNumberType = double>
virtual SymmetricTensor< 2, dim, RangeNumberType > Function< dim, RangeNumberType >::hessian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_hessian()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_hessian ( const Point< dim > &  p,
std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &  values 
) const
virtualinherited

Compute the Hessian of all components at point p and store them in values.

◆ hessian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::hessian_list ( const std::vector< Point< dim > > &  points,
std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &  values,
const unsigned int  component = 0 
) const
virtualinherited

Compute the Hessian of one component at a set of points.

◆ vector_hessian_list()

template<int dim, typename RangeNumberType = double>
virtual void Function< dim, RangeNumberType >::vector_hessian_list ( const std::vector< Point< dim > > &  points,
std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType > > > &  values 
) const
virtualinherited

Compute the Hessians of all components at a set of points.

◆ memory_consumption()

template<int dim, typename RangeNumberType = double>
virtual std::size_t Function< dim, RangeNumberType >::memory_consumption ( ) const
virtualinherited

◆ get_time()

template<typename Number = double>
Number FunctionTime< Number >::get_time ( ) const
inherited

Return the value of the time variable.

◆ set_time()

template<typename Number = double>
virtual void FunctionTime< Number >::set_time ( const Number  new_time)
virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

template<typename Number = double>
virtual void FunctionTime< Number >::advance_time ( const Number  delta_t)
virtualinherited

Advance the time by the given time step delta_t.

Member Data Documentation

◆ center

template<int dim>
const Point<dim> Functions::SignedDistance::Ellipsoid< dim >::center
private

Definition at line 210 of file function_signed_distance.h.

◆ radii

template<int dim>
const std::array<double, dim> Functions::SignedDistance::Ellipsoid< dim >::radii
private

Definition at line 211 of file function_signed_distance.h.

◆ tolerance

template<int dim>
const double Functions::SignedDistance::Ellipsoid< dim >::tolerance
private

Definition at line 212 of file function_signed_distance.h.

◆ max_iter

template<int dim>
const unsigned int Functions::SignedDistance::Ellipsoid< dim >::max_iter
private

Definition at line 213 of file function_signed_distance.h.

◆ dimension

template<int dim, typename RangeNumberType = double>
constexpr unsigned int Function< dim, RangeNumberType >::dimension = dim
staticconstexprinherited

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 159 of file function.h.

◆ n_components

template<int dim, typename RangeNumberType = double>
const unsigned int Function< dim, RangeNumberType >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.

◆ time

template<typename Number = double>
Number FunctionTime< Number >::time
privateinherited

Store the present time.

Definition at line 113 of file function_time.h.


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