manifold_lib.h

// ---------------------------------------------------------------------
//
// Copyright (C) 1999 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii__manifold_lib_h
#define dealii__manifold_lib_h


#include <deal.II/base/config.h>
#include <deal.II/grid/manifold.h>
#include <deal.II/base/function.h>
#include <deal.II/base/function_parser.h>

DEAL_II_NAMESPACE_OPEN

template <int dim, int spacedim = dim>
class PolarManifold : public ChartManifold<dim, spacedim, spacedim>
{
public:
  PolarManifold(const Point<spacedim> center = Point<spacedim>());

  virtual Point<spacedim>
  pull_back(const Point<spacedim> &space_point) const;

  virtual Point<spacedim>
  push_forward(const Point<spacedim> &chart_point) const;

  virtual
  DerivativeForm<1,spacedim,spacedim>
  push_forward_gradient(const Point<spacedim> &chart_point) const;

  const Point<spacedim> center;
private:

  static Tensor<1,spacedim> get_periodicity();
};


template <int dim, int spacedim = dim>
class SphericalManifold : public Manifold<dim, spacedim>
{
public:
  SphericalManifold(const Point<spacedim> center = Point<spacedim>());

  virtual
  Point<spacedim>
  get_intermediate_point(const Point<spacedim> &p1,
                         const Point<spacedim> &p2,
                         const double w) const;

  virtual
  Tensor<1,spacedim>
  get_tangent_vector (const Point<spacedim> &x1,
                      const Point<spacedim> &x2) const;

  virtual
  Point<spacedim>
  get_new_point(const ::Quadrature<spacedim> &quadrature) const DEAL_II_DEPRECATED;

  virtual
  Point<spacedim>
  get_new_point (const std::vector<Point<spacedim> > &vertices,
                 const std::vector<double> &weights) const;

  const Point<spacedim> center;
};


template <int dim, int spacedim = dim>
class CylindricalManifold : public Manifold<dim,spacedim>
{
public:
  CylindricalManifold (const unsigned int axis = 0,
                       const double tolerance = 1e-10);

  CylindricalManifold (const Point<spacedim> &direction,
                       const Point<spacedim> &point_on_axis,
                       const double tolerance = 1e-10);

  virtual Point<spacedim>
  get_new_point(const Quadrature<spacedim> &quad) const DEAL_II_DEPRECATED;

  virtual Point<spacedim>
  get_new_point(const std::vector<Point<spacedim> > &surrounding_points,
                const std::vector<double>           &weights) const;

protected:
  const Point<spacedim> direction;

  const Point<spacedim> point_on_axis;

private:
  FlatManifold<dim,spacedim> flat_manifold;

  double tolerance;
};


template <int dim, int spacedim=dim, int chartdim=dim>
class FunctionManifold : public ChartManifold<dim, spacedim, chartdim>
{
public:
  FunctionManifold(const Function<chartdim> &push_forward_function,
                   const Function<spacedim> &pull_back_function,
                   const Tensor<1,chartdim> &periodicity=Tensor<1,chartdim>(),
                   const double tolerance=1e-10);

  FunctionManifold(const std::string push_forward_expression,
                   const std::string pull_back_expression,
                   const Tensor<1,chartdim> &periodicity=Tensor<1,chartdim>(),
                   const typename FunctionParser<spacedim>::ConstMap = typename FunctionParser<spacedim>::ConstMap(),
                   const std::string chart_vars=FunctionParser<chartdim>::default_variable_names(),
                   const std::string space_vars=FunctionParser<spacedim>::default_variable_names(),
                   const double tolerance=1e-10,
                   const double h=1e-8);

  ~FunctionManifold();

  virtual Point<spacedim>
  push_forward(const Point<chartdim> &chart_point) const;

  virtual
  DerivativeForm<1,chartdim,spacedim>
  push_forward_gradient(const Point<chartdim> &chart_point) const;

  virtual Point<chartdim>
  pull_back(const Point<spacedim> &space_point) const;

private:
  const typename FunctionParser<spacedim>::ConstMap const_map;

  SmartPointer<const Function<chartdim>,
               FunctionManifold<dim,spacedim,chartdim> > push_forward_function;

  SmartPointer<const Function<spacedim>,
               FunctionManifold<dim,spacedim,chartdim> > pull_back_function;

  const double tolerance;

  const bool owns_pointers;
};


template <int dim>
class TorusManifold : public ChartManifold<dim,3,3>
{
public:
  static const int chartdim = 3;
  static const int spacedim = 3;

  TorusManifold (const double R, const double r);

  virtual Point<3>
  pull_back(const Point<3> &p) const;

  virtual Point<3>
  push_forward(const Point<3> &chart_point) const;

  virtual
  DerivativeForm<1,3,3>
  push_forward_gradient(const Point<3> &chart_point) const;

private:
  double r, R;
};

DEAL_II_NAMESPACE_CLOSE

#endif