function_signed_distance.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2019 - 2023 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.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_function_signed_distance_h
#define dealii_function_signed_distance_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/bounding_box.h>
#include <deal.II/base/function.h>
 
#include <array>
 
DEAL_II_NAMESPACE_OPEN
 
namespace Functions
{
  namespace SignedDistance
  {
    template <int dim>
    class Sphere : public Function<dim>
    {
    public:
      Sphere(const Point<dim> &center = Point<dim>(), const double radius = 1);
 
      double
      value(const Point<dim> & point,
            const unsigned int component = 0) const override;
 
      Tensor<1, dim>
      gradient(const Point<dim> & point,
               const unsigned int component = 0) const override;
 
      SymmetricTensor<2, dim>
      hessian(const Point<dim> & point,
              const unsigned int component = 0) const override;
 
    private:
      const Point<dim> center;
      const double     radius;
    };
 
 
    template <int dim>
    class Plane : public Function<dim>
    {
    public:
      Plane(const Point<dim> &point, const Tensor<1, dim> &normal);
 
      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;
 
      SymmetricTensor<2, dim>
      hessian(const Point<dim> &,
              const unsigned int component = 0) const override;
 
    private:
      const Point<dim>     point_in_plane;
      const Tensor<1, dim> normal;
    };
 
 
    template <int dim>
    class Ellipsoid : public Function<dim>
    {
    public:
      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;
 
    private:
      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;
 
      const Point<dim>              center;
      const std::array<double, dim> radii;
      const double                  tolerance;
      const unsigned int            max_iter;
    };
 
 
    template <int dim>
    class Rectangle : public Function<dim>
    {
    public:
      Rectangle(const Point<dim> &bottom_left, const Point<dim> &top_right);
      Rectangle(const BoundingBox<dim> bounding_box);
 
      double
      value(const Point<dim> & p,
            const unsigned int component = 0) const override;
 
    private:
      const BoundingBox<dim> bounding_box;
    };
 
 
    template <int dim>
    class ZalesakDisk : public Function<dim>
    {
    public:
      ZalesakDisk(const Point<dim> &center,
                  const double      radius,
                  const double      notch_width,
                  const double      notch_height);
 
      double
      value(const Point<dim> & p,
            const unsigned int component = 0) const override;
 
    private:
      const Functions::SignedDistance::Sphere<dim> sphere;
 
      const Functions::SignedDistance::Rectangle<dim> notch;
    };
  } // namespace SignedDistance
} // namespace Functions
 
DEAL_II_NAMESPACE_CLOSE
 
#endif