sphere.h

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2018 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// This library is free software; you can 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.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



#ifndef LIBMESH_SPHERE_H
#define LIBMESH_SPHERE_H

// Local includes
#include "libmesh/surface.h"
#include "libmesh/libmesh.h"

// C++ includes
#include <cstdlib> // *must* precede <cmath> for proper std:abs() on PGI, Sun Studio CC
#include <cmath>

namespace libMesh
{

class Sphere : public Surface
{
public:

  Sphere ();

  Sphere (const Point & c, const Real r);

  Sphere (const Point &, const Point &, const Point &, const Point &);

  Sphere (const Sphere & other_sphere);

  ~Sphere ();

  void create_from_center_radius (const Point & c, const Real r);

  bool intersects (const Sphere & other_sphere) const;

  Real distance (const Sphere & other_sphere) const;

  virtual bool above_surface (const Point & p) const override;

  virtual bool below_surface (const Point & p) const override;

  virtual bool on_surface (const Point & p) const override;

  virtual Point closest_point (const Point & p) const override;

  virtual Point unit_normal (const Point & p) const override;

  Real radius() const { return _rad; }

  Real & radius() { return _rad; }

  const Point & center() const { return _cent; }

  Point & center() { return _cent; }

  virtual Point surface_coords (const Point & cart) const override;

  virtual Point world_coords (const Point & sph) const override;


private:

  Point _cent;

  Real  _rad;
};



// ------------------------------------------------------------
// Sphere inline functions
inline
Point Sphere::surface_coords (const Point & cart) const
{
  // constant translation in the origin
  const Point c (cart-this->center());

  // phi: special care, so that it gives 0..2pi results
  const Real phi = std::atan2(c(1), c(0));

  return Point(/* radius */ c.norm(),
               /* theta  */ std::atan2( std::sqrt( c(0)*c(0) + c(1)*c(1) ), c(2) ),
               /* phi    */ ( (phi < 0)  ?  2.*libMesh::pi+phi  :  phi ) );
}



inline
Point Sphere::world_coords (const Point & sph) const
{
  const Real r     = sph(0);
  const Real theta = sph(1);
  const Real phi   = sph(2);

  // constant translation out of the origin
  return Point (/* x */ r*std::sin(theta)*std::cos(phi) + this->center()(0),
                /* y */ r*std::sin(theta)*std::sin(phi) + this->center()(1),
                /* z */ r*std::cos(theta)               + this->center()(2));
}



} // namespace libMesh


#endif // LIBMESH_SPHERE_H