///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// 
/// =========================================================================
//! @examplefile sphere.icc The level set function for the sphere geometry
struct p {
  Float operator() (const point& x) const {
    if (d == 2) return 26*(pow(x[0],5) - 10*pow(x[0],3)*sqr(x[1]) 
                                       + 5*x[0]*pow(x[1],4));
    else        return 3*sqr(x[0])*x[1] - pow(x[1],3);
  }
  p (size_t d1) : d(d1) {}
  protected: size_t d;
};
struct f {
  Float operator() (const point& x) const {
    if (d == 2) return _p(x)/pow(norm(x),5);
    else        return alpha*_p(x);
  }
  f (size_t d1) : d(d1), _p(d1), alpha(0) {
    Float pi = acos(Float(-1));
    alpha = -(13./8.)*sqrt(35./pi);
  }
  protected: size_t d; p _p; Float alpha;
};
struct u_exact {
  Float operator() (const point& x) const {
    if (d == 2) return _f(x)/(25+sqr(norm(x)));
    else        return sqr(norm(x))/(12+sqr(norm(x)))*_f(x);
  }
  u_exact (size_t d1) : d(d1), _f(d1) {}
  protected: size_t d; f _f;
};
Float phi (const point& x) { return norm(x) - 1; }
