NGon2D.ih

/**
 *  This program 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 3 of the
 *  License, or  (at your option) any later version.
 *
 *  This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 **/
 
/**
 * @file NGon2D.ih
 * @author David Coeurjolly (\c david.coeurjolly@liris.cnrs.fr )
 * Laboratoire d'InfoRmatique en Image et Systèmes d'information - LIRIS (CNRS, UMR 5205), CNRS, France
 * @author Jacques-Olivier Lachaud (\c jacques-olivier.lachaud@univ-savoie.fr )
 * Laboratory of Mathematics (CNRS, UMR 5807), University of Savoie, France
 *
 * @date 2011/04/12
 *
 * Implementation of inline methods defined in NGon2D.h
 *
 * This file is part of the DGtal library.
 */
 
 
//////////////////////////////////////////////////////////////////////////////
#include <cstdlib>
//////////////////////////////////////////////////////////////////////////////
 
#define NGON2D_2_PI (2. * M_PI)
 
///////////////////////////////////////////////////////////////////////////////
// IMPLEMENTATION of inline methods.
///////////////////////////////////////////////////////////////////////////////
 
///////////////////////////////////////////////////////////////////////////////
// ----------------------- Standard services ------------------------------
 
template <typename T>
inline
DGtal::NGon2D<T>::NGon2D(const double x0, const double y0, 
       const double radius, const unsigned int k,
       const double phi):
  myCenter(x0,y0), myRadius(radius), myK(k), myPhi(phi)
{}
 
 
template <typename T>
inline
DGtal::NGon2D<T>::NGon2D(const RealPoint &aPoint,
       const double radius, const unsigned int k,
       const double phi):
  myCenter(aPoint), myRadius(radius) , myK(k), myPhi(phi)
{}
 
template <typename T>
inline
DGtal::NGon2D<T>::NGon2D(const NGon2D& other):
  myCenter(other.myCenter), myRadius(other.myRadius),
  myK(other.myK), myPhi(other.myPhi)
{}
 
/////////////////////////////////////////////////////////////////////////////
// ------------- Implementation of 'StarShaped' services ------------------
 
/**
 * @param p any point in the plane.
 *
 * @return the angle parameter between 0 and 2*Pi corresponding to
 * this point for the shape.
 */
template <typename T>
inline
double
DGtal::NGon2D<T>::parameter( const RealPoint & p ) const
{
  const double angle = atan2( p[1]-myCenter[1], p[0]-myCenter[0] );
  return angle < 0. ? angle + NGON2D_2_PI : angle;
}
 
/**
 * @param t any angle between 0 and 2*Pi.
 *
 * @return the vector (x(t),y(t)) which is the position on the
 * shape boundary.
 */
template <typename T>
inline
typename DGtal::NGon2D<T>::RealPoint 
DGtal::NGon2D<T>::x( const double t ) const
{
  double angle = t - myPhi;
  angle = (angle < 0.0) ? angle + NGON2D_2_PI : angle;
 
  // seek the vertices between the point, then compute the vector from one vertex to the next one.
 
  const unsigned int intervale_lower = static_cast<unsigned int>( floor( angle * myK / NGON2D_2_PI ) );
  const unsigned int intervale_upper = intervale_lower == ( myK - 1 ) ? 0 : intervale_lower + 1;
  const RealPoint s1 ( myRadius * cos( myPhi + intervale_lower * NGON2D_2_PI / myK ),
                       myRadius * sin( myPhi + intervale_lower * NGON2D_2_PI / myK ));
  const RealPoint s2 ( myRadius * cos( myPhi + intervale_upper * NGON2D_2_PI / myK ),
                       myRadius * sin( myPhi + intervale_upper * NGON2D_2_PI / myK ));
 
  const double line_angle = atan2( s2[1]-s1[1], s2[0]-s1[0] );
  //line_angle = (line_angle < 0.0) ? angle + 2 * M_PI : line_angle;
  const double rho = myRadius * cos(M_PI / myK) / cos(t - line_angle - M_PI_2);
 
  return RealPoint(
    -rho * cos(t) + myCenter[0],
    -rho * sin(t) + myCenter[1]
  );
}
 
 
/**
 * @param t any angle between 0 and 2*Pi.
 *
 * @return the vector (x'(t),y'(t)) which is the tangent to the
 * shape boundary.
 */
template <typename T>
inline
typename DGtal::NGon2D<T>::RealVector 
DGtal::NGon2D<T>::xp( const double t ) const
{
  // seek the vertices between the point, then compute the vector from one vertex to the next one.
  // TODO check if angle equals that of a vertex ?
  double angle = t - myPhi; 
  while ( angle < 0.0 )
    angle += NGON2D_2_PI;
  
  unsigned int intervalle_lower = static_cast<unsigned int>( floor( angle * myK / (NGON2D_2_PI ) ) );
  unsigned int intervalle_upper = intervalle_lower == ( myK -1 ) ? 0 : intervalle_lower+1;
 
  const RealPoint s(
        myRadius*cos(myPhi + intervalle_upper*NGON2D_2_PI/myK)
      - myRadius*cos(myPhi + intervalle_lower*NGON2D_2_PI/myK),
        myRadius*sin(myPhi + intervalle_upper*NGON2D_2_PI/myK)
      - myRadius*sin(myPhi + intervalle_lower*NGON2D_2_PI/myK)
  );
  
  //normalize
  return s / s.norm();
}
 
/**
 *
 * @return the vector (x''(t),y''(t)).
 */
template <typename T>
inline
typename DGtal::NGon2D<T>::RealVector
DGtal::NGon2D<T>::xpp( const double /*t*/ ) const
{
  return RealVector(0.,0.);
}
 
 
///////////////////////////////////////////////////////////////////////////////
// Interface - public :
 
/**
 * Writes/Displays the object on an output stream.
 * @param out the output stream where the object is written.
 */
template <typename T>
inline
void
DGtal::NGon2D<T>::selfDisplay ( std::ostream & out ) const
{
  out << "[NGon2D] center= " << myCenter
      << " radius=" << myRadius
      << " number of sides=" << myK
      << " phase-shift=" << myPhi;
}
 
/**
 * Checks the validity/consistency of the object.
 * @return 'true' if the object is valid, 'false' otherwise.
 */
template <typename T>
inline
bool
DGtal::NGon2D<T>::isValid() const
{
    return true;
}
 
 
 
///////////////////////////////////////////////////////////////////////////////
// Implementation of inline functions                                        //
 
template <typename T>
inline
std::ostream&
DGtal::operator<< ( std::ostream & out, 
      const NGon2D<T> & object )
{
  object.selfDisplay( out );
  return out;
}
 
//                                                                           //
///////////////////////////////////////////////////////////////////////////////