JMathToolkit.hh

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#ifndef __JMATHTOOLKIT__
#define __JMATHTOOLKIT__
 
#include <limits>
#include <cmath>
 
#include "JLang/JException.hh"
 
 
/**
 * \file
 * Auxiliary methods for geometrical methods.
 * In this, the action of each global method is transferred to 
 * the corresponding member method of the leading (first) argument, e.g:
 *
 * <tt>getXXX(first, second, ...)</tt>
 *
 * becomes
 *
 * <tt>first.getXXX(second, ...)</tt>
 *\author mdejong
 */
 
/**
 * Auxiliary classes and methods for mathematical operations.
 */
namespace JMATH {}
namespace JPP { using namespace JMATH; }
 
namespace JMATH {
 
  using JLANG::JValueOutOfRange;
 
 
  /**
   * Determine factorial.
   *
   * \param  n        number
   * \return          factorial (= n!)
   */
  inline long long int factorial(const long long int n)
  {
    if (n < 0) {
      THROW(JValueOutOfRange, "JMATH::factorial(): invalid argument " << n);
    }
 
    if (n != 1)
      return n * factorial(n - 1);
    else
      return 1;
  }
 
 
  /**
   * Determine combinatorics.
   *
   * \param  n        number
   * \param  m        number
   * \return          n!/(m!*(n-m)!)
   */
  inline long long int factorial(const long long int n, const long long int m)
  {
    if (n < 0 || m < 0 || n < m) {
      THROW(JValueOutOfRange, "JMATH::factorial(): invalid argument " << n << ' ' << m);
    }
 
    if      (n == m)
      return 1;
    else if (m == 0)
      return 1;
    else
      return factorial(n - 1, m - 1) + factorial(n - 1, m);
  }
 
 
  /**
   * Check equality.
   *
   * \param  first          first  object
   * \param  second         second object
   * \param  precision      precision
   * \return                true if two objects are equals; else false
   */
  template<class JFirst_t, class JSecond_t>
  inline bool equals(const JFirst_t&  first,
                     const JSecond_t& second,
                     const double     precision = std::numeric_limits<double>::min())
  {
    return first.equals(second, precision);
  }
 
 
  /**
   * Get square of distance between objects.
   *
   * \param  first          first  object
   * \param  second         second object
   * \return                square of distance
   */
  template<class JFirst_t, class JSecond_t>
  inline double getDistanceSquared(const JFirst_t&  first,
                                   const JSecond_t& second)
  {
    return first.getDistanceSquared(second);    
  }
 
 
  /**
   * Get distance between objects.
   *
   * \param  first          first  object
   * \param  second         second object
   * \return                distance
   */
  template<class JFirst_t, class JSecond_t>
  inline double getDistance(const JFirst_t&  first,
                            const JSecond_t& second)
  {
    return first.getDistance(second);
  }
 
 
  /**
   * Get dot product of objects.
   *
   * \param  first          first  object
   * \param  second         second object
   * \return                dot product
   */
  template<class JFirst_t, class JSecond_t>
  inline double getDot(const JFirst_t&  first,
                       const JSecond_t& second)
  {
    return first.getDot(second);
  }
 
 
  /**
   * Get space angle between objects.
   *
   * \param  first          first  object
   * \param  second         second object
   * \return                angle [deg]
   */
  template<class JFirst_t, class JSecond_t>
  inline double getAngle(const JFirst_t&  first,
                         const JSecond_t& second)
  {
    const double dot = getDot(first,second);
 
    if      (dot >= +1.0)
      return   0.0;
    else if (dot <= -1.0)
      return 180.0;
    else
      return acos(dot) * 180.0 / acos(-1.0);
  }
 
 
  /**
   * Get perpendicular dot product of objects.
   *
   * \param  first          first  object
   * \param  second         second object
   * \return                perpendicular dot product
   */
  template<class JFirst_t, class JSecond_t>
  inline double getPerpDot(const JFirst_t&  first,
                           const JSecond_t& second)
  {
    return first.getPerpDot(second);
  }
 
 
  /**
   * Interpolation between objects.
   * The result is equal to <tt>result = (1 - alpha) x (first) + (alpha) x (second)</tt>.
   *
   * \param  first          first  object
   * \param  second         second object
   * \param  alpha          interpolation factor (normally between 0 and 1)
   * \return                result
   */
  template<class T>
  inline T interpolate(const T&     first,
                       const T&     second, 
                       const double alpha)
  {
    return T(first).interpolate(second, alpha);
  }
}
 
#endif