text: /* ========================================================================= *
   *                                                                           *
   *                               OpenMesh                                    *
   *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
   *           Department of Computer Graphics and Multimedia                  *
   *                          All rights reserved.                             *
   *                            www.openmesh.org                               *
   *                                                                           *
   *---------------------------------------------------------------------------*
   * This file is part of OpenMesh.                                            *
   *---------------------------------------------------------------------------*
   *                                                                           *
   * Redistribution and use in source and binary forms, with or without        *
   * modification, are permitted provided that the following conditions        *
   * are met:                                                                  *
   *                                                                           *
   * 1. Redistributions of source code must retain the above copyright notice, *
   *    this list of conditions and the following disclaimer.                  *
   *                                                                           *
   * 2. Redistributions in binary form must reproduce the above copyright      *
   *    notice, this list of conditions and the following disclaimer in the    *
   *    documentation and/or other materials provided with the distribution.   *
   *                                                                           *
   * 3. Neither the name of the copyright holder nor the names of its          *
   *    contributors may be used to endorse or promote products derived from   *
   *    this software without specific prior written permission.               *
   *                                                                           *
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
   * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
   * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
   * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
   * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
   * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
   * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
   * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
   * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
   * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
   * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
   *                                                                           *
   * ========================================================================= */
  
  
  
  
  #ifndef MATHDEFS_HH
  #define MATHDEFS_HH
  
  #include <cmath>
  #include <cfloat>
  
  #ifndef M_PI
    #define M_PI      3.14159265359
  #endif
  
  namespace OpenMesh
  {
  
  /** comparison operators with user-selected precision control
  */
  template <class T, typename Real>
  inline bool is_zero(const T& _a, Real _eps)
  { return fabs(_a) < _eps; }
  
  template <class T1, class T2, typename Real>
  inline bool is_eq(const T1& a, const T2& b, Real _eps)
  { return is_zero(a-b, _eps); }
  
  template <class T1, class T2, typename Real>
  inline bool is_gt(const T1& a, const T2& b, Real _eps)
  { return (a > b) && !is_eq(a,b,_eps); }
  
  template <class T1, class T2, typename Real>
  inline bool is_ge(const T1& a, const T2& b, Real _eps)
  { return (a > b) || is_eq(a,b,_eps); }
  
  template <class T1, class T2, typename Real>
  inline bool is_lt(const T1& a, const T2& b, Real _eps)
  { return (a < b) && !is_eq(a,b,_eps); }
  
  template <class T1, class T2, typename Real>
  inline bool is_le(const T1& a, const T2& b, Real _eps)
  { return (a < b) || is_eq(a,b,_eps); }
  
  /*const float flt_eps__ = 10*FLT_EPSILON;
  const double dbl_eps__ = 10*DBL_EPSILON;*/
  const float flt_eps__ = (float)1e-05;
  const double dbl_eps__ = 1e-09;
  
  inline float eps__(float) 
  { return flt_eps__; }
  
  inline double eps__(double)
  { return dbl_eps__; }
  
  template <class T>
  inline bool is_zero(const T& a)
  { return is_zero(a, eps__(a)); }
  
  template <class T1, class T2>
  inline bool is_eq(const T1& a, const T2& b)
  { return is_zero(a-b); }
  
  template <class T1, class T2>
  inline bool is_gt(const T1& a, const T2& b)
  { return (a > b) && !is_eq(a,b); }
  
  template <class T1, class T2>
  inline bool is_ge(const T1& a, const T2& b)
  { return (a > b) || is_eq(a,b); }
  
  template <class T1, class T2>
  inline bool is_lt(const T1& a, const T2& b)
  { return (a < b) && !is_eq(a,b); }
  
  template <class T1, class T2>
  inline bool is_le(const T1& a, const T2& b)
  { return (a < b) || is_eq(a,b); }
  
  /// Trigonometry/angles - related
  
  template <class T>
  inline T sane_aarg(T _aarg)
  {
    if (_aarg < -1)
    {
      _aarg = -1;
    }
    else if (_aarg >  1)
    {
      _aarg = 1;
    }
    return _aarg;
  }
  
  /** returns the angle determined by its cos and the sign of its sin
      result is positive if the angle is in [0:pi]
      and negative if it is in [pi:2pi]
  */
  template <class T>
  T angle(T _cos_angle, T _sin_angle)
  {//sanity checks - otherwise acos will return nan
    _cos_angle = sane_aarg(_cos_angle);
    return (T) _sin_angle >= 0 ? acos(_cos_angle) : -acos(_cos_angle);
  }
  
  template <class T>
  inline T positive_angle(T _angle)
  { return _angle < 0 ? (2*M_PI + _angle) : _angle; }
  
  template <class T>
  inline T positive_angle(T _cos_angle, T _sin_angle)
  { return positive_angle(angle(_cos_angle, _sin_angle)); }
  
  template <class T>
  inline T deg_to_rad(const T& _angle)
  { return M_PI*(_angle/180); }
  
  template <class T>
  inline T rad_to_deg(const T& _angle)
  { return 180*(_angle/M_PI); }
  
  inline double log_(double _value)
  { return log(_value); }
  
  }//namespace OpenMesh
  
  #endif//MATHDEFS_HH
  