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# Core/Math/MathDefs.hh

    00001 /*===========================================================================*\
    00002  *                                                                           *
    00003  *                               OpenMesh                                    *
    00004  *      Copyright (C) 2001-2005 by Computer Graphics Group, RWTH Aachen      *
    00005  *                           www.openmesh.org                                *
    00006  *                                                                           *
    00007  *---------------------------------------------------------------------------*
    00008  *                                                                           *
    00009  *                                License                                    *
    00010  *                                                                           *
    00011  *  This library is free software; you can redistribute it and/or modify it  *
    00012  *  under the terms of the GNU Library General Public License as published   *
    00013  *  by the Free Software Foundation, version 2.                              *
    00014  *                                                                           *
    00015  *  This library is distributed in the hope that it will be useful, but      *
    00016  *  WITHOUT ANY WARRANTY; without even the implied warranty of               *
    00017  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU        *
    00018  *  Library General Public License for more details.                         *
    00019  *                                                                           *
    00020  *  You should have received a copy of the GNU Library General Public        *
    00021  *  License along with this library; if not, write to the Free Software      *
    00022  *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.                *
    00023  *                                                                           *
    00024 \*===========================================================================*/
    00025
    00026 #ifndef MATHDEFS_HH
    00027 #define MATHDEFS_HH
    00028
    00029 #include <math.h>
    00030 //#include <float.h>
    00031
    00032 #ifndef M_PI
    00033   #define M_PI      3.14159265359
    00034 #endif
    00035
    00036 namespace OpenMesh
    00037 {
    00038
    00041 template <class T, typename Real>
    00042 inline bool                             is_zero(const T& _a, Real _eps)
    00043 {
    00044   return fabs(_a) < _eps;
    00045 }
    00046
    00047 template <class T1, class T2, typename Real>
    00048 inline bool                             is_eq(const T1& a, const T2& b, Real _eps)
    00049 {
    00050   return is_zero(a-b, _eps);
    00051 }
    00052
    00053 template <class T1, class T2, typename Real>
    00054 inline bool                             is_gt(const T1& a, const T2& b, Real _eps)
    00055 {
    00056   return (a > b) && !is_eq(a,b,_eps);
    00057 }
    00058
    00059 template <class T1, class T2, typename Real>
    00060 inline bool                             is_ge(const T1& a, const T2& b, Real _eps)
    00061 {
    00062   return (a > b) || is_eq(a,b,_eps);
    00063 }
    00064
    00065 template <class T1, class T2, typename Real>
    00066 inline bool                             is_lt(const T1& a, const T2& b, Real _eps)
    00067 {
    00068   return (a < b) && !is_eq(a,b,_eps);
    00069 }
    00070
    00071 template <class T1, class T2, typename Real>
    00072 inline bool                             is_le(const T1& a, const T2& b, Real _eps)
    00073 {
    00074   return (a < b) || is_eq(a,b,_eps);
    00075 }
    00076
    00083 const double __flt_eps = 1e-5;
    00084 const double __dbl_eps = 1e-11;
    00085
    00086 inline bool                             is_zero(const float a)
    00087 {
    00088   return is_zero(a, __flt_eps);
    00089 }
    00090
    00091 inline bool                             is_zero(const double a)
    00092 {
    00093   return is_zero(a, __dbl_eps);
    00094 }
    00095
    00096 template <class T1, class T2>
    00097 inline bool                             is_eq(const T1& a, const T2& b)
    00098 {
    00099   return is_zero(a-b);
    00100 }
    00101
    00102 template <class T1, class T2>
    00103 inline bool                             is_gt(const T1& a, const T2& b)
    00104 {
    00105   return (a > b) && !is_eq(a,b);
    00106 }
    00107
    00108 template <class T1, class T2>
    00109 inline bool                             is_ge(const T1& a, const T2& b)
    00110 {
    00111   return (a > b) || is_eq(a,b);
    00112 }
    00113
    00114 template <class T1, class T2>
    00115 inline bool                             is_lt(const T1& a, const T2& b)
    00116 {
    00117   return (a < b) && !is_eq(a,b);
    00118 }
    00119
    00120 template <class T1, class T2>
    00121 inline bool                             is_le(const T1& a, const T2& b)
    00122 {
    00123   return (a < b) || is_eq(a,b);
    00124 }
    00125
    00127
    00128 template <class T>
    00129 T                                      sane_aarg(T _aarg)
    00130 {
    00131   if (_aarg < -1)
    00132   {
    00133     _aarg = -1;
    00134   }
    00135   else if (_aarg >  1)
    00136   {
    00137     _aarg = 1;
    00138   }
    00139   return _aarg;
    00140 }
    00141
    00146 template <class T>
    00147 T                                           angle(T _cos_angle, T _sin_angle)
    00148 {//sanity checks - otherwise acos will return nan
    00149   _cos_angle = sane_aarg(_cos_angle);
    00150   return (T) _sin_angle >= 0 ? acos(_cos_angle) : -acos(_cos_angle);
    00151 }
    00152
    00153 template <class T>
    00154 inline T                               positive_angle(T _angle)
    00155 {
    00156   return _angle < 0 ? (2*M_PI + _angle) : _angle;
    00157 }
    00158
    00159 template <class T>
    00160 inline T                               positive_angle(T _cos_angle, T _sin_angle)
    00161 {
    00162   return positive_angle(angle(_cos_angle, _sin_angle));
    00163 }
    00164
    00165 template <class T>
    00166 inline T                               deg_to_rad(const T& _angle)
    00167 {
    00168   return M_PI*(_angle/180);
    00169 }
    00170
    00171 template <class T>
    00172 inline T                               rad_to_deg(const T& _angle)
    00173 {
    00174   return 180*(_angle/M_PI);
    00175 }
    00176
    00177 };//namespace OpenMesh
    00178
    00179 #endif//MATHDEFS_HH