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MathDefs.hh
1 /*===========================================================================*\
2 * *
3 * OpenMesh *
4 * Copyright (C) 2001-2012 by Computer Graphics Group, RWTH Aachen *
5 * www.openmesh.org *
6 * *
7 *---------------------------------------------------------------------------*
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9 * *
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13 * the License, or (at your option) any later version with the *
14 * following exceptions: *
15 * *
16 * If other files instantiate templates or use macros *
17 * or inline functions from this file, or you compile this file and *
18 * link it with other files to produce an executable, this file does *
19 * not by itself cause the resulting executable to be covered by the *
20 * GNU Lesser General Public License. This exception does not however *
21 * invalidate any other reasons why the executable file might be *
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23 * *
24 * OpenMesh is distributed in the hope that it will be useful, *
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33 \*===========================================================================*/
34
35 /*===========================================================================*\
36 * *
37 * $Revision: 736 $ *
38 * $Date: 2012-10-08 09:30:49 +0200 (Mo, 08 Okt 2012) $ *
39 * *
40 \*===========================================================================*/
41
42 #ifndef MATHDEFS_HH
43 #define MATHDEFS_HH
44
45 #include <math.h>
46 #include <float.h>
47
48 #ifndef M_PI
49 #define M_PI 3.14159265359
50 #endif
51
52 namespace OpenMesh
53 {
54
57 template <class T, typename Real>
58 inline bool is_zero(const T& _a, Real _eps)
59 { return fabs(_a) < _eps; }
60
61 template <class T1, class T2, typename Real>
62 inline bool is_eq(const T1& a, const T2& b, Real _eps)
63 { return is_zero(a-b, _eps); }
64
65 template <class T1, class T2, typename Real>
66 inline bool is_gt(const T1& a, const T2& b, Real _eps)
67 { return (a > b) && !is_eq(a,b,_eps); }
68
69 template <class T1, class T2, typename Real>
70 inline bool is_ge(const T1& a, const T2& b, Real _eps)
71 { return (a > b) || is_eq(a,b,_eps); }
72
73 template <class T1, class T2, typename Real>
74 inline bool is_lt(const T1& a, const T2& b, Real _eps)
75 { return (a < b) && !is_eq(a,b,_eps); }
76
77 template <class T1, class T2, typename Real>
78 inline bool is_le(const T1& a, const T2& b, Real _eps)
79 { return (a < b) || is_eq(a,b,_eps); }
80
81 /*const float flt_eps__ = 10*FLT_EPSILON;
82 const double dbl_eps__ = 10*DBL_EPSILON;*/
83 const float flt_eps__ = (float)1e-05;
84 const double dbl_eps__ = 1e-09;
85
86 inline float eps__(float)
87 { return flt_eps__; }
88
89 inline double eps__(double)
90 { return dbl_eps__; }
91
92 template <class T>
93 inline bool is_zero(const T& a)
94 { return is_zero(a, eps__(a)); }
95
96 template <class T1, class T2>
97 inline bool is_eq(const T1& a, const T2& b)
98 { return is_zero(a-b); }
99
100 template <class T1, class T2>
101 inline bool is_gt(const T1& a, const T2& b)
102 { return (a > b) && !is_eq(a,b); }
103
104 template <class T1, class T2>
105 inline bool is_ge(const T1& a, const T2& b)
106 { return (a > b) || is_eq(a,b); }
107
108 template <class T1, class T2>
109 inline bool is_lt(const T1& a, const T2& b)
110 { return (a < b) && !is_eq(a,b); }
111
112 template <class T1, class T2>
113 inline bool is_le(const T1& a, const T2& b)
114 { return (a < b) || is_eq(a,b); }
115
117
118 template <class T>
119 inline T sane_aarg(T _aarg)
120 {
121 if (_aarg < -1)
122 {
123 _aarg = -1;
124 }
125 else if (_aarg > 1)
126 {
127 _aarg = 1;
128 }
129 return _aarg;
130 }
131
136 template <class T>
137 T angle(T _cos_angle, T _sin_angle)
138 {//sanity checks - otherwise acos will return nan
139 _cos_angle = sane_aarg(_cos_angle);
140 return (T) _sin_angle >= 0 ? acos(_cos_angle) : -acos(_cos_angle);
141 }
142
143 template <class T>
144 inline T positive_angle(T _angle)
145 { return _angle < 0 ? (2*M_PI + _angle) : _angle; }
146
147 template <class T>
148 inline T positive_angle(T _cos_angle, T _sin_angle)
149 { return positive_angle(angle(_cos_angle, _sin_angle)); }
150
151 template <class T>
152 inline T deg_to_rad(const T& _angle)
153 { return M_PI*(_angle/180); }
154
155 template <class T>
156 inline T rad_to_deg(const T& _angle)
157 { return 180*(_angle/M_PI); }
158
159 inline double log_(double _value)
160 { return log(_value); }
161
162 }//namespace OpenMesh
163
164 #endif//MATHDEFS_HH