-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathturns.hpp
More file actions
173 lines (156 loc) · 6.65 KB
/
turns.hpp
File metadata and controls
173 lines (156 loc) · 6.65 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
#ifndef TURNS_HPP
#define TURNS_HPP
#include <numbers>
#include <cmath>
/**
* Turns are a way of measuring angles in way where we don't have to care about arbitrary constants when we talk
* about a single turn, when we're working in degrees that arbitrary choice was 360, and when we're working in radians
* that value is pi, but the only way we attach meaning to those values is that they map back to one turn around the
* circle, so why not just cut out the middle man and work with turns directly?
*/
namespace turns {
extern const double one_sixth_turn;
extern const double one_third_turn;
extern const double one_half_turn;
extern const double two_thirds_turn;
extern const double five_sixths_turn;
extern const double one_eighth_turn;
extern const double three_eighths_turn;
extern const double five_eighths_turn;
extern const double seven_eighths_turn;
extern const double one_quarter_turn;
extern const double three_quarters_turn;
extern const double full_turn;
constexpr double turns_to_radians(double turns) { return turns * 2.0 * std::numbers::pi; }
constexpr double radians_to_turns(double radians) { return radians / (2.0 * std::numbers::pi); }
constexpr double turns_to_degrees(double turns) { return turns * 360.0; }
constexpr double degrees_to_turns(double degrees) { return degrees / 360.0; }
constexpr double cos_turns(double t) { return std::cos(turns_to_radians(t)); }
constexpr double sin_turns(double t) { return std::sin(turns_to_radians(t)); }
}; // namespace turns
/** @namespace turns full circle
@code
ooo OOO OOO ooo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oOO OOo
oO OOo
oOO OOo
oOO OOo
ooo OOO OOO ooo
@endcode
*/
/** @namespace turns circle cut into thirds
@code
ooo OOO OOO ooo
oOO OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO XXXXXXXXXXXXXXXXXXXXXXXOOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO OOo
ooo OOO OOO ooo
@endcode
*/
/** @namespace turns circle cut into sixths
@code
ooo OOO OOO ooo
oOO OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXOOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO X X OOo
oOO OOo
ooo OOO OOO ooo
@endcode
*/
/** @namespace turns circle cut into quaters
@code
ooo OOO OOO ooo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXOOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X OOo
oO X OOo
oOO X OOo
oOO X OOo
ooo OOO OOO ooo
@endcode
*/
/** @namespace turns circle cut into eighths
@code
ooo OOO OOO ooo
oOO X OOo
oOO X OOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOOXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXOOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOO X X X OOo
oOO X OOo
oOO X OOo
oOO X OOo
ooo OOO OOO ooo
@endcode
*/
#endif // TURNS_HPP