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
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
|
#include "maths.h"
#include <cmath>
#include <glm/glm.hpp>
#include <glm/gtx/rotate_vector.hpp>
#include <glm/gtx/transform.hpp>
#include <stdexcept>
glm::mat4
flat_orientation(const Direction3D & diff)
{
static const auto oneeighty {glm::rotate(pi, up)};
const auto flatdiff {glm::normalize(diff.xy() || 0.F)};
auto e {glm::orientation(flatdiff, north)};
// Handle if diff is exactly opposite to north
return (std::isnan(e[0][0])) ? oneeighty : e;
}
// Helper to lookup into a matrix given an xy vector coordinate
template<typename M, typename I>
inline auto &
operator^(M & m, glm::vec<2, I> xy)
{
return m[xy.x][xy.y];
}
// Create a matrix for the angle, given the targets into the matrix
template<typename M, typename I>
inline auto
rotation(typename M::value_type a, glm::vec<2, I> c1, glm::vec<2, I> s1, glm::vec<2, I> c2, glm::vec<2, I> ms2)
{
M m(1);
sincosf(a, m ^ s1, m ^ c1);
m ^ c2 = m ^ c1;
m ^ ms2 = -(m ^ s1);
return m;
}
// Create a flat (2D) transformation matrix
glm::mat2
rotate_flat(float a)
{
return rotation<glm::mat2, glm::length_t>(a, {0, 0}, {0, 1}, {1, 1}, {1, 0});
}
// Create a yaw transformation matrix
glm::mat4
rotate_yaw(float a)
{
return rotation<glm::mat4, glm::length_t>(a, {0, 0}, {1, 0}, {1, 1}, {0, 1});
}
// Create a roll transformation matrix
glm::mat4
rotate_roll(float a)
{
return rotation<glm::mat4, glm::length_t>(a, {0, 0}, {2, 0}, {2, 2}, {0, 2});
}
// Create a pitch transformation matrix
glm::mat4
rotate_pitch(float a)
{
return rotation<glm::mat4, glm::length_t>(a, {1, 1}, {1, 2}, {2, 2}, {2, 1});
}
// Create a combined yaw, pitch, roll transformation matrix
glm::mat4
rotate_ypr(Rotation3D a)
{
return rotate_yaw(a.y) * rotate_pitch(a.x) * rotate_roll(a.z);
}
glm::mat4
rotate_yp(Rotation2D a)
{
return rotate_yaw(a.y) * rotate_pitch(a.x);
}
float
vector_yaw(const Direction3D & diff)
{
return std::atan2(diff.x, diff.y);
}
float
vector_pitch(const Direction3D & diff)
{
return std::atan(diff.z);
}
float
round_frac(const float & v, const float & frac)
{
return std::round(v / frac) * frac;
}
float
normalize(float ang)
{
while (ang > pi) {
ang -= two_pi;
}
while (ang <= -pi) {
ang += two_pi;
}
return ang;
}
Arc::Arc(const Position3D & centre3, const Position3D & e0p, const Position3D & e1p) :
Arc([&]() -> Arc {
const auto diffa = e0p - centre3;
const auto diffb = e1p - centre3;
const auto anga = vector_yaw(diffa);
const auto angb = [&diffb, &anga]() {
const auto angb = vector_yaw(diffb);
return (angb < anga) ? angb + two_pi : angb;
}();
return {anga, angb};
}())
{
}
std::pair<Position2D, bool>
find_arc_centre(Position2D as, float entrys, Position2D bs, float entrye)
{
if (as == bs) {
return {as, false};
}
return find_arc_centre(as, sincosf(entrys + half_pi), bs, sincosf(entrye - half_pi));
}
std::pair<Position2D, bool>
find_arc_centre(Position2D as, Position2D ad, Position2D bs, Position2D bd)
{
const auto det = bd.x * ad.y - bd.y * ad.x;
if (det != 0) { // near parallel line will yield noisy results
const auto d = bs - as;
const auto u = (d.y * bd.x - d.x * bd.y) / det;
return {as + ad * u, u < 0};
}
throw std::runtime_error("no intersection");
}
std::pair<float, float>
find_arcs_radius(Position2D start, float entrys, Position2D end, float entrye)
{
const auto getrad = [&](float leftOrRight) {
return find_arcs_radius(start, sincosf(entrys + leftOrRight), end, sincosf(entrye + leftOrRight));
};
return {getrad(-half_pi), getrad(half_pi)};
}
float
find_arcs_radius(Position2D start, Position2D ad, Position2D end, Position2D bd)
{
// Short name functions for big forula
auto sqrt = [](float v) {
return std::sqrt(v);
};
// Calculates path across both arcs along the normals... pythagorean theorem... for some known radius r
// (2r)^2 = ((m + (X*r)) - (o + (Z*r)))^2 + ((n + (Y*r)) - (p + (W*r)))^2
// According to symbolabs.com equation tool, that solves for r to give:
// r=(-2 m X+2 X o+2 m Z-2 o Z-2 n Y+2 Y p+2 n W-2 p W-sqrt((2 m X-2 X o-2 m Z+2 o Z+2 n Y-2 Y p-2 n W+2 p W)^(2)-4
// (X^(2)-2 X Z+Z^(2)+Y^(2)-2 Y W+W^(2)-4) (m^(2)-2 m o+o^(2)+n^(2)-2 n p+p^(2))))/(2 (X^(2)-2 X Z+Z^(2)+Y^(2)-2 Y
// W+W^(2)-4))
// These exist cos limitations of online formula rearrangement, and I'm OK with that.
const auto &m {start.x}, &n {start.y}, &o {end.x}, &p {end.y};
const auto &X {ad.x}, &Y {ad.y}, &Z {bd.x}, &W {bd.y};
return (2 * m * X - 2 * X * o - 2 * m * Z + 2 * o * Z + 2 * n * Y - 2 * Y * p - 2 * n * W + 2 * p * W
- sqrt(sq(-2 * m * X + 2 * X * o + 2 * m * Z - 2 * o * Z - 2 * n * Y + 2 * Y * p + 2 * n * W
- 2 * p * W)
- (4 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4)
* (sq(m) - 2 * m * o + sq(o) + sq(n) - 2 * n * p + sq(p)))))
/ (2 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4));
}
float
operator"" _mph(const long double v)
{
return static_cast<float>(mph_to_ms(v));
}
float
operator"" _kph(const long double v)
{
return static_cast<float>(kph_to_ms(v));
}
|
