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#pragma once
#include "config/types.h"
#include <cmath>
#include <glm/glm.hpp>
#include <glm/gtc/constants.hpp>
#include <numeric>
#include <stdexcept>
#include <utility>
struct Arc : public std::pair<float, float> {
using std::pair<float, float>::pair;
template<typename T, glm::qualifier Q>
Arc(const glm::vec<3, T, Q> & centre3, const glm::vec<3, T, Q> & e0p, const glm::vec<3, T, Q> & e1p);
auto
operator[](bool i) const
{
return i ? second : first;
}
};
constexpr const RelativePosition3D up {0, 0, 1};
constexpr const RelativePosition3D down {0, 0, -1};
constexpr const RelativePosition3D north {0, 1, 0};
constexpr const RelativePosition3D south {0, -1, 0};
constexpr const RelativePosition3D east {1, 0, 0};
constexpr const RelativePosition3D west {-1, 0, 0};
constexpr auto half_pi {glm::half_pi<float>()};
constexpr auto quarter_pi {half_pi / 2};
constexpr auto pi {glm::pi<float>()};
constexpr auto two_pi {glm::two_pi<float>()};
template<glm::length_t D>
constexpr inline GlobalPosition<D>
operator+(const GlobalPosition<D> & g, const RelativePosition<D> & r)
{
return g + GlobalPosition<D>(glm::round(r));
}
template<glm::length_t D>
constexpr inline GlobalPosition<D>
operator+(const GlobalPosition<D> & g, const CalcPosition<D> & r)
{
return g + GlobalPosition<D>(r);
}
template<glm::length_t D>
constexpr inline GlobalPosition<D>
operator-(const GlobalPosition<D> & g, const RelativePosition<D> & r)
{
return g - GlobalPosition<D>(glm::round(r));
}
template<glm::length_t D>
constexpr inline GlobalPosition<D>
operator-(const GlobalPosition<D> & g, const CalcPosition<D> & r)
{
return g - GlobalPosition<D>(r);
}
glm::mat4 flat_orientation(const Rotation3D & diff);
// C++ wrapper for C's sincosf, but with references, not pointers
inline auto
sincosf(float a, float & s, float & c)
{
return sincosf(a, &s, &c);
}
inline Rotation2D
sincosf(float a)
{
Rotation2D sc;
sincosf(a, sc.x, sc.y);
return sc;
}
glm::mat2 rotate_flat(float);
glm::mat4 rotate_roll(float);
glm::mat4 rotate_yaw(float);
glm::mat4 rotate_pitch(float);
glm::mat4 rotate_yp(Rotation2D);
glm::mat4 rotate_ypr(Rotation3D);
float vector_yaw(const Direction3D & diff);
float vector_pitch(const Direction3D & diff);
float round_frac(const float & v, const float & frac);
template<typename T>
inline constexpr auto
sq(T v)
{
return v * v;
}
template<glm::qualifier Q>
inline constexpr glm::vec<3, int64_t, Q>
crossProduct(const glm::vec<3, int64_t, Q> a, const glm::vec<3, int64_t, Q> b)
{
return {
(a.y * b.z) - (a.z * b.y),
(a.z * b.x) - (a.x * b.z),
(a.x * b.y) - (a.y * b.x),
};
}
template<std::integral T, glm::qualifier Q>
inline constexpr glm::vec<3, T, Q>
crossProduct(const glm::vec<3, T, Q> a, const glm::vec<3, T, Q> b)
{
return crossProduct<int64_t, Q>(a, b);
}
template<std::floating_point T, glm::qualifier Q>
inline constexpr glm::vec<3, T, Q>
crossProduct(const glm::vec<3, T, Q> a, const glm::vec<3, T, Q> b)
{
return glm::cross(a, b);
}
template<typename R = float, typename Ta, typename Tb>
inline constexpr auto
ratio(Ta a, Tb b)
{
return (static_cast<R>(a) / static_cast<R>(b));
}
template<typename R = float, typename T, glm::qualifier Q>
inline constexpr auto
ratio(glm::vec<2, T, Q> v)
{
return ratio<R>(v.x, v.y);
}
template<glm::length_t L = 3, typename T, glm::qualifier Q>
inline constexpr glm::vec<L, T, Q>
perspective_divide(glm::vec<4, T, Q> v)
{
return v / v.w;
}
template<glm::length_t L1, glm::length_t L2, typename T, glm::qualifier Q>
inline constexpr glm::vec<L1 + L2, T, Q>
operator||(const glm::vec<L1, T, Q> v1, const glm::vec<L2, T, Q> v2)
{
return {v1, v2};
}
template<glm::length_t L, typename T, glm::qualifier Q>
inline constexpr glm::vec<L + 1, T, Q>
operator||(const glm::vec<L, T, Q> v1, const T v2)
{
return {v1, v2};
}
template<glm::length_t L, typename T, glm::qualifier Q>
inline constexpr glm::vec<L, T, Q>
operator%(const glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation)
{
const auto p2 = mutation * (p || T(1));
return p2 / p2.w;
}
template<glm::length_t L, typename T, glm::qualifier Q>
inline constexpr glm::vec<L, T, Q>
operator%=(glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation)
{
return p = p % mutation;
}
constexpr inline float
arc_length(const Arc & arc)
{
return arc.second - arc.first;
}
float normalize(float ang);
template<typename T, glm::qualifier Q>
std::pair<glm::vec<2, T, Q>, bool>
find_arc_centre(glm::vec<2, T, Q> start, Rotation2D startDir, glm::vec<2, T, Q> end, Rotation2D endDir)
{
const auto det = endDir.x * startDir.y - endDir.y * startDir.x;
if (det != 0) { // near parallel line will yield noisy results
const glm::vec<2, RelativeDistance, Q> d = end - start;
const auto u = (d.y * endDir.x - d.x * endDir.y) / det;
return {start + glm::vec<2, T, Q>(startDir * u), u < 0};
}
throw std::runtime_error("no intersection");
}
template<typename T, glm::qualifier Q>
std::pair<glm::vec<2, T, Q>, bool>
find_arc_centre(glm::vec<2, T, Q> start, Angle entrys, glm::vec<2, T, Q> end, Angle entrye)
{
if (start == end) {
return {start, false};
}
return find_arc_centre(start, sincosf(entrys + half_pi), end, sincosf(entrye - half_pi));
}
template<typename T, glm::qualifier Q>
Angle
find_arcs_radius(glm::vec<2, T, Q> start, Rotation2D ad, glm::vec<2, T, Q> end, Rotation2D bd)
{
using std::sqrt;
// 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))
// Locally simplified to work relative, removing one half of the problem and operating on relative positions.
// These exist cos limitations of online formula rearrangement, and I'm OK with that.
const RelativePosition2D diff {end - start};
const auto &o {diff.x}, &p {diff.y};
const auto &X {ad.x}, &Y {ad.y}, &Z {bd.x}, &W {bd.y};
return (-2 * X * o + 2 * o * Z - 2 * Y * p + 2 * p * W
- sqrt(sq(2 * X * o - 2 * o * Z + 2 * Y * p - 2 * p * W)
- (4 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4) * (sq(o) + sq(p)))))
/ (2 * (sq(X) - 2 * X * Z + sq(Z) + sq(Y) - 2 * Y * W + sq(W) - 4));
}
template<typename T, glm::qualifier Q>
std::pair<Angle, Angle>
find_arcs_radius(glm::vec<2, T, Q> start, Angle entrys, glm::vec<2, T, Q> end, Angle entrye)
{
const auto getrad = [&](auto leftOrRight) {
return find_arcs_radius(start, sincosf(entrys + leftOrRight), end, sincosf(entrye + leftOrRight));
};
return {getrad(-half_pi), getrad(half_pi)};
}
template<typename T>
auto
midpoint(const std::pair<T, T> & v)
{
return std::midpoint(v.first, v.second);
}
template<typename T, glm::qualifier Q>
Arc::Arc(const glm::vec<3, T, Q> & centre3, const glm::vec<3, T, Q> & e0p, const glm::vec<3, T, Q> & 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};
}())
{
}
// Conversions
template<typename T>
inline constexpr auto
mph_to_ms(T v)
{
return v / 2.237L;
}
template<typename T>
inline constexpr auto
kph_to_ms(T v)
{
return v / 3.6L;
}
// ... literals are handy for now, probably go away when we load stuff externally
float operator"" _mph(const long double v);
float operator"" _kph(const long double v);
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