diff options
Diffstat (limited to 'lib')
| -rw-r--r-- | lib/maths.cpp | 101 | ||||
| -rw-r--r-- | lib/maths.h | 310 |
2 files changed, 238 insertions, 173 deletions
diff --git a/lib/maths.cpp b/lib/maths.cpp index 51e27fe..3a9bf9b 100644 --- a/lib/maths.cpp +++ b/lib/maths.cpp @@ -19,96 +19,17 @@ flat_orientation(const Direction3D & diff) 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 Direction2D & 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; -} +static_assert(pow(1, 0) == 1); +static_assert(pow(1, 1) == 1); +static_assert(pow(1, 2) == 1); +static_assert(pow(2, 0) == 1); +static_assert(pow(2, 1) == 2); +static_assert(pow(2, 2) == 4); +static_assert(pow(2, 3) == 8); +static_assert(pow(3, 0) == 1); +static_assert(pow(3, 1) == 3); +static_assert(pow(3, 2) == 9); +static_assert(pow(pi, 3) == 31.006278991699219F); float operator"" _mph(const long double v) diff --git a/lib/maths.h b/lib/maths.h index 3127d3c..90ddb69 100644 --- a/lib/maths.h +++ b/lib/maths.h @@ -17,22 +17,22 @@ struct Arc : public std::pair<Angle, Angle> { } Arc(const RelativePosition2D & dir0, const RelativePosition2D & dir1); - Arc(const Angle angb, const Angle anga); + Arc(Angle anga, Angle angb); auto - operator[](bool i) const + operator[](bool getSecond) const { - return i ? second : first; + return getSecond ? second : first; } - [[nodiscard]] constexpr inline float + [[nodiscard]] constexpr float length() const { return second - first; } }; -constexpr const RelativePosition3D up {0, 0, 1}; +constexpr const RelativePosition3D up {0, 0, 1}; // NOLINT(readability-identifier-length) constexpr const RelativePosition3D down {0, 0, -1}; constexpr const RelativePosition3D north {0, 1, 0}; constexpr const RelativePosition3D south {0, -1, 0}; @@ -40,7 +40,7 @@ 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 pi {glm::pi<float>()}; // NOLINT(readability-identifier-length) constexpr auto two_pi {glm::two_pi<float>()}; constexpr auto degreesToRads = pi / 180.F; @@ -48,152 +48,283 @@ constexpr auto earthMeanRadius = 6371.01F; // In km constexpr auto astronomicalUnit = 149597890.F; // In km template<glm::length_t D> -constexpr inline GlobalPosition<D> -operator+(const GlobalPosition<D> & g, const RelativePosition<D> & r) +constexpr GlobalPosition<D> +operator+(const GlobalPosition<D> & global, const RelativePosition<D> & relative) { - return g + GlobalPosition<D>(glm::round(r)); + return global + GlobalPosition<D>(glm::round(relative)); } template<glm::length_t D> -constexpr inline GlobalPosition<D> -operator+(const GlobalPosition<D> & g, const CalcPosition<D> & r) +constexpr GlobalPosition<D> +operator+(const GlobalPosition<D> & global, const CalcPosition<D> & relative) { - return g + GlobalPosition<D>(r); + return global + GlobalPosition<D>(relative); } template<glm::length_t D> -constexpr inline GlobalPosition<D> -operator-(const GlobalPosition<D> & g, const RelativePosition<D> & r) +constexpr GlobalPosition<D> +operator-(const GlobalPosition<D> & global, const RelativePosition<D> & relative) { - return g - GlobalPosition<D>(glm::round(r)); + return global - GlobalPosition<D>(glm::round(relative)); } template<glm::length_t D> -constexpr inline GlobalPosition<D> -operator-(const GlobalPosition<D> & g, const CalcPosition<D> & r) +constexpr GlobalPosition<D> +operator-(const GlobalPosition<D> & global, const CalcPosition<D> & relative) { - return g - GlobalPosition<D>(r); + return global - GlobalPosition<D>(relative); +} + +template<glm::length_t D, std::integral T, glm::qualifier Q> +constexpr RelativePosition<D> +difference(const glm::vec<D, T, Q> & globalA, const glm::vec<D, T, Q> & globalB) +{ + return globalA - globalB; } 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) +namespace { + // Helpers + // C++ wrapper for C's sincosf, but with references, not pointers + template<std::floating_point T> + constexpr void + sincos(T angle, T & sinOut, T & cosOut) + { + if consteval { + sinOut = std::sin(angle); + cosOut = std::cos(angle); + } + else { + if constexpr (std::is_same_v<T, float>) { + ::sincosf(angle, &sinOut, &cosOut); + } + else if constexpr (std::is_same_v<T, double>) { + ::sincos(angle, &sinOut, &cosOut); + } + else if constexpr (std::is_same_v<T, long double>) { + ::sincosl(angle, &sinOut, &cosOut); + } + } + } + + template<std::floating_point T, glm::qualifier Q = glm::qualifier::defaultp> + constexpr auto + sincos(const T angle) + { + glm::vec<2, T, Q> sincosOut {}; + sincos(angle, sincosOut.x, sincosOut.y); + return sincosOut; + } + + // Helper to lookup into a matrix given an xy vector coordinate + template<glm::length_t C, glm::length_t R, typename T, glm::qualifier Q, std::integral I = glm::length_t> + constexpr auto & + operator^(glm::mat<C, R, T, Q> & matrix, const glm::vec<2, I> rowCol) + { + return matrix[rowCol.x][rowCol.y]; + } + + // Create a matrix for the angle, given the targets into the matrix + template<glm::length_t D, std::floating_point T, glm::qualifier Q, std::integral I = glm::length_t> + constexpr auto + rotation(const T angle, const glm::vec<2, I> cos1, const glm::vec<2, I> sin1, const glm::vec<2, I> cos2, + const glm::vec<2, I> negSin1) + { + glm::mat<D, D, T, Q> out(1); + sincos(angle, out ^ sin1, out ^ cos1); + out ^ cos2 = out ^ cos1; + out ^ negSin1 = -(out ^ sin1); + return out; + } +} + +// Create a flat transformation matrix +template<glm::length_t D = 2, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 2) +constexpr auto +rotate_flat(const T angle) +{ + return rotation<D, T, Q>(angle, {0, 0}, {0, 1}, {1, 1}, {1, 0}); +} + +// Create a yaw transformation matrix +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 2) +constexpr auto +rotate_yaw(const T angle) +{ + return rotation<D, T, Q>(angle, {0, 0}, {1, 0}, {1, 1}, {0, 1}); +} + +// Create a roll transformation matrix +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 3) +constexpr auto +rotate_roll(const T angle) +{ + return rotation<D, T, Q>(angle, {0, 0}, {2, 0}, {2, 2}, {0, 2}); +} + +// Create a pitch transformation matrix +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 3) +constexpr auto +rotate_pitch(const T angle) +{ + return rotation<D, T, Q>(angle, {1, 1}, {1, 2}, {2, 2}, {2, 1}); +} + +// Create a combined yaw, pitch, roll transformation matrix +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 3) +constexpr auto +rotate_ypr(const glm::vec<3, T, Q> & angles) +{ + return rotate_yaw<D>(angles.y) * rotate_pitch<D>(angles.x) * rotate_roll<D>(angles.z); +} + +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 3) +constexpr auto +rotate_yp(const T yaw, const T pitch) { - return sincosf(a, &s, &c); + return rotate_yaw<D>(yaw) * rotate_pitch<D>(pitch); } -inline Rotation2D -sincosf(float a) +template<glm::length_t D = 3, glm::qualifier Q = glm::qualifier::defaultp, std::floating_point T> + requires(D >= 3) +constexpr auto +rotate_yp(const glm::vec<2, T, Q> & angles) { - Rotation2D sc; - sincosf(a, sc.x, sc.y); - return sc; + return rotate_yp<D>(angles.y, angles.x); } -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); +template<glm::length_t D, glm::qualifier Q = glm::qualifier::defaultp, typename T> + requires(D >= 2) +constexpr auto +vector_yaw(const glm::vec<D, T, Q> & diff) +{ + return std::atan2(diff.x, diff.y); +} -float vector_yaw(const Direction2D & diff); -float vector_pitch(const Direction3D & diff); +template<glm::length_t D, glm::qualifier Q = glm::qualifier::defaultp, typename T> + requires(D >= 3) +constexpr auto +vector_pitch(const glm::vec<D, T, Q> & diff) +{ + return std::atan(diff.z); +} template<typename T, glm::qualifier Q> -glm::vec<2, T, Q> -vector_normal(const glm::vec<2, T, Q> & v) +constexpr glm::vec<2, T, Q> +vector_normal(const glm::vec<2, T, Q> & vector) { - return {-v.y, v.x}; + return {-vector.y, vector.x}; }; -float round_frac(const float & v, const float & frac); +template<std::floating_point T> +constexpr auto +round_frac(const T value, const T frac) +{ + return std::round(value / frac) * frac; +} template<typename T> -inline constexpr auto -sq(T v) + requires requires(T value) { value * value; } +constexpr auto +sq(T value) { - return v * v; + return value * value; } 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) +constexpr glm::vec<3, int64_t, Q> +crossProduct(const glm::vec<3, int64_t, Q> & valueA, const glm::vec<3, int64_t, Q> & valueB) { 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), + (valueA.y * valueB.z) - (valueA.z * valueB.y), + (valueA.z * valueB.x) - (valueA.x * valueB.z), + (valueA.x * valueB.y) - (valueA.y * valueB.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) +constexpr glm::vec<3, T, Q> +crossProduct(const glm::vec<3, T, Q> & valueA, const glm::vec<3, T, Q> & valueB) { - return crossProduct<Q>(a, b); + return crossProduct<Q>(valueA, valueB); } 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) +constexpr glm::vec<3, T, Q> +crossProduct(const glm::vec<3, T, Q> & valueA, const glm::vec<3, T, Q> & valueB) { - return glm::cross(a, b); + return glm::cross(valueA, valueB); } template<typename R = float, typename Ta, typename Tb> -inline constexpr auto -ratio(Ta a, Tb b) +constexpr auto +ratio(const Ta valueA, const Tb valueB) { - return (static_cast<R>(a) / static_cast<R>(b)); + return (static_cast<R>(valueA) / static_cast<R>(valueB)); } template<typename R = float, typename T, glm::qualifier Q> -inline constexpr auto -ratio(glm::vec<2, T, Q> v) +constexpr auto +ratio(const glm::vec<2, T, Q> & value) { - return ratio<R>(v.x, v.y); + return ratio<R>(value.x, value.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) +template<glm::length_t L = 3, std::floating_point T, glm::qualifier Q> +constexpr auto +perspective_divide(const glm::vec<4, T, Q> & value) { - return v / v.w; + return value / value.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) +constexpr glm::vec<L1 + L2, T, Q> +operator||(const glm::vec<L1, T, Q> valueA, const glm::vec<L2, T, Q> valueB) { - return {v1, v2}; + return {valueA, valueB}; } 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) +constexpr glm::vec<L + 1, T, Q> +operator||(const glm::vec<L, T, Q> valueA, const T valueB) { - return {v1, v2}; + return {valueA, valueB}; } -template<glm::length_t L, typename T, glm::qualifier Q> -inline constexpr glm::vec<L, T, Q> -perspectiveMultiply(const glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation) +template<glm::length_t L, std::floating_point T, glm::qualifier Q> +constexpr glm::vec<L, T, Q> +perspectiveMultiply(const glm::vec<L, T, Q> & base, const glm::mat<L + 1, L + 1, T, Q> & mutation) { - const auto p2 = mutation * (p || T(1)); - return p2 / p2.w; + const auto mutated = mutation * (base || T(1)); + return mutated / mutated.w; } -template<glm::length_t L, typename T, glm::qualifier Q> -inline constexpr glm::vec<L, T, Q> -perspectiveApply(glm::vec<L, T, Q> & p, const glm::mat<L + 1, L + 1, T, Q> & mutation) +template<glm::length_t L, std::floating_point T, glm::qualifier Q> +constexpr glm::vec<L, T, Q> +perspectiveApply(glm::vec<L, T, Q> & base, const glm::mat<L + 1, L + 1, T, Q> & mutation) { - return p = perspectiveMultiply(p, mutation); + return base = perspectiveMultiply(base, mutation); } -float normalize(float ang); +template<std::floating_point T> +constexpr T +normalize(T ang) +{ + while (ang > glm::pi<T>()) { + ang -= glm::two_pi<T>(); + } + while (ang <= -glm::pi<T>()) { + ang += glm::two_pi<T>(); + } + return ang; +} template<typename T, glm::qualifier Q> std::pair<glm::vec<2, T, Q>, bool> @@ -215,7 +346,7 @@ find_arc_centre(glm::vec<2, T, Q> start, Angle entrys, glm::vec<2, T, Q> end, An if (start == end) { return {start, false}; } - return find_arc_centre(start, sincosf(entrys + half_pi), end, sincosf(entrye - half_pi)); + return find_arc_centre(start, sincos(entrys + half_pi), end, sincos(entrye - half_pi)); } template<typename T, glm::qualifier Q> @@ -248,7 +379,7 @@ 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 find_arcs_radius(start, sincos(entrys + leftOrRight), end, sincos(entrye + leftOrRight)); }; return {getrad(-half_pi), getrad(half_pi)}; } @@ -260,16 +391,29 @@ midpoint(const std::pair<T, T> & v) return std::midpoint(v.first, v.second); } +// std::pow is not constexpr +template<typename T> + requires requires(T n) { n *= n; } +constexpr T +pow(const T base, std::integral auto exp) +{ + T res {1}; + while (exp--) { + res *= base; + } + return res; +} + // Conversions template<typename T> -inline constexpr auto +constexpr auto mph_to_ms(T v) { return v / 2.237L; } template<typename T> -inline constexpr auto +constexpr auto kph_to_ms(T v) { return v / 3.6L; |