Math.hpp File Reference
#include <PlayRho/Common/Settings.hpp>#include <PlayRho/Common/BoundedValue.hpp>#include <PlayRho/Common/Span.hpp>#include <PlayRho/Common/UnitVec.hpp>#include <PlayRho/Common/Vector2.hpp>#include <PlayRho/Common/Vector3.hpp>#include <PlayRho/Common/Position.hpp>#include <PlayRho/Common/Velocity.hpp>#include <PlayRho/Common/Acceleration.hpp>#include <PlayRho/Common/Transformation.hpp>#include <PlayRho/Common/Sweep.hpp>#include <PlayRho/Common/Matrix.hpp>#include <PlayRho/Common/FixedMath.hpp>#include <cmath>#include <vector>#include <numeric>Go to the source code of this file.
Namespaces | |
| playrho | |
| playrho::d2 | |
Functions | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto & | playrho::GetX (T &value) |
| Gets the "X" element of the given value - i.e. the first element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto & | playrho::GetY (T &value) |
| Gets the "Y" element of the given value - i.e. the second element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto & | playrho::GetZ (T &value) |
| Gets the "Z" element of the given value - i.e. the third element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetX (const T &value) |
| Gets the "X" element of the given value - i.e. the first element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetY (const T &value) |
| Gets the "Y" element of the given value - i.e. the second element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetZ (const T &value) |
| Gets the "Z" element of the given value - i.e. the third element. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR std::enable_if_t< std::is_signed< T >::value, std::make_unsigned_t< T > > | playrho::MakeUnsigned (const T &arg) noexcept |
| Makes the given value into an unsigned value. More... | |
| template<typename T , LoValueCheck lo, HiValueCheck hi> | |
| PLAYRHO_CONSTEXPR auto | playrho::StripUnit (const BoundedValue< T, lo, hi > &v) |
| Strips the unit from the given value. More... | |
| template<typename T , typename U > | |
| PLAYRHO_CONSTEXPR U | playrho::Secant (T target, U a1, T s1, U a2, T s2) noexcept |
| Secant method. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR T | playrho::Bisect (T a1, T a2) noexcept |
| Bisection method. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR bool | playrho::IsOdd (T val) noexcept |
| Is-odd. More... | |
| template<class TYPE > | |
| PLAYRHO_CONSTEXPR auto | playrho::Square (TYPE t) noexcept |
| Squares the given value. More... | |
| template<typename T > | |
| auto | playrho::Atan2 (T y, T x) |
| Computes the arc-tangent of the given y and x values. More... | |
| template<typename T , typename = std::enable_if_t< IsIterable<T>::value && IsAddable<decltype(*begin(std::declval<T>()))>::value> | |
| auto | playrho::Average (const T &span) |
| Computes the average of the given values. More... | |
| template<typename T > | |
| std::enable_if_t< IsArithmetic< T >::value, T > | playrho::RoundOff (T value, unsigned precision=100000) |
| Computes the rounded value of the given value. More... | |
| Vec2 | playrho::RoundOff (Vec2 value, std::uint32_t precision=100000) |
| Computes the rounded value of the given value. More... | |
| template<typename T , std::size_t N> | |
| PLAYRHO_CONSTEXPR Vector< T, N > | playrho::abs (const Vector< T, N > &v) noexcept |
| Absolute value function for vectors. More... | |
| d2::UnitVec | playrho::abs (const d2::UnitVec &v) noexcept |
| Gets the absolute value of the given value. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR std::enable_if_t< std::is_arithmetic< T >::value, bool > | playrho::AlmostZero (T value) |
| Gets whether a given value is almost zero. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR std::enable_if_t< std::is_floating_point< T >::value, bool > | playrho::AlmostEqual (T x, T y, int ulp=2) |
| Determines whether the given two values are "almost equal". More... | |
| template<typename T > | |
| auto | playrho::ModuloViaFmod (T dividend, T divisor) noexcept |
Modulo operation using std::fmod. More... | |
| template<typename T > | |
| auto | playrho::ModuloViaTrunc (T dividend, T divisor) noexcept |
Modulo operation using std::trunc. More... | |
| Angle | playrho::GetNormalized (Angle value) noexcept |
| Gets the "normalized" value of the given angle. More... | |
| template<class T > | |
| Angle | playrho::GetAngle (const Vector2< T > value) |
| Gets the angle. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetMagnitudeSquared (T value) noexcept |
| Gets the square of the magnitude of the given iterable value. More... | |
| template<typename T > | |
| auto | playrho::GetMagnitude (T value) |
| Gets the magnitude of the given value. More... | |
| template<typename T1 , typename T2 > | |
| PLAYRHO_CONSTEXPR auto | playrho::Dot (const T1 a, const T2 b) noexcept |
| Performs the dot product on two vectors (A and B). More... | |
| template<class T1 , class T2 , std::enable_if_t< std::tuple_size< T1 >::value==2 &&std::tuple_size< T2 >::value==2, int > = 0> | |
| PLAYRHO_CONSTEXPR auto | playrho::Cross (T1 a, T2 b) noexcept |
| Performs the 2-element analog of the cross product of two vectors. More... | |
| template<typename T , typename U > | |
| PLAYRHO_CONSTEXPR auto | playrho::Solve (const Matrix22< U > mat, const Vector2< T > b) noexcept |
| Solves A * x = b, where b is a column vector. More... | |
| template<class IN_TYPE > | |
| PLAYRHO_CONSTEXPR auto | playrho::Invert (const Matrix22< IN_TYPE > value) noexcept |
| Inverts the given value. More... | |
| PLAYRHO_CONSTEXPR Vec3 | playrho::Solve33 (const Mat33 &mat, const Vec3 b) noexcept |
| Solves A * x = b, where b is a column vector. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR T | playrho::Solve22 (const Mat33 &mat, const T b) noexcept |
| Solves A * x = b, where b is a column vector. More... | |
| PLAYRHO_CONSTEXPR Mat33 | playrho::GetInverse22 (const Mat33 &value) noexcept |
| Gets the inverse of the given matrix as a 2-by-2. More... | |
| PLAYRHO_CONSTEXPR Mat33 | playrho::GetSymInverse33 (const Mat33 &value) noexcept |
| Gets the symmetric inverse of this matrix as a 3-by-3. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetRevPerpendicular (const T vector) noexcept |
| Gets a vector counter-clockwise (reverse-clockwise) perpendicular to the given vector. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR auto | playrho::GetFwdPerpendicular (const T vector) noexcept |
| Gets a vector clockwise (forward-clockwise) perpendicular to the given vector. More... | |
| template<std::size_t M, typename T1 , std::size_t N, typename T2 > | |
| PLAYRHO_CONSTEXPR auto | playrho::Transform (const Vector< T1, M > v, const Matrix< T2, M, N > &m) noexcept |
| Multiplies an M-element vector by an M-by-N matrix. More... | |
| PLAYRHO_CONSTEXPR Vec2 | playrho::Transform (const Vec2 v, const Mat33 &A) noexcept |
| Multiplies a vector by a matrix. More... | |
| PLAYRHO_CONSTEXPR Vec2 | playrho::InverseTransform (const Vec2 v, const Mat22 &A) noexcept |
| PLAYRHO_CONSTEXPR Mat22 | playrho::MulT (const Mat22 &A, const Mat22 &B) noexcept |
| Computes A^T * B. More... | |
| Mat22 | playrho::abs (const Mat22 &A) |
| Gets the absolute value of the given value. More... | |
| std::uint64_t | playrho::NextPowerOfTwo (std::uint64_t x) |
| Gets the next largest power of 2. More... | |
| Real | playrho::Normalize (Vec2 &vector) |
| Converts the given vector into a unit vector and returns its original length. More... | |
| Length2 | playrho::ComputeCentroid (const Span< const Length2 > &vertices) |
| Computes the centroid of a counter-clockwise array of 3 or more vertices. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR T | playrho::GetModuloNext (T value, T count) noexcept |
| Gets the modulo next value. More... | |
| template<typename T > | |
| PLAYRHO_CONSTEXPR T | playrho::GetModuloPrev (T value, T count) noexcept |
| Gets the modulo previous value. More... | |
| Angle | playrho::GetDelta (Angle a1, Angle a2) noexcept |
| Gets the shortest angular distance to go from angle 1 to angle 2. More... | |
| PLAYRHO_CONSTEXPR Angle | playrho::GetRevRotationalAngle (Angle a1, Angle a2) noexcept |
| std::vector< Length2 > | playrho::GetCircleVertices (Length radius, unsigned slices, Angle start=0_deg, Real turns=Real{1}) |
| Gets the vertices for a circle described by the given parameters. More... | |
| NonNegative< Area > | playrho::GetAreaOfCircle (Length radius) |
| Gets the area of a circle. More... | |
| NonNegative< Area > | playrho::GetAreaOfPolygon (Span< const Length2 > vertices) |
| Gets the area of a polygon. More... | |
| SecondMomentOfArea | playrho::GetPolarMoment (Span< const Length2 > vertices) |
| Gets the polar moment of the area enclosed by the given vertices. More... | |
| PLAYRHO_CONSTEXPR Vec2 | playrho::d2::GetVec2 (const UnitVec value) |
Gets a Vec2 representation of the given value. More... | |
| Angle | playrho::d2::GetAngle (const UnitVec value) |
| Gets the angle of the given unit vector. More... | |
| template<class T , LoValueCheck lo, HiValueCheck hi> | |
| PLAYRHO_CONSTEXPR Vector2< T > | playrho::d2::operator* (BoundedValue< T, lo, hi > s, UnitVec u) noexcept |
| Multiplication operator. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR Vector2< T > | playrho::d2::operator* (const T s, const UnitVec u) noexcept |
| Multiplication operator. More... | |
| template<class T , LoValueCheck lo, HiValueCheck hi> | |
| PLAYRHO_CONSTEXPR Vector2< T > | playrho::d2::operator* (UnitVec u, BoundedValue< T, lo, hi > s) noexcept |
| Multiplication operator. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR Vector2< T > | playrho::d2::operator* (const UnitVec u, const T s) noexcept |
| Multiplication operator. More... | |
| PLAYRHO_CONSTEXPR Vec2 | playrho::d2::operator/ (const UnitVec u, const UnitVec::value_type s) noexcept |
| Division operator. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR auto | playrho::d2::Rotate (const Vector2< T > vector, const UnitVec &angle) noexcept |
| Rotates a vector by a given angle. More... | |
| template<class T > | |
| PLAYRHO_CONSTEXPR auto | playrho::d2::InverseRotate (const Vector2< T > vector, const UnitVec &angle) noexcept |
| Inverse rotates a vector. More... | |
| template<class T > | |
| UnitVec | playrho::d2::GetUnitVector (Vector2< T > value, UnitVec fallback=UnitVec::GetDefaultFallback()) |
| Position | playrho::d2::GetNormalized (const Position &val) noexcept |
| Gets the "normalized" position. More... | |
| Sweep | playrho::d2::GetNormalized (Sweep sweep) noexcept |
| Gets a sweep with the given sweep's angles normalized. More... | |
| PLAYRHO_CONSTEXPR Length2 | playrho::d2::Transform (const Length2 v, const Transformation xfm) noexcept |
| Transforms the given 2-D vector with the given transformation. More... | |
| PLAYRHO_CONSTEXPR Length2 | playrho::d2::InverseTransform (const Length2 v, const Transformation T) noexcept |
| Inverse transforms the given 2-D vector with the given transformation. More... | |
| PLAYRHO_CONSTEXPR Transformation | playrho::d2::Mul (const Transformation &A, const Transformation &B) noexcept |
| Multiplies a given transformation by another given transformation. More... | |
| PLAYRHO_CONSTEXPR Transformation | playrho::d2::MulT (const Transformation &A, const Transformation &B) noexcept |
| Inverse multiplies a given transformation by another given transformation. More... | |
| PLAYRHO_CONSTEXPR Transformation | playrho::d2::GetTransformation (const Length2 ctr, const UnitVec rot, const Length2 localCtr) noexcept |
| Gets the transformation for the given values. More... | |
| Transformation | playrho::d2::GetTransformation (const Position pos, const Length2 local_ctr) noexcept |
| Gets the transformation for the given values. More... | |
| Transformation | playrho::d2::GetTransformation (const Sweep &sweep, const Real beta) noexcept |
| Gets the interpolated transform at a specific time. More... | |
| Transformation | playrho::d2::GetTransform0 (const Sweep &sweep) noexcept |
| Gets the transform at "time" zero. More... | |
| Transformation | playrho::d2::GetTransform1 (const Sweep &sweep) noexcept |
| Gets the transform at "time" one. More... | |
| LinearVelocity2 | playrho::d2::GetContactRelVelocity (const Velocity velA, const Length2 relA, const Velocity velB, const Length2 relB) noexcept |
| Gets the contact relative velocity. More... | |
| bool | playrho::d2::IsUnderActive (Velocity velocity, LinearVelocity linSleepTol, AngularVelocity angSleepTol) noexcept |
| Gets whether the given velocity is "under active" based on the given tolerances. More... | |
| PLAYRHO_CONSTEXPR auto | playrho::d2::GetReflectionMatrix (UnitVec axis) |
| Gets the reflection matrix for the given unit vector that defines the normal of the line through the origin that points should be reflected against. More... | |
