Additional functions for common mathematical operations. More...

Functions
template<typename T >
constexpr auto	playrho::AlmostEqual (T a, T b, int ulp=4) -> std::enable_if_t< IsArithmeticV< T >, bool >
	Determines whether the given two values are "almost equal". More...

template<typename T >
constexpr auto	playrho::AlmostZero (const T &value) -> decltype(abs(value)< std::numeric_limits< T >::min())
	Gets whether a given value is almost zero. 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 >
auto	playrho::Average (const T &span)
	Computes the average of the given values.

template<typename T >
constexpr auto	playrho::Bisect (const T &a1, const T &a2) -> decltype((a1+a2)/2)
	Bisection method. More...

template<class T >
constexpr auto	playrho::cfloor (T v) noexcept
	Constant expression enhanced floor function. More...

Length2	playrho::ComputeCentroid (const Span< const Length2 > &vertices)
	Computes the centroid of a counter-clockwise array of 3 or more vertices. More...

template<class T1 , class T2 , std::enable_if_t< std::tuple_size_v< T1 >==2 &&std::tuple_size_v< T2 >==2, int > = 0>
constexpr auto	playrho::Cross (const T1 &a, const T2 &b) noexcept
	Performs the 2-element analog of the cross product of two vectors. More...

template<class T >
constexpr auto	playrho::ctrunc (T v) noexcept
	Constant expression enhanced truncate function. More...

template<typename T1 , typename T2 >
constexpr auto	playrho::Dot (const T1 &a, const T2 &b) noexcept
	Performs the dot product on two vectors (A and B). More...

template<class T >
Angle	playrho::GetAngle (const Vector2< T > &value)
	Gets the angle. More...

NonNegativeFF< Area >	playrho::GetAreaOfCircle (Length radius)
	Gets the area of a circle.

NonNegativeFF< Area >	playrho::GetAreaOfPolygon (const Span< const Length2 > &vertices)
	Gets the area of a polygon. More...

std::vector< Length2 >	playrho::GetCircleVertices (Length radius, std::size_t slices, Angle start=0_deg, Real turns=Real(1))
	Gets the vertices for a circle described by the given parameters.

constexpr Angle	playrho::GetFwdRotationalAngle (const Angle &a1, const Angle &a2) noexcept
	Gets the forward/clockwise rotational angle to go from angle 1 to angle 2. More...

constexpr auto	playrho::GetInverse22 (const Mat33 &value) noexcept -> Mat33
	Gets the inverse of the given matrix as a 2-by-2. More...

template<typename T >
auto	playrho::GetMagnitude (const T &value) noexcept(noexcept(sqrt(GetMagnitudeSquared(value)))) -> decltype(sqrt(GetMagnitudeSquared(value)))
	Gets the magnitude of the given value. More...

template<typename T >
constexpr auto	playrho::GetMagnitudeSquared (const T &value) noexcept
	Gets the square of the magnitude of the given iterable value. More...

template<typename T >
constexpr auto	playrho::GetModuloNext (T value, const T count) noexcept -> decltype(++value,(value< count)? value:static_cast< T >(0), T())
	Gets the modulo next value. More...

template<typename T >
constexpr auto	playrho::GetModuloPrev (const T value, const T count) noexcept -> decltype((value ? value :count) - static_cast< T >(1), T())
	Gets the modulo previous value. More...

Angle	playrho::GetNormalized (Angle value) noexcept
	Gets the "normalized" value of the given angle. More...

SecondMomentOfArea	playrho::GetPolarMoment (const Span< const Length2 > &vertices)
	Gets the polar moment of the area enclosed by the given vertices. More...

constexpr Angle	playrho::GetRevRotationalAngle (const Angle &a1, const Angle &a2) noexcept
	Gets the reverse (counter) clockwise rotational angle to go from angle 1 to angle 2. More...

Angle	playrho::GetShortestDelta (Angle a0, Angle a1) noexcept
	Gets the shortest angular distance to go from angle 0 to angle 1. More...

constexpr auto	playrho::GetSymInverse33 (const Mat33 &value) noexcept -> Mat33
	Gets the symmetric inverse of this matrix as a 3-by-3. More...

constexpr Vec2	playrho::InverseTransform (const Vec2 &v, const Mat22 &A) noexcept

template<class IN_TYPE >
constexpr auto	playrho::Invert (const Matrix22< IN_TYPE > &value) noexcept
	Inverts the given value.

template<typename T >
constexpr auto	playrho::IsOdd (const T &val) -> decltype((val % 2) !=T{})
	Is-odd. More...

template<typename T >
constexpr auto	playrho::IsPowerOfTwo (const T &n) -> decltype(n &&!(n &(n - 1)))
	Reports whether or not the given value is a power of two.

template<typename T >
auto	playrho::ModuloViaFmod (T dividend, T divisor)
	Modulo operation using `std::fmod`. More...

template<typename T >
auto	playrho::ModuloViaTrunc (T dividend, T divisor) noexcept
	Modulo operation using `std::trunc`. More...

constexpr Mat22	playrho::MulT (const Mat22 &A, const Mat22 &B) noexcept
	Computes A^T * B.

template<typename T >
constexpr auto	playrho::NextPowerOfTwo (T x) -> decltype((x\|(x >> 1u)), 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.

template<typename T >
auto	playrho::RoundOff (const T &value, unsigned precision=DefaultRoundOffPrecission) -> decltype(round(value *static_cast< T >(precision))/static_cast< T >(precision))
	Computes the rounded value of the given value.

auto	playrho::RoundOff (const Vec2 &value, std::uint32_t precision=DefaultRoundOffPrecission) -> Vec2
	Computes the rounded value of the given value. More...

template<typename T , typename U >
constexpr auto	playrho::Secant (const T &target, const U &a1, const T &s1, const U &a2, const T &s2) -> decltype(a1+(target - s1) *(a2 - a1)/(s2 - s1))
	Secant method. More...

template<typename T , typename U >
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<typename T >
constexpr auto	playrho::Solve22 (const Mat33 &mat, const Vector2< T > &b) noexcept -> Vector2< T >
	Solves A * x = b, where b is a column vector. More...

template<typename T >
constexpr auto	playrho::Solve33 (const Mat33 &mat, const Vector3< T > &b) noexcept -> Vector3< T >
	Solves A * x = b, where b is a column vector. More...

template<class T >
constexpr auto	playrho::Square (T t) noexcept(noexcept(t t)) -> decltype(t t)
	Squares the given value.

template<class T >
constexpr auto	playrho::ToSigned (const T &value) -> decltype(static_cast< std::make_signed_t< T >>(value))
	Converts the given value to its closest signed equivalent.

constexpr Vec2	playrho::Transform (const Vec2 &v, const Mat33 &A) noexcept
	Multiplies a vector by a matrix.

template<std::size_t M, typename T1 , std::size_t N, typename T2 >
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...

Variables
constexpr auto	playrho::DefaultRoundOffPrecission = unsigned{100000}
	Default round-off precision.

Detailed Description

Additional functions for common mathematical operations.

These are non-member non-friend functions for mathematical operations especially those with mixed input and output types.

Function Documentation

◆ AlmostEqual()

template<typename T >

constexpr auto playrho::AlmostEqual	(	T	a,
		T	b,
		int	ulp = `4`
	)		-> std::enable_if_t<IsArithmeticV<T>, bool>

constexpr

Determines whether the given two values are "almost equal".

Note: A default ULP of 4 is what googletest uses in its kMaxUlps setting for its AlmostEquals function found in its gtest/internal/gtest-internal.h file.

See also: https://github.com/google/googletest/blob/main/googletest/include/gtest/internal/gtest-internal.h

Examples: World.cpp.

Referenced by playrho::GaussSeidel::SolvePositionConstraint().

◆ AlmostZero()

template<typename T >

constexpr auto playrho::AlmostZero ( const T & value ) -> decltype(abs(value) < std::numeric_limits<T>::min())

constexpr

Gets whether a given value is almost zero.

An almost zero value is "subnormal". Dividing by these values can lead to odd results like a divide by zero trap occurring.

Returns: true if the given value is almost zero, false otherwise.

Referenced by playrho::ComputeCentroid(), playrho::d2::DistanceProxy::Distance(), playrho::d2::GetMassData(), playrho::ToiOutput::GetToiViaSat(), playrho::Invert(), playrho::Normalize(), playrho::d2::DistanceProxy::RayCast(), playrho::d2::RayCast(), and playrho::Solve().

◆ Atan2()

template<typename T >

auto playrho::Atan2	(	T	y,
		T	x
	)

inline

Computes the arc-tangent of the given y and x values.

Returns: Normalized angle - an angle between -Pi and Pi inclusively.

See also: https://en.cppreference.com/w/cpp/numeric/math/atan2

Referenced by playrho::d2::GetAngle(), and playrho::GetAngle().

◆ Bisect()

template<typename T >

constexpr auto playrho::Bisect	(	const T &	a1,
		const T &	a2
	)		-> decltype((a1 + a2) / 2)

constexpr

Bisection method.

See also: https://en.wikipedia.org/wiki/Bisection_method

Referenced by playrho::ToiOutput::GetToiViaSat().

◆ cfloor()

template<class T >

constexpr auto playrho::cfloor ( T v )

constexprnoexcept

Constant expression enhanced floor function.

Note: Unlike std::floor, this function is only defined for finite values.

See also: https://en.cppreference.com/w/cpp/numeric/math/floor

Referenced by playrho::GetNormalized(), and playrho::d2::Position::GetPosition().

◆ ComputeCentroid()

Length2 playrho::ComputeCentroid ( const Span< const Length2 > & vertices )

Computes the centroid of a counter-clockwise array of 3 or more vertices.

Precondition: vertices Has 3 or more elements and they're in counter-clockwise order.

◆ Cross()

template<class T1 , class T2 , std::enable_if_t< std::tuple_size_v< T1 >==2 &&std::tuple_size_v< T2 >==2, int > = 0>

constexpr auto playrho::Cross	(	const T1 &	a,
		const T2 &	b
	)

constexprnoexcept

Performs the 2-element analog of the cross product of two vectors.

Cross-products the given two values.

Defined as the result of: (a.x * b.y) - (a.y * b.x).

Note: This operation is dimension squashing. I.e. A cross of a 2-D length by a 2-D unit vector results in a 1-D length value.; The unit of the result is the 1-D product of the inputs.; This operation is anti-commutative. I.e. Cross(a, b) == -Cross(b, a).; The result will be 0 if any of the following are true: vector A or vector B has a length of zero; vectors A and B point in the same direction; or vectors A and B point in exactly opposite direction of each other.; The result will be positive if: neither vector A nor B has a length of zero; and vector B is at an angle from vector A of greater than 0 and less than 180 degrees (counter-clockwise from A being a positive angle).; Result will be negative if: neither vector A nor B has a length of zero; and vector B is at an angle from vector A of less than 0 and greater than -180 degrees (clockwise from A being a negative angle).; The absolute value of the result is the area of the parallelogram formed by the vectors A and B.

See also: https://en.wikipedia.org/wiki/Cross_product

Returns: Cross product of the two values.

Note: This operation is anti-commutative. I.e. Cross(a, b) == -Cross(b, a).

See also: https://en.wikipedia.org/wiki/Cross_product

Parameters

a	Value A of a 3-element type.
b	Value B of a 3-element type.

Returns: Cross product of the two values.

◆ ctrunc()

template<class T >

constexpr auto playrho::ctrunc ( T v )

constexprnoexcept

Constant expression enhanced truncate function.

Note: Unlike std::trunc, this function is only defined for finite values.

See also: https://en.cppreference.com/w/cpp/numeric/math/trunc

◆ Dot()

template<typename T1 , typename T2 >

constexpr auto playrho::Dot	(	const T1 &	a,
		const T2 &	b
	)

constexprnoexcept

Performs the dot product on two vectors (A and B).

The dot product of two vectors is defined as: the magnitude of vector A, multiplied by, the magnitude of vector B, multiplied by, the cosine of the angle between the two vectors (A and B). Thus the dot product of two vectors is a value ranging between plus and minus the magnitudes of each vector times each other. The middle value of 0 indicates that two vectors are perpendicular to each other (at an angle of +/- 90 degrees from each other).

Note: This operation is commutative. I.e. Dot(a, b) == Dot(b, a).; If A and B are the same vectors, GetMagnitudeSquared(Vec2) returns the same value using effectively one less input parameter.; This is similar to the std::inner_product standard library algorithm except benchmark tests suggest this implementation is faster at least for Vec2 like instances.

See also: https://en.wikipedia.org/wiki/Dot_product

Parameters

a	Vector A.
b	Vector B.

Returns: Dot product of the vectors (0 means the two vectors are perpendicular).

◆ GetAngle()

template<class T >

Angle playrho::GetAngle ( const Vector2< T > & value )

inline

Gets the angle.

Returns: Angular value in the range of -Pi to +Pi radians.

Referenced by playrho::d2::Body::SetAcceleration(), and playrho::d2::Body::SetTransformation().

◆ GetAreaOfPolygon()

NonNegativeFF< Area > playrho::GetAreaOfPolygon ( const Span< const Length2 > & vertices )

Gets the area of a polygon.

Note: This function is valid for any non-self-intersecting (simple) polygon, which can be convex or concave.; Winding order doesn't matter.

◆ GetFwdRotationalAngle()

constexpr Angle playrho::GetFwdRotationalAngle	(	const Angle &	a1,
		const Angle &	a2
	)

constexprnoexcept

Gets the forward/clockwise rotational angle to go from angle 1 to angle 2.

Returns: Angular rotation in the clockwise direction to go from angle 1 to angle 2.

Referenced by playrho::d2::GearJointConf::SolvePosition().

◆ GetInverse22()

constexpr auto playrho::GetInverse22 ( const Mat33 & value ) -> Mat33

constexprnoexcept

Gets the inverse of the given matrix as a 2-by-2.

Returns: Zero matrix if singular.

Referenced by playrho::d2::WeldJointConf::InitVelocity().

◆ GetMagnitude()

template<typename T >

auto playrho::GetMagnitude ( const T & value ) -> decltype(sqrt(GetMagnitudeSquared(value)))

inlinenoexcept

Gets the magnitude of the given value.

Note: Works for any type for which GetMagnitudeSquared also works.

See also: GetMagnitudeSquared.

Examples: DistanceJoint.cpp, PulleyJoint.cpp, and World.cpp.

Referenced by playrho::d2::Simplex::CalcMetric(), playrho::d2::World::GetCentripetalForce(), playrho::d2::World::GetCurrentLengthA(), playrho::d2::World::GetCurrentLengthB(), playrho::d2::World::GetDistanceJointConf(), playrho::d2::ChainShapeConf::GetMassData(), playrho::d2::GetMassData(), playrho::d2::World::GetPulleyJointConf(), playrho::Normalize(), and playrho::d2::WeldJointConf::SolvePosition().

◆ GetMagnitudeSquared()

template<typename T >

constexpr auto playrho::GetMagnitudeSquared ( const T & value )

constexprnoexcept

Gets the square of the magnitude of the given iterable value.

Note: For performance, use this instead of GetMagnitude(T value) (if possible).

Returns: Non-negative value from 0 to infinity, or NaN.

See also: GetMagnitude.

Referenced by playrho::d2::World::CalcGravitationalAcceleration(), playrho::d2::Position::Cap(), playrho::d2::Velocity::Cap(), playrho::d2::DistanceProxy::Distance(), playrho::d2::VertexSet::find(), playrho::d2::World::FindClosestBody(), playrho::d2::GetConvexHullAsVector(), playrho::d2::Body::GetLocalRotInertia(), playrho::d2::World::GetLocalRotInertia(), playrho::GetMagnitude(), playrho::d2::GetManifold(), playrho::d2::GetMassData(), playrho::ToiOutput::GetToiViaSat(), playrho::d2::IsUnderActive(), playrho::d2::RayCast(), playrho::d2::Body::SetAcceleration(), playrho::d2::World::SetMassData(), playrho::d2::GearJointConf::SolvePosition(), playrho::d2::RevoluteJointConf::SolvePosition(), playrho::d2::FrictionJointConf::SolveVelocity(), playrho::d2::MotorJointConf::SolveVelocity(), playrho::d2::TargetJointConf::SolveVelocity(), playrho::d2::DistanceProxy::TestOverlap(), and playrho::d2::DistanceProxy::TestPoint().

◆ GetModuloNext()

template<typename T >

constexpr auto playrho::GetModuloNext	(	T	value,
		const T	count
	)		-> decltype(++value, (value < count)? value: static_cast<T>(0), T())

constexprnoexcept

Gets the modulo next value.

Parameters

value	To get the modulo next value for.
count	Count to wrap around at. Must be greater-than zero.

Precondition: value is less than count.; count is greater-than zero.; value plus one is greater-than zero.

See also: GetModuloPrev.

Referenced by playrho::ComputeCentroid(), playrho::GetAreaOfPolygon(), playrho::d2::GetFwdNormalsArray(), playrho::d2::GetFwdNormalsVector(), playrho::d2::GetManifold(), playrho::d2::GetMassData(), playrho::d2::GetNextIndex(), playrho::GetPolarMoment(), playrho::d2::DistanceProxy::RayCast(), playrho::d2::DistanceProxy::TestPoint(), and playrho::d2::Validate().

◆ GetModuloPrev()

template<typename T >

constexpr auto playrho::GetModuloPrev	(	const T	value,
		const T	count
	)		-> decltype((value ? value : count) - static_cast<T>(1), T())

constexprnoexcept

Gets the modulo previous value.

Parameters

value	To get the modulo previous value for.
count	Count to wrap around at. Must be greater-than zero.

Precondition: count is greater-than zero and value is less than count.

See also: GetModuloNext.

Referenced by playrho::GetAreaOfPolygon().

◆ GetNormalized()

Angle playrho::GetNormalized ( Angle value )

noexcept

Gets the "normalized" value of the given angle.

Note: An angle of zero (0), represents the positive X-axis.; Both -Pi and +Pi normalize to -Pi.

Parameters

value A finite angular value. Behavior of this function is not defined if given a non-finite value.

Returns: Angle that's greater than or equal to -Pi and that's less than +Pi radians. I.e. the value returned will be a value within the half-open interval of [-Pi, +Pi).

See also: Atan2

Referenced by playrho::d2::GetNormalized(), playrho::d2::Sweep::GetNormalized(), and playrho::GetShortestDelta().

◆ GetPolarMoment()

SecondMomentOfArea playrho::GetPolarMoment ( const Span< const Length2 > & vertices )

Gets the polar moment of the area enclosed by the given vertices.

Parameters

vertices Collection of three or more vertices.

Precondition: vertices has 3 or more elements.

Referenced by playrho::d2::GetMassData().

◆ GetRevRotationalAngle()

constexpr Angle playrho::GetRevRotationalAngle	(	const Angle &	a1,
		const Angle &	a2
	)

constexprnoexcept

Gets the reverse (counter) clockwise rotational angle to go from angle 1 to angle 2.

Returns: Angular rotation in the counter clockwise direction to go from angle 1 to angle 2.

Referenced by playrho::d2::GearJointConf::SolvePosition().

◆ GetShortestDelta()

Angle playrho::GetShortestDelta	(	Angle	a0,
		Angle	a1
	)

noexcept

Gets the shortest angular distance to go from angle 0 to angle 1.

This gets the angle to rotate angle 0 by, in order to get to angle 1, with the least amount of rotation.

Returns: Angle between -Pi and Pi radians inclusively.

See also: GetNormalized

Referenced by playrho::d2::Position::GetPosition().

◆ GetSymInverse33()

constexpr auto playrho::GetSymInverse33 ( const Mat33 & value ) -> Mat33

constexprnoexcept

Gets the symmetric inverse of this matrix as a 3-by-3.

Returns: Zero matrix if singular.

Referenced by playrho::d2::WeldJointConf::InitVelocity().

◆ InverseTransform()

constexpr Vec2 playrho::InverseTransform	(	const Vec2 &	v,
		const Mat22 &	A
	)

constexprnoexcept

Multiply a matrix transpose times a vector. If a rotation matrix is provided, then this transforms the vector from one frame to another (inverse transform).

◆ IsOdd()

template<typename T >

constexpr auto playrho::IsOdd ( const T & val ) -> decltype((val % 2) != T{})

constexpr

Is-odd.

Determines whether the given integral value is odd (as opposed to being even).

Referenced by playrho::ToiOutput::GetToiViaSat().

◆ ModuloViaFmod()

template<typename T >

auto playrho::ModuloViaFmod	(	T	dividend,
		T	divisor
	)

Modulo operation using std::fmod.

Note: Modulo via std::fmod appears slower than via std::trunc.

See also: ModuloViaTrunc

Referenced by playrho::GetNormalized().

◆ ModuloViaTrunc()

template<typename T >

auto playrho::ModuloViaTrunc	(	T	dividend,
		T	divisor
	)

noexcept

Modulo operation using std::trunc.

Note: Modulo via std::fmod appears slower than via std::trunc.; This function won't behave like ModuloViaFmod when divisor is infinite.

Parameters

dividend	Dividend value for which `isfinite` returns true.
divisor	Divisor value for which `isfinite` returns true.

See also: ModuloViaFmod

Referenced by playrho::GetNormalized(), and playrho::GetShortestDelta().

◆ NextPowerOfTwo()

template<typename T >

constexpr auto playrho::NextPowerOfTwo ( T x ) -> decltype((x | (x >> 1u)), T(++x))

constexpr

Gets the next largest power of 2.

Given a binary integer value x, the next largest power of 2 can be computed by a S.W.A.R. algorithm that recursively "folds" the upper bits into the lower bits. This process yields a bit vector with the same most significant 1 as x, but all one's below it. Adding 1 to that value yields the next largest power of 2.

Referenced by playrho::d2::DynamicTree::Reserve().

◆ RoundOff()

auto playrho::RoundOff	(	const Vec2 &	value,
		std::uint32_t	precision = `DefaultRoundOffPrecission`
	)		-> Vec2

inline

Computes the rounded value of the given value.

Todo:: Consider making this function generic to any Vector.

◆ Secant()

template<typename T , typename U >

constexpr auto playrho::Secant	(	const T &	target,
		const U &	a1,
		const T &	s1,
		const U &	a2,
		const T &	s2
	)		-> decltype(a1 + (target - s1) * (a2 - a1) / (s2 - s1))

constexpr

Secant method.

See also: https://en.wikipedia.org/wiki/Secant_method

Referenced by playrho::ToiOutput::GetToiViaSat().

◆ Solve()

template<typename T , typename U >

constexpr auto playrho::Solve	(	const Matrix22< U > &	mat,
		const Vector2< T > &	b
	)

constexprnoexcept

Solves A * x = b, where b is a column vector.

Note: This is more efficient than computing the inverse in one-shot cases.

Referenced by playrho::d2::PrismaticJointConf::SolvePosition(), and playrho::d2::RevoluteJointConf::SolvePosition().

◆ Solve22()

template<typename T >

constexpr auto playrho::Solve22	(	const Mat33 &	mat,
		const Vector2< T > &	b
	)		-> Vector2<T>

constexprnoexcept

Solves A * x = b, where b is a column vector.

Note: This is more efficient than computing the inverse in one-shot cases.; Solves only the upper 2-by-2 matrix equation.

Referenced by playrho::d2::WeldJointConf::SolvePosition(), playrho::d2::PrismaticJointConf::SolveVelocity(), and playrho::d2::RevoluteJointConf::SolveVelocity().

◆ Solve33()

template<typename T >

constexpr auto playrho::Solve33	(	const Mat33 &	mat,
		const Vector3< T > &	b
	)		-> Vector3<T>

constexprnoexcept

Solves A * x = b, where b is a column vector.

Note: This is more efficient than computing the inverse in one-shot cases.

Referenced by playrho::d2::PrismaticJointConf::SolvePosition(), playrho::d2::WeldJointConf::SolvePosition(), playrho::d2::PrismaticJointConf::SolveVelocity(), and playrho::d2::RevoluteJointConf::SolveVelocity().

◆ Transform()

template<std::size_t M, typename T1 , std::size_t N, typename T2 >

constexpr auto playrho::Transform	(	const Vector< T1, M > &	v,
		const Matrix< T2, M, N > &	m
	)

constexprnoexcept

Multiplies an M-element vector by an M-by-N matrix.

Parameters

v	Vector that's interpreted as a matrix with 1 row and M-columns.
m	An M-row by N-column transformation matrix to multiply the vector by.

See also: https://en.wikipedia.org/wiki/Transformation_matrix

Functions

Variables

Detailed Description

Function Documentation

◆ AlmostEqual()

◆ AlmostZero()

◆ Atan2()

◆ Bisect()

◆ cfloor()

◆ ComputeCentroid()

◆ Cross()

◆ ctrunc()

◆ Dot()

◆ GetAngle()

◆ GetAreaOfPolygon()

◆ GetFwdRotationalAngle()

◆ GetInverse22()

◆ GetMagnitude()

◆ GetMagnitudeSquared()

◆ GetModuloNext()

◆ GetModuloPrev()

◆ GetNormalized()

◆ GetPolarMoment()

◆ GetRevRotationalAngle()

◆ GetShortestDelta()

◆ GetSymInverse33()

◆ InverseTransform()

◆ IsOdd()

◆ ModuloViaFmod()

◆ ModuloViaTrunc()

◆ NextPowerOfTwo()

◆ RoundOff()

◆ Secant()

◆ Solve()

◆ Solve22()

◆ Solve33()

◆ Transform()