Namespaces
namespace	Detail
	Square Root.

namespace	InternalUtils

Classes
struct	Mat2
	Minimal 2x2 matrix interface. More...

struct	Mat3
	Minimal 3x3 matrix interface. More...

struct	VBSSample

Concepts
concept	CArithmetic

concept	COrderedWith

concept	CArithmeticAndOrderedWith

Functions
template<std::floating_point T>
JPL_INLINE constexpr T	ToRadians (T degrees) noexcept
	Function to convert degrees to radians.

template<std::floating_point T>
JPL_INLINE constexpr T	ToDegrees (T radians) noexcept
	Function to convert radians to degrees.

template<std::floating_point T>
JPL_INLINE constexpr bool	IsNan (T x) noexcept

template<CArithmetic T>
JPL_INLINE constexpr auto	Abs (const T &value) noexcept
	Standard `abs` is not constexpr in C++20.

template<std::floating_point T>
JPL_INLINE constexpr T	Floor (T value) noexcept
	A constexpr implementation of floor.

template<CArithmetic T>
JPL_INLINE constexpr T	Sign (T value) noexcept
	Sign returns -1 for negative values, 1 for positive, 0 for 0.

template<CArithmetic T>
JPL_INLINE constexpr T	Sign2 (T value) noexcept
	Sign2 returns -1 for negative values, 1 otherwise.

template<CArithmetic T1, CArithmeticAndOrderedWith< T1 > T2>
JPL_INLINE constexpr bool	IsPositiveAndBelow (T1 value, T2 below) noexcept

template<std::floating_point T>
JPL_INLINE constexpr bool	IsNearlyZero (T value, T errorTolerance=JPL_FLOAT_EPS_V< T >) noexcept

template<std::floating_point T>
JPL_INLINE constexpr bool	IsNearlyEqual (T a, T b, T tolerance=JPL_FLOAT_EPS_V< T >) noexcept

template<std::integral T>
JPL_INLINE constexpr bool	IsEven (T number) noexcept

template<std::floating_point T>
JPL_INLINE std::pair< T, T >	SinCos (T value) noexcept

template<std::floating_point T>
JPL_INLINE constexpr T	Lerp (const T &v0, const T &v1, T t) noexcept
	Linearly interpolate v0 towards v1.

template<std::integral T, std::floating_point Tt>
JPL_INLINE constexpr T	Lerp (const T &v0, const T &v1, Tt t) noexcept
	Linearly interpolate v0 towards v1.

template<std::floating_point T>
JPL_INLINE constexpr T	FMA (T a, T b, T c) noexcept
	Inlined fuse multiply-add. Compiler in some circumstances is more eager to optimize this than std::fma.

template<std::floating_point T, int NR = 2>
JPL_INLINE constexpr T	Sqrt (T x) noexcept

template<std::floating_point T, int NR = 2>
JPL_INLINE constexpr T	InvSqrt (T x) noexcept

JPL_INLINE simd	Sqrt (const simd &vec) noexcept
	Component-wise square root.

JPL_INLINE simd	InvSqrt (const simd &vec) noexcept
	Component-wise inverse square root (1 / sqrt(x))

JPL_INLINE simd	Sign2 (const simd &vec) noexcept
	Sign2 returns -1 for negative values, 1 otherwise.

JPL_INLINE simd_mask	IsNearlyZero (const simd &vec, float tolerance=JPL_FLOAT_EPS) noexcept

JPL_INLINE simd	FMA (const simd &mul1, const simd &mul2, const simd &addV) noexcept
	An overload to match our scalar version in Math.h.

JPL_INLINE simd	Lerp (const simd &a, const simd &b, const simd &t) noexcept

template<int NR> requires (NR > 0 && NR <= 2)
JPL_INLINE simd	InvSqrtImpl (const simd &vec) noexcept

JPL_INLINE simd	InvSqrtFast (const simd &vec) noexcept

void	SinCos (simd x, simd &outSin, simd &outCos) noexcept
	Sin and Cos for 4-wide 32-bit float vector.

template<CVec3 Vec3>
JPL_INLINE constexpr bool	IsNearlyEqual (const Vec3 &a, const Vec3 &b, Internal::FloatOf< Vec3 > tolerance=JPL_FLOAT_EPS_V< Internal::FloatOf< Vec3 > >) noexcept

template<CVec3 Vec3>
JPL_INLINE constexpr bool	IsNearlyZero (const Vec3 &a, Internal::FloatOf< Vec3 > tolerance=JPL_FLOAT_EPS_V< Internal::FloatOf< Vec3 > >) noexcept

template<CVec3 Vec3>
JPL_INLINE bool	HasNans (const Vec3 &vec)

template<CVec3 Vec3>
Vec3	GetNormalizedPerpendicular (const Vec3 &vec) noexcept

template<CVec3 Vec3>
void	CreateOrthonormalBasis (const Vec3 &normal, Vec3 &tangent, Vec3 &bitangent) noexcept

template<CVec3 Vec3>
JPL_INLINE Vec3	RotateVector (const Vec3 &vector, const Vec3 &rotationAxis, float angleRad) noexcept

template<CVec3 Vec3>
JPL_INLINE Vec3	Lerp (const Vec3 &v0, const Vec3 &v1, float t) noexcept

JPL_INLINE Vec3Pack	Lerp (const Vec3Pack &v0, const Vec3Pack &v1, simd t) noexcept

template<CVec3 Vec3>
JPL_INLINE Vec3	Nlerp (const Vec3 &v0, const Vec3 &v1, float t) noexcept

JPL_INLINE Vec3Pack	Nlerp (const Vec3Pack &v0, const Vec3Pack &v1, simd t) noexcept

template<CVec3 Vec3>
Vec3	Slerp (const Vec3 &v0, const Vec3 &v1, float t) noexcept
	Input vectors must be normalized.

void	Slerp (Vec3Pack &inOutV0, const Vec3Pack &V1, const simd &t) noexcept
	Input vectors must be normalized.

template<class Vec3 >
JPL_INLINE float	ComputePDF (const Vec3 &normal, const Vec3 &outDirection, float diffusion, bool bIsSpecular)

Function Documentation

◆ Abs()

template<CArithmetic T>

JPL_INLINE constexpr auto JPL::Math::Abs ( const T & value )

constexprnoexcept

Standard abs is not constexpr in C++20.

◆ ComputePDF()

template<class Vec3 >

JPL_INLINE float JPL::Math::ComputePDF	(	const Vec3 &	normal,
		const Vec3 &	outDirection,
		float	diffusion,
		bool	bIsSpecular
	)

◆ CreateOrthonormalBasis()

template<CVec3 Vec3>

void JPL::Math::CreateOrthonormalBasis	(	const Vec3 &	normal,
		Vec3 &	tangent,
		Vec3 &	bitangent
	)

inlinenoexcept

◆ Floor()

template<std::floating_point T>

JPL_INLINE constexpr T JPL::Math::Floor ( T value )

constexprnoexcept

A constexpr implementation of floor.

A constexpr implementation of floor. Note: NaN-s and inf-s are not handled.

◆ FMA() [1/2]

JPL_INLINE simd JPL::Math::FMA	(	const simd &	mul1,
		const simd &	mul2,
		const simd &	addV
	)

noexcept

An overload to match our scalar version in Math.h.

◆ FMA() [2/2]

template<std::floating_point T>

JPL_INLINE constexpr T JPL::Math::FMA	(	T	a,
		T	b,
		T	c
	)

constexprnoexcept

Inlined fuse multiply-add. Compiler in some circumstances is more eager to optimize this than std::fma.

◆ GetNormalizedPerpendicular()

template<CVec3 Vec3>

Vec3 JPL::Math::GetNormalizedPerpendicular ( const Vec3 & vec )

inlinenoexcept

◆ HasNans()

template<CVec3 Vec3>

JPL_INLINE bool JPL::Math::HasNans ( const Vec3 & vec )

◆ InvSqrt() [1/2]

JPL_INLINE simd JPL::Math::InvSqrt ( const simd & vec )

noexcept

Component-wise inverse square root (1 / sqrt(x))

◆ InvSqrt() [2/2]

template<std::floating_point T, int NR = 2>

JPL_INLINE constexpr T JPL::Math::InvSqrt ( T x )

constexprnoexcept

Inverse square root: constexpr at compile time, 1 / std::sqrt at runtime Tempalte param 'NR' (used for consteval path): number of Newton–Raphson refinement steps on 1/sqrt(x). NR=2 is a decent default for float.

◆ InvSqrtFast()

JPL_INLINE simd JPL::Math::InvSqrtFast ( const simd & vec )

noexcept

◆ InvSqrtImpl()

template<int NR>
requires (NR > 0 && NR <= 2)

JPL_INLINE simd JPL::Math::InvSqrtImpl ( const simd & vec )

noexcept

◆ IsEven()

template<std::integral T>

JPL_INLINE constexpr bool JPL::Math::IsEven ( T number )

constexprnoexcept

◆ IsNan()

template<std::floating_point T>

JPL_INLINE constexpr bool JPL::Math::IsNan ( T x )

constexprnoexcept

◆ IsNearlyEqual() [1/2]

template<CVec3 Vec3>

JPL_INLINE constexpr bool JPL::Math::IsNearlyEqual	(	const Vec3 &	a,
		const Vec3 &	b,
		Internal::FloatOf< Vec3 >	tolerance = `JPL_FLOAT_EPS_V<Internal::FloatOf<Vec3>>`
	)

constexprnoexcept

◆ IsNearlyEqual() [2/2]

template<std::floating_point T>

JPL_INLINE constexpr bool JPL::Math::IsNearlyEqual	(	T	a,
		T	b,
		T	tolerance = `JPL_FLOAT_EPS_V<T>`
	)

constexprnoexcept

◆ IsNearlyZero() [1/3]

JPL_INLINE simd_mask JPL::Math::IsNearlyZero	(	const simd &	vec,
		float	tolerance = `JPL_FLOAT_EPS`
	)

noexcept

◆ IsNearlyZero() [2/3]

template<CVec3 Vec3>

JPL_INLINE constexpr bool JPL::Math::IsNearlyZero	(	const Vec3 &	a,
		Internal::FloatOf< Vec3 >	tolerance = `JPL_FLOAT_EPS_V<Internal::FloatOf<Vec3>>`
	)

constexprnoexcept

◆ IsNearlyZero() [3/3]

template<std::floating_point T>

JPL_INLINE constexpr bool JPL::Math::IsNearlyZero	(	T	value,
		T	errorTolerance = `JPL_FLOAT_EPS_V<T>`
	)

constexprnoexcept

◆ IsPositiveAndBelow()

template<CArithmetic T1, CArithmeticAndOrderedWith< T1 > T2>

JPL_INLINE constexpr bool JPL::Math::IsPositiveAndBelow	(	T1	value,
		T2	below
	)

constexprnoexcept

◆ Lerp() [1/5]

JPL_INLINE simd JPL::Math::Lerp	(	const simd &	a,
		const simd &	b,
		const simd &	t
	)

noexcept

◆ Lerp() [2/5]

template<std::floating_point T>

JPL_INLINE constexpr T JPL::Math::Lerp	(	const T &	v0,
		const T &	v1,
		T	t
	)

constexprnoexcept

Linearly interpolate v0 towards v1.

◆ Lerp() [3/5]

template<std::integral T, std::floating_point Tt>

JPL_INLINE constexpr T JPL::Math::Lerp	(	const T &	v0,
		const T &	v1,
		Tt	t
	)

constexprnoexcept

Linearly interpolate v0 towards v1.

◆ Lerp() [4/5]

template<CVec3 Vec3>

JPL_INLINE Vec3 JPL::Math::Lerp	(	const Vec3 &	v0,
		const Vec3 &	v1,
		float	t
	)

noexcept

◆ Lerp() [5/5]

JPL_INLINE Vec3Pack JPL::Math::Lerp	(	const Vec3Pack &	v0,
		const Vec3Pack &	v1,
		simd	t
	)

noexcept

◆ Nlerp() [1/2]

template<CVec3 Vec3>

JPL_INLINE Vec3 JPL::Math::Nlerp	(	const Vec3 &	v0,
		const Vec3 &	v1,
		float	t
	)

noexcept

Linearly interpolate v0 towards v1 and normalize. Input vectors must be normalized

◆ Nlerp() [2/2]

JPL_INLINE Vec3Pack JPL::Math::Nlerp	(	const Vec3Pack &	v0,
		const Vec3Pack &	v1,
		simd	t
	)

noexcept

◆ RotateVector()

template<CVec3 Vec3>

JPL_INLINE Vec3 JPL::Math::RotateVector	(	const Vec3 &	vector,
		const Vec3 &	rotationAxis,
		float	angleRad
	)

noexcept

Rotate a 3D vector using Rodrigues' formula

Parameters

v	: vector to rotate
k	: axis to rotate 'v' around
theta	: angle to rotate 'v' around 'k' axis

◆ Sign()

template<CArithmetic T>

JPL_INLINE constexpr T JPL::Math::Sign ( T value )

constexprnoexcept

Sign returns -1 for negative values, 1 for positive, 0 for 0.

◆ Sign2() [1/2]

JPL_INLINE simd JPL::Math::Sign2 ( const simd & vec )

noexcept

Sign2 returns -1 for negative values, 1 otherwise.

◆ Sign2() [2/2]

template<CArithmetic T>

JPL_INLINE constexpr T JPL::Math::Sign2 ( T value )

constexprnoexcept

Sign2 returns -1 for negative values, 1 otherwise.

◆ SinCos() [1/2]

void JPL::Math::SinCos	(	simd	x,
		simd &	outSin,
		simd &	outCos
	)

inlinenoexcept

Sin and Cos for 4-wide 32-bit float vector.

◆ SinCos() [2/2]

template<std::floating_point T>

JPL_INLINE std::pair< T, T > JPL::Math::SinCos ( T value )

noexcept

◆ Slerp() [1/2]

template<CVec3 Vec3>

Vec3 JPL::Math::Slerp	(	const Vec3 &	v0,
		const Vec3 &	v1,
		float	t
	)

inlinenoexcept

Input vectors must be normalized.

◆ Slerp() [2/2]

void JPL::Math::Slerp	(	Vec3Pack &	inOutV0,
		const Vec3Pack &	V1,
		const simd &	t
	)

inlinenoexcept

Input vectors must be normalized.

◆ Sqrt() [1/2]

JPL_INLINE simd JPL::Math::Sqrt ( const simd & vec )

noexcept

Component-wise square root.

◆ Sqrt() [2/2]

template<std::floating_point T, int NR = 2>

JPL_INLINE constexpr T JPL::Math::Sqrt ( T x )

constexprnoexcept

Square root: constexpr at compile time, std::sqrt at runtime Tempalte param 'NR' (used for consteval path): number of Newton–Raphson refinement steps on 1/sqrt(x). NR=2 is a decent default for float.

◆ ToDegrees()

template<std::floating_point T>

JPL_INLINE constexpr T JPL::Math::ToDegrees ( T radians )

constexprnoexcept

Function to convert radians to degrees.

◆ ToRadians()

template<std::floating_point T>

JPL_INLINE constexpr T JPL::Math::ToRadians ( T degrees )

constexprnoexcept

Function to convert degrees to radians.

Namespaces

Classes

Concepts

Functions

Function Documentation

◆ Abs()

◆ ComputePDF()

◆ CreateOrthonormalBasis()

◆ Floor()

◆ FMA() [1/2]

◆ FMA() [2/2]

◆ GetNormalizedPerpendicular()

◆ HasNans()

◆ InvSqrt() [1/2]

◆ InvSqrt() [2/2]

◆ InvSqrtFast()

◆ InvSqrtImpl()

◆ IsEven()

◆ IsNan()

◆ IsNearlyEqual() [1/2]

◆ IsNearlyEqual() [2/2]

◆ IsNearlyZero() [1/3]

◆ IsNearlyZero() [2/3]

◆ IsNearlyZero() [3/3]

◆ IsPositiveAndBelow()

◆ Lerp() [1/5]

◆ Lerp() [2/5]

◆ Lerp() [3/5]

◆ Lerp() [4/5]

◆ Lerp() [5/5]

◆ Nlerp() [1/2]

◆ Nlerp() [2/2]

◆ RotateVector()

◆ Sign()

◆ Sign2() [1/2]

◆ Sign2() [2/2]

◆ SinCos() [1/2]

◆ SinCos() [2/2]

◆ Slerp() [1/2]

◆ Slerp() [2/2]

◆ Sqrt() [1/2]

◆ Sqrt() [2/2]

◆ ToDegrees()

◆ ToRadians()