Mathematical operations and algorithms. More...

Files
file	Crux/src/Crux/Math/Detail/TrigPolyImpl.inl
	Estrin-based polynomial evaluation for sine and cosine.

Classes
struct	Crux::AABB
	Axis-aligned bounding box defined by a min and max corner in 3D space. More...
struct	Crux::BoundingSphere
	Bounding sphere defined by a center point and radius. More...
struct	Crux::Frustum
	View frustum represented as six half-space planes. More...

Functions
template<typename T>
constexpr T	Crux::Lerp (T a, T b, f32 t)
	Linear interpolation between a and b by factor t.
template<typename T>
constexpr T	Crux::Min (T a, T b)
	Return the minimum of two values.
template<typename T>
constexpr T	Crux::Max (T a, T b)
	Return the maximum of two values.
template<typename T>
constexpr T	Crux::Clamp (T value, T min, T max)
	Clamp a value between a minimum and maximum.
template<typename T>
constexpr T	Crux::Saturate (T value)
	Clamp a value to the [0,1] range.
template<typename T>
constexpr T	Crux::Sign (T value)
	Signum function: returns -1, 0, or +1.
template<typename T>
constexpr T	Crux::Abs (T value)
	Absolute value.
template<typename T>
constexpr T	Crux::Floor (T value)
	Floor function for f32ing-point values.
template<typename T>
constexpr T	Crux::Ceil (T value)
	Ceiling function for f32ing-point values.
template<typename T>
constexpr T	Crux::Fract (T value)
	Fractional part of a value.
template<typename T>
constexpr T	Crux::Square (T value)
	Square of a value.
template<typename T>
constexpr T	Crux::Cube (T value)
	Cube of a value.
constexpr f32	Crux::Smoothstep (f32 edge0, f32 edge1, f32 x)
	Smoothstep interpolation between edge0 and edge1.
constexpr f32	Crux::CTInverseSqrt (f32 x)
	Fast compile-time inverse square root (single Newton step).
constexpr f32	Crux::CTSqrt (const f32 x)
	Fast compile-time square root using bit manipulation.
f32	Crux::InverseSqrt (const f32 x)
	Inverse square root using hardware rsqrt.
f32	Crux::Sqrt (const f32 x)
	Standard square root using hardware sqrt.
constexpr f32	Crux::Radians (f32 degrees)
	Convert degrees to radians.
constexpr Vector< f32, 3 >	Crux::Radians (Vector< f32, 3 > vector)
	Convert a Vector3s components from degrees to radians.
constexpr f32	Crux::Degrees (f32 radians)
	Convert radians to degrees.
template<typename T>
constexpr Vector< T, 3 >	Crux::Degrees (Vector< T, 3 > vector)
	Convert a Vector3s components from radians to degrees.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
f32	Crux::Sin (f32 radians)
	Computes the sine of an angle in radians using a fast polynomial approximation.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
f32	Crux::Cos (f32 radians)
	Computes the cosine of an angle in radians using a fast polynomial approximation.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
f32	Crux::Tan (f32 radians)
	Computes the tangent of an angle in radians using a fast polynomial approximation.

Detailed Description

Mathematical operations and algorithms.

Houses core arithmetic and math utilities.

Function Documentation

◆ Abs()

template<typename T>

T Crux::Abs ( T value )

inlineconstexpr

Absolute value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: Non-negative absolute of value.

◆ Ceil()

template<typename T>

T Crux::Ceil ( T value )

inlineconstexpr

Ceiling function for f32ing-point values.

Template Parameters

T	f32ing-point type.

Parameters

value Input value.

Returns: Smallest integer >= value as T.

◆ Clamp()

template<typename T>

T Crux::Clamp	(	T	value,
		T	min,
		T	max )

inlineconstexpr

Clamp a value between a minimum and maximum.

Template Parameters

T	Arithmetic type.

Parameters

value	Input value.
min	Minimum allowed.
max	Maximum allowed.

Returns: Clamped value in [min, max].

◆ Cos()

template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>

f32 Crux::Cos ( f32 radians )

inline

Computes the cosine of an angle in radians using a fast polynomial approximation.

Performs a branchless range-reduction into [-pi/4, pi/4], shifts the quadrant index for the pi/2 phase offset (cos(x)=sin(x+pi/2)), evaluates a minimax polynomial of degree determined by the PrecisionMode template (Standard=7), and applies the correct sign.

Template Parameters

PrecisionMode

Selects the polynomial degree:

Fast (degree 5)
Standard (degree 7, default)
High (degree 9) It is recommended to use Standard for most applications.

Parameters

radians Angle in radians.

Returns: Approximation of cos(radians).

Note: This uses the internal Detail::ReduceAngle and Detail::PolyCos<PrecisionMode> routines.

See also: Detail::ReduceAngle, Detail::PolyCos

◆ CTInverseSqrt()

f32 Crux::CTInverseSqrt ( f32 x )

inlineconstexpr

Fast compile-time inverse square root (single Newton step).

Note: This is an approximation and may not be accurate for all values. Prefer using the provided Hardware InverseSqrt function. Only use if you need the value at Compile-Time

Warning: Entering 0.0f will result in a really large number.

Parameters

x	Input value.

Returns: Approximate 1/sqrt(x).

◆ CTSqrt()

f32 Crux::CTSqrt ( const f32 x )

inlineconstexpr

Fast compile-time square root using bit manipulation.

Note: This is an approximation and may not be accurate for all values. Prefer using the provided Hardware Sqrt function. Only use if you need the value at Compile-Time

Warning: Entering a negative value will result in inf.

Parameters

x	Input value.

Returns: Approximate sqrt(x).

◆ Cube()

template<typename T>

T Crux::Cube ( T value )

inlineconstexpr

Cube of a value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: value * value * value.

◆ Degrees() [1/2]

f32 Crux::Degrees ( f32 radians )

inlineconstexpr

Convert radians to degrees.

Parameters

radians Angle in radians.

Returns: Angle in degrees.

◆ Degrees() [2/2]

template<typename T>

Vector< T, 3 > Crux::Degrees ( Vector< T, 3 > vector )

inlineconstexpr

Convert a Vector3s components from radians to degrees.

Parameters

vector The Vector to convert

Returns: A vector with all its components turned from radians to degrees

◆ Floor()

template<typename T>

T Crux::Floor ( T value )

inlineconstexpr

Floor function for f32ing-point values.

Template Parameters

T	f32ing-point type.

Parameters

value Input value.

Returns: Largest integer <= value as T.

◆ Fract()

template<typename T>

T Crux::Fract ( T value )

inlineconstexpr

Fractional part of a value.

Template Parameters

T	f32ing-point type.

Parameters

value Input value.

Returns: value - floor(value).

◆ InverseSqrt()

f32 Crux::InverseSqrt ( const f32 x )

inline

Inverse square root using hardware rsqrt.

Warning: Entering 0.0f will result in infinity.

Parameters

x	Input value.

Returns: 1.0f / sqrt(x).

◆ Lerp()

template<typename T>

T Crux::Lerp	(	T	a,
		T	b,
		f32	t )

inlineconstexpr

Linear interpolation between a and b by factor t.

Template Parameters

T	Arithmetic type of endpoints.

Parameters

a	Start value.
b	End value.
t	Interpolation factor in [0,1].

Returns: Interpolated value.

◆ Max()

template<typename T>

T Crux::Max	(	T	a,
		T	b )

inlineconstexpr

Return the maximum of two values.

Template Parameters

T	Arithmetic type.

Parameters

a	First value.
b	Second value.

Returns: Larger of a and b.

◆ Min()

template<typename T>

T Crux::Min	(	T	a,
		T	b )

inlineconstexpr

Return the minimum of two values.

Template Parameters

T	Arithmetic type.

Parameters

a	First value.
b	Second value.

Returns: Smaller of a and b.

◆ Radians() [1/2]

f32 Crux::Radians ( f32 degrees )

inlineconstexpr

Convert degrees to radians.

Parameters

degrees Angle in degrees.

Returns: Angle in radians.

◆ Radians() [2/2]

Vector< f32, 3 > Crux::Radians ( Vector< f32, 3 > vector )

inlineconstexpr

Convert a Vector3s components from degrees to radians.

Parameters

vector The Vector to convert

Returns: A vector with all its components turned from degress to radians

◆ Saturate()

template<typename T>

T Crux::Saturate ( T value )

inlineconstexpr

Clamp a value to the [0,1] range.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: Saturated value in [0,1].

◆ Sign()

template<typename T>

T Crux::Sign ( T value )

inlineconstexpr

Signum function: returns -1, 0, or +1.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: +1 if value > 0, -1 if value < 0, 0 if value == 0.

◆ Sin()

template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>

f32 Crux::Sin ( f32 radians )

inline

Computes the sine of an angle in radians using a fast polynomial approximation.

Performs a branchless range-reduction into [-pi/4, pi/4], evaluates a minimax polynomial of degree determined by the PrecisionMode template (Standard=7), and applies the correct sign based on the original quadrant.

Template Parameters

PrecisionMode

Selects the polynomial degree:

Fast (degree 5)
Standard (degree 7, default)
High (degree 9)

It is recommended to use Standard for most applications.

Parameters

radians Angle in radians.

Returns: Approximation of sin(radians).

Note: This uses the internal Detail::ReduceAngle and Detail::PolySin<PrecisionMode> routines.

See also: Detail::ReduceAngle, Detail::PolySin

◆ Smoothstep()

f32 Crux::Smoothstep	(	f32	edge0,
		f32	edge1,
		f32	x )

inlineconstexpr

Smoothstep interpolation between edge0 and edge1.

Parameters

edge0	Lower edge of interpolation.
edge1	Upper edge of interpolation.
x	Value to interpolate.

Returns: Interpolated result in [0,1].

◆ Sqrt()

f32 Crux::Sqrt ( const f32 x )

inline

Standard square root using hardware sqrt.

Warning: Entering a negative value will result in -nan.

Parameters

x	Input value.

Returns: sqrt(x).

◆ Square()

template<typename T>

T Crux::Square ( T value )

inlineconstexpr

Square of a value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: value * value.

◆ Tan()

template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>

f32 Crux::Tan ( f32 radians )

inline

Computes the tangent of an angle in radians using a fast polynomial approximation.

Performs a branchless range-reduction into [-pi/4, pi/4], evaluates minimax polynomials for both sine and cosine of degree determined by the PrecisionMode template (Standard=7), applies quadrant-based transformations, and computes the ratio sin/cos.

This implementation is optimized to share the range reduction and polynomial evaluation between the sine and cosine components, making it more efficient than calling Sin and Cos separately.

Template Parameters

PrecisionMode

Selects the polynomial degree:

Fast (degree 5)
Standard (degree 7, default)
High (degree 9) It is recommended to use Standard for most applications.

Parameters

radians Angle in radians.

Returns: Approximation of tan(radians).

Note: This uses the internal Detail::ReduceAngle, Detail::PolySin<PrecisionMode>, and Detail::PolyCos<PrecisionMode> routines.; The result is undefined at odd multiples of pi/2 where cos(radians) = 0.

See also: Detail::ReduceAngle, Detail::PolySin, Detail::PolyCos

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Files

Classes

Functions

Detailed Description

Function Documentation

◆ Abs()

◆ Ceil()

◆ Clamp()

◆ Cos()

◆ CTInverseSqrt()

◆ CTSqrt()

◆ Cube()

◆ Degrees() [1/2]

◆ Degrees() [2/2]

◆ Floor()

◆ Fract()

◆ InverseSqrt()

◆ Lerp()

◆ Max()

◆ Min()

◆ Radians() [1/2]

◆ Radians() [2/2]

◆ Saturate()

◆ Sign()

◆ Sin()

◆ Smoothstep()

◆ Sqrt()

◆ Square()

◆ Tan()