Math

Provides various math utility functions. More...

Functions
bool	nnl::utl::math::IsNan (float value)
	Checks if a floating-point value is not a number.
template<typename TContainer>
bool	nnl::utl::math::IsNan (const TContainer &value)
	Checks if a container has any floating-point values that are not numbers.
bool	nnl::utl::math::IsFinite (float value)
	Checks if a floating-point value is finite.
template<typename TContainer>
bool	nnl::utl::math::IsFinite (const TContainer &container)
	Checks if all floating-point values in a container are finite.
glm::quat	nnl::utl::math::EulerToQuat (glm::vec3 euler)
	Converts Euler angles in degrees (Pitch X, Yaw Y, Roll Z) to a quaternion.
glm::vec3	nnl::utl::math::QuatToEuler (glm::quat quat)
	Converts quaternion to Euler angles (Pitch X, Yaw Y, Roll Z)
std::tuple< glm::vec3, glm::quat, glm::vec3 >	nnl::utl::math::Decompose (const glm::mat4 &matrix)
	Decomposes a transformation matrix into scale, rotation, and translation.
glm::mat4	nnl::utl::math::Compose (glm::vec3 scale, glm::quat rotation, glm::vec3 translation)
	Composes a transformation matrix from scale, rotation, and translation.
glm::mat4	nnl::utl::math::InverseSafe (const glm::mat4 &m)
	Computes the inverse of a matrix safely.
glm::mat3	nnl::utl::math::InverseSafe (const glm::mat3 &m)
	Computes the inverse of a matrix safely.
glm::mat4	nnl::utl::math::Inverse (const glm::mat4 &m)
	Computes the inverse of a matrix.
glm::mat3	nnl::utl::math::Inverse (const glm::mat3 &m)
	Computes the inverse of a matrix.
glm::vec3	nnl::utl::math::NormalizeSafe (const glm::vec3 &vec)
	Normalizes a vector safely.
template<typename T>
constexpr T	nnl::utl::math::Sqr (T value)
	Calculates the square of a value.
template<typename T>
bool	nnl::utl::math::IsPow2 (T n)
	Checks whether a number can be expressed as an integer power of 2.
u32	nnl::utl::math::RoundUpPow2 (u32 v)
	Rounds up the number to the next power of 2.
u32	nnl::utl::math::RoundDownPow2 (u32 v)
	Rounds down to the previous power of 2.
template<typename T>
T	nnl::utl::math::RoundNum (T number, std::size_t multiple)
	Rounds number up to the nearest multiple.
template<typename T, std::size_t num_int = 0>
constexpr T	nnl::utl::math::FloatToFixed (f32 value)
	Converts a float value to a fixed point value.
template<typename T, std::size_t num_int = 0>
constexpr f32	nnl::utl::math::FixedToFloat (T value)
	Converts a fixed-point value to a float value.
bool	nnl::utl::math::IsApproxEqual (float a, float b, float range=NNL_EPSILON)
	Checks if floating-point numbers are approximately equal.
template<typename TContainer>
bool	nnl::utl::math::IsApproxEqual (TContainer a, TContainer b, float range=NNL_EPSILON)
	Checks if two vectors or matrices are approximately equal.

Detailed Description

Provides various math utility functions.

Function Documentation

Compose()

glm::mat4 nnl::utl::math::Compose	(	glm::vec3	scale,
		glm::quat	rotation,
		glm::vec3	translation )

Composes a transformation matrix from scale, rotation, and translation.

Parameters

scale
rotation
translation

Returns

A glm::mat4

Decompose()

std::tuple< glm::vec3, glm::quat, glm::vec3 > nnl::utl::math::Decompose

(

const glm::mat4 &

matrix

)

Decomposes a transformation matrix into scale, rotation, and translation.

Parameters

matrix

The 4x4 transformation matrix to decompose

Returns

Tuple containing scale (glm::vec3), rotation (glm::quat), and translation (glm::vec3)

Note

If any scale component is 0, the rotation is set to the identity

EulerToQuat()

glm::quat nnl::utl::math::EulerToQuat

(

glm::vec3

euler

)

Converts Euler angles in degrees (Pitch X, Yaw Y, Roll Z) to a quaternion.

Parameters

euler

The angles to convert

Returns

glm::quat

FixedToFloat()

template<typename T, std::size_t num_int = 0>

f32 nnl::utl::math::FixedToFloat ( T value )

constexpr

Converts a fixed-point value to a float value.

Template Parameters

T	Integral type
num_int	Num of bits for the integer part

Parameters

value

Integer value to convert

Returns

A float value

FloatToFixed()

template<typename T, std::size_t num_int = 0>

T nnl::utl::math::FloatToFixed ( f32 value )

constexpr

Converts a float value to a fixed point value.

Template Parameters

T	Integral type
num_int	Num of bits for the integer part

Parameters

value

Float value to convert

Returns

A fixed point value

Inverse() [1/2]

glm::mat3 nnl::utl::math::Inverse

(

const glm::mat3 &

m

)

Computes the inverse of a matrix.

This function takes a matrix and returns its inverse. If the matrix is not invertible, the result is undefined.

Parameters

m	The matrix to be inverted.

Returns

A matrix representing the inverse.

Inverse() [2/2]

glm::mat4 nnl::utl::math::Inverse

(

const glm::mat4 &

m

)

Computes the inverse of a matrix.

This function takes a matrix and returns its inverse. If the matrix is not invertible, the result is undefined.

Parameters

m	The matrix to be inverted.

Returns

A matrix representing the inverse.

InverseSafe() [1/2]

glm::mat3 nnl::utl::math::InverseSafe

(

const glm::mat3 &

m

)

Computes the inverse of a matrix safely.

This function takes a matrix and returns its inverse. If the matrix is not invertible, a small value is added to its diagonal elements. If the adjusted matrix is still not invertible, the function will return the identity matrix.

Parameters

m	The matrix to be inverted.

Returns

A matrix representing the inverse or an identity matrix.

InverseSafe() [2/2]

glm::mat4 nnl::utl::math::InverseSafe

(

const glm::mat4 &

m

)

Computes the inverse of a matrix safely.

This function takes a matrix and returns its inverse. If the matrix is not invertible, a small value is added to its diagonal elements. If the adjusted matrix is still not invertible, the function will return the identity matrix.

Parameters

m	The matrix to be inverted.

Returns

A matrix representing the inverse or an identity matrix.

IsApproxEqual() [1/2]

bool nnl::utl::math::IsApproxEqual ( float a, float b, float range = NNL_EPSILON )

inline

Checks if floating-point numbers are approximately equal.

Parameters

a	First float
b	Second float
range	Tolerance range

Returns

true if |a - b| <= range

IsApproxEqual() [2/2]

template<typename TContainer>

bool nnl::utl::math::IsApproxEqual	(	TContainer	a,
		TContainer	b,
		float	range = NNL_EPSILON )

Checks if two vectors or matrices are approximately equal.

Template Parameters

T	Container type

Parameters

a	First value
b	Second value
range	Tolerance range per element

Returns

true if all elements are approximately equal

IsFinite() [1/2]

template<typename TContainer>

bool nnl::utl::math::IsFinite

(

const TContainer &

container

)

Checks if all floating-point values in a container are finite.

Template Parameters

TContainer

Container type

Parameters

container

The container to check.

Returns

true if all values are finite.

IsFinite() [2/2]

bool nnl::utl::math::IsFinite ( float value )

inline

Checks if a floating-point value is finite.

Parameters

value

The value to check.

Returns

true if the input value is finite.

IsNan() [1/2]

template<typename TContainer>

bool nnl::utl::math::IsNan

(

const TContainer &

value

)

Checks if a container has any floating-point values that are not numbers.

Template Parameters

TContainer

Container type

Parameters

value

The container to check.

Returns

true if the input container has any NaN values.

IsNan() [2/2]

bool nnl::utl::math::IsNan ( float value )

inline

Checks if a floating-point value is not a number.

Parameters

value

The value to check.

Returns

true if the input value is NaN.

IsPow2()

template<typename T>

bool nnl::utl::math::IsPow2

(

T

n

)

Checks whether a number can be expressed as an integer power of 2.

Template Parameters

T	Integral type

Parameters

n	The number to check

Returns

true if n is a power of 2, false otherwise

NormalizeSafe()

glm::vec3 nnl::utl::math::NormalizeSafe

(

const glm::vec3 &

vec

)

Normalizes a vector safely.

Returns a unit vector pointing in the same direction as the input. If the input vector has a length of zero (or is near-zero), it returns a default vector.

Parameters

vec	The vector to be normalized.

Returns

The normalized unit vector, or a default vector.

QuatToEuler()

glm::vec3 nnl::utl::math::QuatToEuler

(

glm::quat

quat

)

Converts quaternion to Euler angles (Pitch X, Yaw Y, Roll Z)

Parameters

quat	The quaternion to convert

Returns

glm::vec3 containing Euler angles in degrees

Note

Conversion from Euler -> Quaternion -> Euler may not yield the same set of angles since there are multiple Euler combinations that represent the same rotation.

RoundDownPow2()

u32 nnl::utl::math::RoundDownPow2 ( u32 v )

inline

Rounds down to the previous power of 2.

Parameters

v	32-bit unsigned integer to round

Returns

Previous power of 2 or the number itself

RoundNum()

template<typename T>

T nnl::utl::math::RoundNum	(	T	number,
		std::size_t	multiple )

Rounds number up to the nearest multiple.

Template Parameters

T	Integral type

Parameters

number	Number to round
multiple	Rounding multiple

Returns

Rounded number

RoundUpPow2()

u32 nnl::utl::math::RoundUpPow2 ( u32 v )

inline

Rounds up the number to the next power of 2.

Parameters

v	32-bit unsigned integer to round

Returns

Next power of 2 or the number itself

Sqr()

template<typename T>

T nnl::utl::math::Sqr ( T value )

inlineconstexpr

Calculates the square of a value.

Template Parameters

T	Numeric type

Parameters

value

The value to square

Returns

value * value