Classes
class	Nz::BoundingVolume< T >
	Math class that represents a bounding volume, a combination of a box and an oriented box. More...

class	Nz::Box< T >
	Math class that represents a three dimensional box. More...

class	Nz::EulerAngles< T >
	Math class that represents an Euler angle. Those describe a rotation transformation by rotating an object on its various axes in specified amounts per axis, and a specified axis order. More...

class	Nz::Frustum< T >
	Math class that represents a frustum in the three dimensional vector space. More...

class	Nz::Matrix4< T >
	Math class that represents a transformation of the four dimensional vector space with the notion of projectivity. More...

class	Nz::OrientedBox< T >
	Math class that represents an oriented three dimensional box. More...

class	Nz::Plane< T >
	Math class that represents a plane in 3D. More...

class	Nz::Quaternion< T >
	Math class that represents an element of the quaternions. More...

class	Nz::Ray< T >
	Math class that represents a ray or a straight line in 3D space. More...

class	Nz::Rect< T >
	Math class that represents an axis-aligned rectangle in two dimensions. More...

class	Nz::Sphere< T >
	Math class that represents a sphere "S2" in a three dimensional euclidean space. More...

class	Nz::Vector2< T >
	Math class that represents an element of the two dimensional vector space. More...

class	Nz::Vector3< T >
	Math class that represents an element of the three dimensional vector space. More...

class	Nz::Vector4< T >
	Math class that represents an element of the three dimensional vector space with the notion of projectivity. When the fourth component is 1, it describes an 'usual' point and when it is 0, it represents the point at infinity. More...

Functions
template<typename T >
T	Nz::Approach (T value, T objective, T increment)
	Approaches the objective, beginning with value and with increment. More...

template<typename T >
constexpr T	Nz::Clamp (T value, T min, T max)
	Clamps value between min and max and returns the expected value. More...

template<typename T >
std::size_t	Nz::CountBits (T value)
	Gets number of bits set in the number. More...

template<typename T >
constexpr T	Nz::DegreeToRadian (T degrees)
	Converts degree to radian. More...

template<typename T >
constexpr T	Nz::FromDegrees (T degrees)
	Gets the unit from degree and convert it according to NAZARA_MATH_ANGLE_RADIAN. More...

template<typename T >
constexpr T	Nz::FromRadians (T radians)
	Gets the unit from radian and convert it according to NAZARA_MATH_ANGLE_RADIAN. More...

template<typename T >
T	Nz::GetNearestPowerOfTwo (T number)
	Gets the nearest power of two for the number. More...

unsigned int	Nz::GetNumberLength (signed char number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (unsigned char number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (int number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (unsigned int number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (long long number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (unsigned long long number)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (float number, UInt8 precision)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (double number, UInt8 precision)
	Gets the number of digits to represent the number in base 10. More...

unsigned int	Nz::GetNumberLength (long double number, UInt8 precision)
	Gets the number of digits to represent the number in base 10. More...

template<typename T >
unsigned int	Nz::IntegralLog2 (T number)
	Gets the log in base 2 of integral number. More...

template<typename T >
unsigned int	Nz::IntegralLog2Pot (T pot)
	Gets the log in base 2 of integral number, only works for power of two ! More...

template<typename T >
T	Nz::IntegralPow (T base, unsigned int exponent)
	Gets the power of integrals. More...

template<typename T , typename T2 >
constexpr T	Nz::Lerp (const T &from, const T &to, const T2 &interpolation)
	Interpolates the value to other one with a factor of interpolation. More...

template<typename T >
constexpr T	Nz::MultiplyAdd (T x, T y, T z)
	Multiplies X and Y, then add Z. More...

template<typename T >
T	Nz::NormalizeAngle (T angle)
	Normalizes the angle. More...

template<typename T >
bool	Nz::NumberEquals (T a, T b)
	Checks whether two numbers are equal. More...

template<typename T >
bool	Nz::NumberEquals (T a, T b, T maxDifference)
	Checks whether two numbers are equal. More...

String	Nz::NumberToString (long long number, UInt8 radix)
	Converts the number to String. More...

template<typename T >
constexpr T	Nz::RadianToDegree (T radians)
	Converts radian to degree. More...

long long	Nz::StringToNumber (String str, UInt8 radix, bool *ok)
	Converts the string to number. More...

template<typename T >
constexpr T	Nz::ToDegrees (T angle)
	Gets the degree from unit and convert it according to NAZARA_MATH_ANGLE_RADIAN. More...

template<typename T >
constexpr T	Nz::ToRadians (T angle)
	Gets the radian from unit and convert it according to NAZARA_MATH_ANGLE_RADIAN. More...

Detailed Description

2D/3D mathematics module including matrix, vector, box, sphere, quaternion, ...

Function Documentation

◆ Approach()

template<typename T >

T Nz::Approach	(	T	value,
		T	objective,
		T	increment
	)

inline

Approaches the objective, beginning with value and with increment.

Returns: The nearest value of the objective you can get with the value and the increment for one step

Parameters

value	Initial value
objective	Target value
increment	One step value

◆ Clamp()

template<typename T >

constexpr T Nz::Clamp	(	T	value,
		T	min,
		T	max
	)

Clamps value between min and max and returns the expected value.

Returns: If value is not in the interval of min..max, value obtained is the nearest limit of this interval

Parameters

value	Value to clamp
min	Minimum of the interval
max	Maximum of the interval

◆ CountBits()

template<typename T >

std::size_t Nz::CountBits ( T value )

inline

Gets number of bits set in the number.

Returns: The number of bits set to 1

Parameters

value The value to count bits

◆ DegreeToRadian()

template<typename T >

constexpr T Nz::DegreeToRadian ( T degrees )

Converts degree to radian.

Returns: The representation in radian of the angle in degree (0..2*pi)

Parameters

degrees Angle in degree (this is expected between 0..360)

◆ FromDegrees()

template<typename T >

constexpr T Nz::FromDegrees ( T degrees )

Gets the unit from degree and convert it according to NAZARA_MATH_ANGLE_RADIAN.

Returns: Express the degrees

Parameters

degrees Convert degree to NAZARA_MATH_ANGLE_RADIAN unit

◆ FromRadians()

template<typename T >

constexpr T Nz::FromRadians ( T radians )

Gets the unit from radian and convert it according to NAZARA_MATH_ANGLE_RADIAN.

Returns: Express the radians

Parameters

radians Convert radian to NAZARA_MATH_ANGLE_RADIAN unit

◆ GetNearestPowerOfTwo()

template<typename T >

T Nz::GetNearestPowerOfTwo ( T number )

inline

Gets the nearest power of two for the number.

Returns: First power of two containing the number

Parameters

number Number to get nearest power

◆ GetNumberLength() [1/9]

unsigned int Nz::GetNumberLength ( signed char number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [2/9]

unsigned int Nz::GetNumberLength ( unsigned char number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [3/9]

unsigned int Nz::GetNumberLength ( int number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [4/9]

unsigned int Nz::GetNumberLength ( unsigned int number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [5/9]

unsigned int Nz::GetNumberLength ( long long number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [6/9]

unsigned int Nz::GetNumberLength ( unsigned long long number )

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits

Parameters

number Number to get number of digits

◆ GetNumberLength() [7/9]

unsigned int Nz::GetNumberLength	(	float	number,
		UInt8	precision
	)

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits + 1 for the dot

Parameters

number	Number to get number of digits
precision	Number of digit after the dot

◆ GetNumberLength() [8/9]

unsigned int Nz::GetNumberLength	(	double	number,
		UInt8	precision
	)

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits + 1 for the dot

Parameters

number	Number to get number of digits
precision	Number of digit after the dot

◆ GetNumberLength() [9/9]

unsigned int Nz::GetNumberLength	(	long double	number,
		UInt8	precision
	)

inline

Gets the number of digits to represent the number in base 10.

Returns: Number of digits + 1 for the dot

Parameters

number	Number to get number of digits
precision	Number of digit after the dot

◆ IntegralLog2()

template<typename T >

unsigned int Nz::IntegralLog2 ( T number )

inline

Gets the log in base 2 of integral number.

Returns: Log of the number (floor)

Parameters

number To get log in base 2

Remarks: If number is 0, 0 is returned

◆ IntegralLog2Pot()

template<typename T >

unsigned int Nz::IntegralLog2Pot ( T pot )

inline

Gets the log in base 2 of integral number, only works for power of two !

Returns: Log of the number

Parameters

pot	To get log in base 2

Remarks: Only works for power of two; If number is 0, 0 is returned

◆ IntegralPow()

template<typename T >

T Nz::IntegralPow	(	T	base,
		unsigned int	exponent
	)

Gets the power of integrals.

Returns: base^exponent for integral

Parameters

base	Base of the exponentation
exponent	Power for the base

◆ Lerp()

template<typename T , typename T2 >

constexpr T Nz::Lerp	(	const T &	from,
		const T &	to,
		const T2 &	interpolation
	)

Interpolates the value to other one with a factor of interpolation.

Returns: A new value which is the interpolation of two values

Parameters

from	Initial value
to	Target value
interpolation	Factor of interpolation

Remarks: interpolation is meant to be between 0 and 1, other values are potentially undefined behavior; With NAZARA_DEBUG, a NazaraWarning is produced

See also: Lerp

◆ MultiplyAdd()

template<typename T >

constexpr T Nz::MultiplyAdd	(	T	x,
		T	y,
		T	z
	)

Multiplies X and Y, then add Z.

Returns: The result of X * Y + Z

Parameters

x	is X
y	is Y
z	is Z

Remarks: This function is meant to use a special faster instruction in CPU if possible

◆ NormalizeAngle()

template<typename T >

T Nz::NormalizeAngle ( T angle )

inline

Normalizes the angle.

Returns: Normalized value between 0..2*(pi if radian or 180 if degrees)

Parameters

angle Angle to normalize

◆ NumberEquals() [1/2]

template<typename T >

bool Nz::NumberEquals	(	T	a,
		T	b
	)

inline

Checks whether two numbers are equal.

Returns: true if they are equal within a certain epsilon

Parameters

a	First value
b	Second value

◆ NumberEquals() [2/2]

template<typename T >

bool Nz::NumberEquals	(	T	a,
		T	b,
		T	maxDifference
	)

inline

Checks whether two numbers are equal.

Returns: true if they are equal within the max difference

Parameters

a	First value
b	Second value
maxDifference	Epsilon of comparison (expected to be positive)

◆ NumberToString()

String Nz::NumberToString	(	long long	number,
		UInt8	radix
	)

inline

Converts the number to String.

Returns: String representation of the number

Parameters

number	Number to represent
radix	Base of the number

Remarks: radix is meant to be between 2 and 36, other values are potentially undefined behavior; With NAZARA_MATH_SAFE, a NazaraError is produced and String() is returned

◆ RadianToDegree()

template<typename T >

constexpr T Nz::RadianToDegree ( T radians )

Converts radian to degree.

Returns: The representation in degree of the angle in radian (0..360)

Parameters

radians Angle in radian (this is expected between 0..2*pi)

◆ StringToNumber()

long long Nz::StringToNumber	(	String	str,
		UInt8	radix,
		bool *	ok
	)

inline

Converts the string to number.

Returns: Number which is represented by the string

Parameters

str	String representation
radix	Base of the number
ok	Optional argument to know if convertion is correct

Remarks: radix is meant to be between 2 and 36, other values are potentially undefined behavior; With NAZARA_MATH_SAFE, a NazaraError is produced and 0 is returned

◆ ToDegrees()

template<typename T >

constexpr T Nz::ToDegrees ( T angle )

Gets the degree from unit and convert it according to NAZARA_MATH_ANGLE_RADIAN.

Returns: Express in degrees

Parameters

angle Convert degree from NAZARA_MATH_ANGLE_RADIAN unit to degrees

◆ ToRadians()

template<typename T >

constexpr T Nz::ToRadians ( T angle )

Gets the radian from unit and convert it according to NAZARA_MATH_ANGLE_RADIAN.

Returns: Express in radians

Parameters

angle Convert degree from NAZARA_MATH_ANGLE_RADIAN unit to radians

Classes

Functions

Detailed Description

Function Documentation

◆ Approach()

◆ Clamp()

◆ CountBits()

◆ DegreeToRadian()

◆ FromDegrees()

◆ FromRadians()

◆ GetNearestPowerOfTwo()

◆ GetNumberLength() [1/9]

◆ GetNumberLength() [2/9]

◆ GetNumberLength() [3/9]

◆ GetNumberLength() [4/9]

◆ GetNumberLength() [5/9]

◆ GetNumberLength() [6/9]

◆ GetNumberLength() [7/9]

◆ GetNumberLength() [8/9]

◆ GetNumberLength() [9/9]

◆ IntegralLog2()

◆ IntegralLog2Pot()

◆ IntegralPow()

◆ Lerp()

◆ MultiplyAdd()

◆ NormalizeAngle()

◆ NumberEquals() [1/2]

◆ NumberEquals() [2/2]

◆ NumberToString()

◆ RadianToDegree()

◆ StringToNumber()

◆ ToDegrees()

◆ ToRadians()