Classes for basic math.

Classes
struct	Dali::Power< mantissa, exponent >
	Compiles time template to calculate base to the power of N. More...
struct	Dali::Power< mantissa, 1 >
	Compiles time template to calculate base to the power of N. More...
struct	Dali::Power< mantissa, 0 >
	Compiles time template to calculate base to the power of N. More...
struct	Dali::Log< number, base >
	Compiles time template to calculate base logarithm of N. More...
struct	Dali::Log< 1, base >
	Compiles time template to calculate base logarithm of N. More...
struct	Dali::Log< 0, base >
	Compiles time template to calculate base logarithm of N. More...
struct	Dali::Epsilon< N >
	Compiles time template to calculate the machine epsilon for a given floating point number. More...
struct	Dali::Epsilon< 1 >
	Compiles time template to calculate the machine epsilon for a given floating point number. More...
struct	Dali::Epsilon< 0 >
	Compiles time template to calculate the machine epsilon for a given floating point number. More...
struct	Dali::Degree
	An angle in degrees. More...
class	Dali::Matrix
	The Matrix class represents transformations and projections. More...
class	Dali::Matrix3
	A 3x3 matrix. More...
class	Dali::Quaternion
	The Quaternion class encapsulates the mathematics of the quaternion. More...
struct	Dali::Radian
	An angle in radians. More...
class	Dali::Uint16Pair
	Simple class for passing around pairs of small unsigned integers. More...
struct	Dali::Vector2
	A two dimensional vector. More...
struct	Dali::Vector3
	A three dimensional vector. More...
struct	Dali::Vector4
	A four dimensional vector. More...
Functions
bool	Dali::operator== (const Degree &lhs, const Degree &rhs)
	Compares equality between two degrees.
bool	Dali::operator!= (const Degree &lhs, const Degree &rhs)
	Compares inequality between two degrees.
Degree	Dali::Clamp (Degree angle, float min, float max)
	Clamps a radian value.
unsigned int	Dali::NextPowerOfTwo (unsigned int i)
	Returns the next power of two.
bool	Dali::IsPowerOfTwo (unsigned int i)
	Whether a number is power of two.
template<typename T >
const T &	Dali::Clamp (const T &value, const T &min, const T &max)
	Clamp a value.
template<typename T >
void	Dali::ClampInPlace (T &value, const T &min, const T &max)
	Clamp a value directly.
template<typename T >
const T	Dali::Lerp (const float offset, const T &low, const T &high)
	Linear interpolation between two values.
float	Dali::GetRangedEpsilon (float a, float b)
	Get an epsilon that is valid for the given range.
bool	Dali::EqualsZero (float value)
	Helper function to compare equality of a floating point value with zero.
bool	Dali::Equals (float a, float b)
	Helper function to compare equality of two floating point values.
bool	Dali::Equals (float a, float b, float epsilon)
	Helper function to compare equality of two floating point values.
float	Dali::Round (float value, int pos)
	Get an float that is rounded at specified place of decimals.
float	Dali::WrapInDomain (float x, float start, float end)
	Wrap x in domain (start) to (end).
float	Dali::ShortestDistanceInDomain (float a, float b, float start, float end)
	Find the shortest distance (magnitude) and direction (sign) from (a) to (b) in domain (start) to (end).
template<typename T >
int	Dali::Sign (T value)
	Extracts the sign of a number.
std::ostream &	Dali::operator<< (std::ostream &o, const Matrix &matrix)
	Prints a matrix.
std::ostream &	Dali::operator<< (std::ostream &o, const Matrix3 &matrix)
	Prints a 3x3 matrix.
std::ostream &	Dali::operator<< (std::ostream &o, const Quaternion &quaternion)
	Prints a Quaternion.
bool	Dali::operator== (Radian lhs, Radian rhs)
	Compares equality between two radians.
bool	Dali::operator!= (Radian lhs, Radian rhs)
	Compares inequality between two radians.
bool	Dali::operator== (Radian lhs, Degree rhs)
	Compares equality between a radian and degree.
bool	Dali::operator!= (Radian lhs, Degree rhs)
	Compares inequality between a radian and a degree.
bool	Dali::operator== (Degree lhs, Radian rhs)
	Compares equality between a degree and a radian.
bool	Dali::operator!= (Degree lhs, Radian rhs)
	Compares inequality between a degree and a radian.
bool	Dali::operator> (Radian lhs, Radian rhs)
	Compares greater than between two radians.
bool	Dali::operator> (Radian lhs, Degree rhs)
	Compares greater than between a radian and a degree.
bool	Dali::operator> (Degree lhs, Radian rhs)
	Compares greater than between a radian and a degree.
bool	Dali::operator< (Radian lhs, Radian rhs)
	Compares less than between two radians.
bool	Dali::operator< (Radian lhs, Degree rhs)
	Compares less than between a radian and a degree.
bool	Dali::operator< (Degree lhs, Radian rhs)
	Compares less than between a degree and a radian.
Radian	Dali::operator* (Radian lhs, float rhs)
	Multiplies Radian with a float.
Radian	Dali::operator- (Radian in)
	Negates the radian.
Radian	Dali::Clamp (Radian angle, float min, float max)
	Clamps a radian value.
std::ostream &	Dali::operator<< (std::ostream &o, const Vector2 &vector)
	Print a Vector2.
Vector2	Dali::Min (const Vector2 &a, const Vector2 &b)
	Returns a vector with components set to the minimum of the corresponding component in a and b.
Vector2	Dali::Max (const Vector2 &a, const Vector2 &b)
	Returns a vector with components set to the maximum of the corresponding component in a and b.
Vector2	Dali::Clamp (const Vector2 &v, const float &min, const float &max)
	Clamps each of vector v's components between minimum and maximum values.
std::ostream &	Dali::operator<< (std::ostream &o, const Vector3 &vector)
	Prints a Vector3.
Vector3	Dali::Min (const Vector3 &a, const Vector3 &b)
	Returns a vector with components set to the minimum of the corresponding component in a and b.
Vector3	Dali::Max (const Vector3 &a, const Vector3 &b)
	Returns a vector with components set to the maximum of the corresponding component in a and b.
Vector3	Dali::Clamp (const Vector3 &v, const float &min, const float &max)
	Clamps each of vector v's components between minimum and maximum values.
std::ostream &	Dali::operator<< (std::ostream &o, const Vector4 &vector)
	Print a Vector4.
Vector4	Dali::Min (const Vector4 &a, const Vector4 &b)
	Returns a vector with components set to the minimum of the corresponding component in a and b.
Vector4	Dali::Max (const Vector4 &a, const Vector4 &b)
	Returns a vector with components set to the maximum of the corresponding component in a and b.
Vector4	Dali::Clamp (const Vector4 &v, const float &min, const float &max)
	Clamps each of vector v's components between minimum and maximum values.
Namespaces
namespace	Dali::Random
	Provides methods to generate and use random values.
Typedefs
typedef Vector2	Dali::Size
	Size is an alias of Dali::Vector2.
typedef Rect< int >	Dali::Viewport
	Typedef for a viewport ( a rectangle representing a screen area ).

Typedef Documentation

typedef Vector2 Dali::Size

Size is an alias of Dali::Vector2.

Since:: 2.4, DALi version 1.0.0

typedef Rect<int> Dali::Viewport

Typedef for a viewport ( a rectangle representing a screen area ).

Since:: 2.4, DALi version 1.0.0

Function Documentation

template<typename T >

const T& Dali::Clamp	(	const T &	value,
		const T &	min,
		const T &	max
	)

Clamp a value.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	value	The value to clamp.
[in]	min	The minimum allowed value.
[in]	max	The maximum allowed value.

Returns:: T the clamped value

Degree Dali::Clamp	(	Degree	angle,
		float	min,
		float	max
	)

Clamps a radian value.

Since:: 2.4, DALi version 1.0.0

Parameters:

angle	to clamp
min	value
max	value

Returns:: The resulting radian

Radian Dali::Clamp	(	Radian	angle,
		float	min,
		float	max
	)

Clamps a radian value.

Since:: 2.4, DALi version 1.0.0

Parameters:

angle	to clamp
min	value
max	value

Returns:: The resulting radian

Vector2 Dali::Clamp	(	const Vector2 &	v,
		const float &	min,
		const float &	max
	)

Clamps each of vector v's components between minimum and maximum values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	v	A vector
[in]	min	The minimum value
[in]	max	The maximum value

Returns:: A vector containing the clamped components of v

Vector3 Dali::Clamp	(	const Vector3 &	v,
		const float &	min,
		const float &	max
	)

Clamps each of vector v's components between minimum and maximum values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	v	A vector
[in]	min	The minimum value
[in]	max	The maximum value

Returns:: A vector containing the clamped components of v

Vector4 Dali::Clamp	(	const Vector4 &	v,
		const float &	min,
		const float &	max
	)

Clamps each of vector v's components between minimum and maximum values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	v	A vector
[in]	min	The minimum value
[in]	max	The maximum value

Returns:: A vector containing the clamped components of v

template<typename T >

void Dali::ClampInPlace	(	T &	value,
		const T &	min,
		const T &	max
	)

Clamp a value directly.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in,out]	value	The value that will be clamped.
[in]	min	The minimum allowed value.
[in]	max	The maximum allowed value.

bool Dali::Equals	(	float	a,
		float	b
	)

Helper function to compare equality of two floating point values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	the first value to compare
[in]	b	the second value to compare

Returns:: true if the values are equal within a minimal epsilon for their values

bool Dali::Equals	(	float	a,
		float	b,
		float	epsilon
	)

Helper function to compare equality of two floating point values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	the first value to compare
[in]	b	the second value to compare
[in]	epsilon	the minimum epsilon value that will be used to consider the values different

Returns:: true if the difference between the values is less than the epsilon

bool Dali::EqualsZero ( float value )

Helper function to compare equality of a floating point value with zero.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in] value the value to compare

Returns:: true if the value is equal to zero

float Dali::GetRangedEpsilon	(	float	a,
		float	b
	)

Get an epsilon that is valid for the given range.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	the first value in the range
[in]	b	the second value in the range.

Returns:: a suitable epsilon

bool Dali::IsPowerOfTwo ( unsigned int i )

Whether a number is power of two.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in] i Input number

Returns:: True if i is power of two.

template<typename T >

const T Dali::Lerp	(	const float	offset,
		const T &	low,
		const T &	high
	)

Linear interpolation between two values.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	offset	The offset through the range `low` to `high`. This value is clamped between 0 and 1.
[in]	low	Lowest value in range
[in]	high	Highest value in range

Returns:: A value between low and high.

Vector2 Dali::Max	(	const Vector2 &	a,
		const Vector2 &	b
	)

Returns a vector with components set to the maximum of the corresponding component in a and b.

If a=0,1 and b=1,0 returns a vector of 1,1.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the maximum of each component from a and b

Vector3 Dali::Max	(	const Vector3 &	a,
		const Vector3 &	b
	)

Returns a vector with components set to the maximum of the corresponding component in a and b.

If a=0,1 and b=1,0 returns a vector of 1,1.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the maximum of each component from a and b

Vector4 Dali::Max	(	const Vector4 &	a,
		const Vector4 &	b
	)

Returns a vector with components set to the maximum of the corresponding component in a and b.

If a=0,1,2,3 and b=4,0,1,2 returns a vector of 4,1,2,3.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the maximum of each component from a and b

Vector2 Dali::Min	(	const Vector2 &	a,
		const Vector2 &	b
	)

Returns a vector with components set to the minimum of the corresponding component in a and b.

If a=0,1 and b=1,0 returns a vector of 0,0.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the minimum of each component from a and b

Vector3 Dali::Min	(	const Vector3 &	a,
		const Vector3 &	b
	)

Returns a vector with components set to the minimum of the corresponding component in a and b.

If a=0,1,2 and b=2,1,0 returns a vector of 2,1,2.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the minimum of each component from a and b

Vector4 Dali::Min	(	const Vector4 &	a,
		const Vector4 &	b
	)

Returns a vector with components set to the minimum of the corresponding component in a and b.

If a=0,1,2,3 and b=4,0,1,2 returns a vector of 0,0,1,2.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	a	A vector
[in]	b	A vector

Returns:: A vector containing the minimum of each component from a and b

unsigned int Dali::NextPowerOfTwo ( unsigned int i )

Returns the next power of two.

In case of numbers which are already a power of two this function returns the original number. If i is zero returns 1.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in] i Input number

Returns:: The next power of two or i itself in case it's a power of two

bool Dali::operator!=	(	const Degree &	lhs,
		const Degree &	rhs
	)

Compares inequality between two degrees.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Degree to compare
[in]	rhs	Degree to compare to

Returns:: True if the values are not identical

bool Dali::operator!=	(	Radian	lhs,
		Radian	rhs
	)

Compares inequality between two radians.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Radian to compare to

Returns:: True if the values are not identical

bool Dali::operator!=	(	Radian	lhs,
		Degree	rhs
	)

Compares inequality between a radian and a degree.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Degree to compare to

Returns:: True if the values are not identical

bool Dali::operator!=	(	Degree	lhs,
		Radian	rhs
	)

Compares inequality between a degree and a radian.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Degree to compare
[in]	rhs	Radian to compare to

Returns:: True if the values are not identical

Radian Dali::operator*	(	Radian	lhs,
		float	rhs
	)

Multiplies Radian with a float.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to multiply
[in]	rhs	float to multiply

Returns:: Result of the multiplication

Radian Dali::operator- ( Radian in )

Negates the radian.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in] in Radian to negate

Returns:: The negative angle

bool Dali::operator<	(	Radian	lhs,
		Radian	rhs
	)

Compares less than between two radians.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Radian to compare to

Returns:: True if lhs is less than rhs

bool Dali::operator<	(	Radian	lhs,
		Degree	rhs
	)

Compares less than between a radian and a degree.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Degree to compare to

Returns:: True if lhs is less than rhs

bool Dali::operator<	(	Degree	lhs,
		Radian	rhs
	)

Compares less than between a degree and a radian.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Degree to compare
[in]	rhs	Radian to compare to

Returns:: True if lhs is less than rhs

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Matrix3 &	matrix
	)

Prints a 3x3 matrix.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	matrix	The matrix to print

Returns:: The output stream operator

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Matrix &	matrix
	)

Prints a matrix.

It is printed in memory order, i.e. each printed row is contiguous in memory.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	matrix	The matrix to print

Returns:: The output stream operator

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Vector2 &	vector
	)

Print a Vector2.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	vector	The vector to print

Returns:: The output stream operator

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Quaternion &	quaternion
	)

Prints a Quaternion.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	quaternion	The quaternion to print

Returns:: The output stream operator

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Vector3 &	vector
	)

Prints a Vector3.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	vector	The vector to print

Returns:: The output stream operator

std::ostream& Dali::operator<<	(	std::ostream &	o,
		const Vector4 &	vector
	)

Print a Vector4.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	o	The output stream operator
[in]	vector	The vector to print

Returns:: The output stream operator

bool Dali::operator==	(	const Degree &	lhs,
		const Degree &	rhs
	)

Compares equality between two degrees.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Degree to compare
[in]	rhs	Degree to compare to

Returns:: True if the values are identical

bool Dali::operator==	(	Radian	lhs,
		Radian	rhs
	)

Compares equality between two radians.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Radian to compare to

Returns:: True if the values are identical

bool Dali::operator==	(	Radian	lhs,
		Degree	rhs
	)

Compares equality between a radian and degree.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Degree to compare to

Returns:: True if the values are identical

bool Dali::operator==	(	Degree	lhs,
		Radian	rhs
	)

Compares equality between a degree and a radian.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Degree to compare
[in]	rhs	Radian to compare to

Returns:: True if the values are identical

bool Dali::operator>	(	Radian	lhs,
		Radian	rhs
	)

Compares greater than between two radians.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Radian to compare to

Returns:: True if lhs is greater than rhs

bool Dali::operator>	(	Radian	lhs,
		Degree	rhs
	)

Compares greater than between a radian and a degree.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Degree to compare to

Returns:: True if lhs is greater than rhs

bool Dali::operator>	(	Degree	lhs,
		Radian	rhs
	)

Compares greater than between a radian and a degree.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	lhs	Radian to compare
[in]	rhs	Degree to compare to

Returns:: True if lhs is greater than rhs

float Dali::Round	(	float	value,
		int	pos
	)

Get an float that is rounded at specified place of decimals.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	value	float value
[in]	pos	decimal place

Returns:: a rounded float

float Dali::ShortestDistanceInDomain	(	float	a,
		float	b,
		float	start,
		float	end
	)

Find the shortest distance (magnitude) and direction (sign) from (a) to (b) in domain (start) to (end).

  (\ / start)               (\ / end)
    |-a                 b<----|

Knowing the shortest distance is useful with wrapped domains to solve problems such as determing the closest object to a given point, or determing whether turning left or turning right is the shortest route to get from angle 10 degrees to angle 350 degrees (clearly in a 0-360 degree domain, turning left 20 degrees is quicker than turning right 340 degrees).

The value returned holds the distance and the direction from value a to value b. For instance in the above example it would return -20. i.e. subtract 20 from current value (10) to reach target wrapped value (350).

Since:: 2.4, DALi version 1.0.0

Parameters:

a	the current value
b	the target value
start	the start of the domain
end	the end of the domain

Returns:: the shortest direction (the sign) and distance (the magnitude)

Note:: Assumes both (a) and (b) are already within the domain (start) to (end).

template<typename T >

int Dali::Sign ( T value )

Extracts the sign of a number.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in] value The value we want to extract the sign

Returns:: -1 for negative values, +1 for positive values and 0 if value is 0

float Dali::WrapInDomain	(	float	x,
		float	start,
		float	end
	)

Wrap x in domain (start) to (end).

This works like a floating point version of the % modulo operation. But with an offset (start).

For instance a domain is specified as: start: 2 end: 8

   2                         8
 (\ / start)               (\ / end)
   |----x                    |

The value x will be confined to this domain. If x is below 2 e.g. 0, then it is wrapped to 6. If x is above or equal to 8 e.g. 8.1 then it is wrapped to 2.1.

Domain wrapping is useful for various problems from calculating positions in a space that repeats, to computing angles that range from 0 to 360.

Since:: 2.4, DALi version 1.0.0

Parameters:

[in]	x	the point to be wrapped within the domain
[in]	start	The start of the domain
[in]	end	The end of the domain

Returns:: the wrapped value over the domain (start) (end)

Note:: If start = end (i.e. size of domain 0), then wrapping will not occur and result will always be equal to start.

Classes

Functions

Namespaces

Typedefs

Typedef Documentation

Function Documentation