Represent an angle in radians, uniquely in the range (-pi, pi]. More...

#include <angle.h>

Detailed Description

Represent an angle in radians, uniquely in the range (-pi, pi].

We include pi in the range, but exclude -pi, because pi and -pi are equivalent mod 2pi.

Equivalence is key to this class. We want only one representation of every equivalent angle. For example, 0 and 2pi are both represented as 0, internally. This unique representation allows for comparison and precise arithmetic.

All operators keep the angle values in the valid range.

Why use instead of Quaternions?

Quaternions are great for three dimensional rotations, but for many applications you only have two dimensional rotations. Instead of the four floats and heavy operations required by quaternions, an angle can represent the rotation in one float and reasonably light operations. Angles are easier to do trigonometry on. Also, they're conceptually simpler.

Public Member Functions
	Angle (float angle)

Angle	Abs () const
	Returns the absolute value of an angle.

Angle &	operator= (const Angle &rhs)

Angle &	operator+= (const Angle &rhs)
	Add `rhs` and ensure result is in the range (-pi,pi].

Angle &	operator-= (const Angle &rhs)
	Subtract `rhs` and ensure result is in the range (-pi,pi].

Angle &	operator*= (const float rhs)
	Multiply `rhs` and ensure result is in the normalized range (-pi,pi].

Angle &	operator/= (const float rhs)
	Divide `rhs` and ensure result is in the normalized range (-pi,pi].

Angle	operator- () const
	Negate the angle and ensure result is in the normalized range (-pi,pi].

float	ToRadians () const
	Return the angle value in radians. Value is in the range (-pi,pi].

float	ToDegrees () const
	Return the angle value in degrees. Value is in the range (-180,180].

mathfu::vec3	ToVectorSystem (const AngleToVectorSystem system) const

mathfu::vec3	ToXYVector () const

mathfu::vec2	ToXYVector2f () const

mathfu::vec3	ToXZVector () const

mathfu::vec3	ToYZVector () const

mathfu::vec3	ToYXVector () const

mathfu::vec2	ToYXVector2f () const

mathfu::vec3	ToZXVector () const

mathfu::vec3	ToZYVector () const

mathfu::mat3	ToRotationMatrix (const AngleToVectorSystem system) const

mathfu::mat3	ToXYRotationMatrix () const
	Returns a matrix that rotates about the Z axis `angle` radians.

mathfu::mat3	ToXZRotationMatrix () const
	Returns a matrix that rotates about the Y axis `angle` radians.

mathfu::mat3	ToYZRotationMatrix () const
	Returns a matrix that rotates about the X axis `angle` radians.

mathfu::mat3	ToYXRotationMatrix () const
	Returns a matrix that rotates about the Z axis `-angle` radians.

mathfu::mat3	ToZXRotationMatrix () const
	Returns a matrix that rotates about the Y axis `-angle` radians.

mathfu::mat3	ToZYRotationMatrix () const
	Returns a matrix that rotates about the X axis `-angle` radians.

bool	IsValid () const

Angle	Clamp (const Angle &center, const Angle &max_diff) const

Static Public Member Functions
static float	WrapAngle (float angle)

static Angle	FromWithinThreePi (const float angle)

static Angle	FromRadians (const float radians)
	Create from `radians`, which is converted to the range (-pi, pi].

static Angle	FromDegrees (const float degrees)
	Create from `degrees`, which is converted to the range (-pi, pi].

static Angle	FromVectorSystem (const mathfu::vec3 &v, const AngleToVectorSystem system)

static Angle	FromXYVector (const mathfu::vec3 &v)

static Angle	FromXZVector (const mathfu::vec3 &v)

static Angle	FromYZVector (const mathfu::vec3 &v)

static Angle	FromYXVector (const mathfu::vec3 &v)

static Angle	FromZXVector (const mathfu::vec3 &v)

static Angle	FromZYVector (const mathfu::vec3 &v)

static bool	IsAngleInRange (const float angle)

Friends
bool	operator== (const Angle &a, const Angle &b)

bool	operator< (const Angle &a, const Angle &b)

bool	operator<= (const Angle &a, const Angle &b)

Constructor & Destructor Documentation

motive::Angle::Angle ( float angle )

inlineexplicit

Create from angle, which is already in the valid range (-pi,pi]. If your angle is outside that range, construct the Angle with the slower FromRadians function to automatically wrap it.

Parameters

angle radians in the range (-pi,pi] – i.e. exclusive of -pi but inclusive of +pi.

Member Function Documentation

Angle motive::Angle::Clamp	(	const Angle &	center,
		const Angle &	max_diff
	)		const

inline

Clamps the angle to the range [center - max_diff, center + max_diff]. max_diff must be in the range [0~pi].

static Angle motive::Angle::FromVectorSystem	(	const mathfu::vec3 &	v,
		const AngleToVectorSystem	system
	)

inlinestatic

Returns a point on the unit circle corresponding to a sweep of angle across the specified vector system.

static Angle motive::Angle::FromWithinThreePi ( const float angle )

inlinestatic

Create from angle, in radians, which is in the range (-3pi,3pi]. This function is significantly faster than WrapAngle since it avoids division. It's also more precise for the same reason. The range may seem strange at first glance; it's a consequence of the implementation. Just know that any two sums of normalized angles will still be in the range (-3pi,3pi].

static Angle motive::Angle::FromXYVector ( const mathfu::vec3 & v )

inlinestatic

Create from the x,y coordinates of a vector, using the system described in ToXYVector().

static Angle motive::Angle::FromXZVector ( const mathfu::vec3 & v )

inlinestatic

Create from the x,z coordinates of a vector, using the system described in ToXZVector().

static Angle motive::Angle::FromYXVector ( const mathfu::vec3 & v )

inlinestatic

Create from the y,x coordinates of a vector, using the system described in ToYXVector().

static Angle motive::Angle::FromYZVector ( const mathfu::vec3 & v )

inlinestatic

Create from the y,z coordinates of a vector, using the system described in ToYZVector().

static Angle motive::Angle::FromZXVector ( const mathfu::vec3 & v )

inlinestatic

Create from the z,x coordinates of a vector, using the system described in ToZXVector().

static Angle motive::Angle::FromZYVector ( const mathfu::vec3 & v )

inlinestatic

Create from the z,y coordinates of a vector, using the system described in ToZYVector().

static bool motive::Angle::IsAngleInRange ( const float angle )

inlinestatic

Return true if 'angle' is within the valid range (-pi,pi], that is, the range inclusive of +pi but exclusive of -pi.

bool motive::Angle::IsValid ( ) const

inline

Check internal consistency. If class is functioning correctly, should always return true.

mathfu::mat3 motive::Angle::ToRotationMatrix ( const AngleToVectorSystem system ) const

inline

Returns a point on the unit circle corresponding to a sweep of angle across the specified vector system.

mathfu::vec3 motive::Angle::ToVectorSystem ( const AngleToVectorSystem system ) const

inline

Returns a point on the unit circle corresponding to a sweep of angle across the specified vector system.

mathfu::vec3 motive::Angle::ToXYVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the x-axis towards the y-axis. 0 ==> ( 1, 0, 0) pi/2 ==> ( 0, 1, 0) pi ==> (-1, 0, 0) 3pi/2 ==> ( 0, -1, 0)

mathfu::vec2 motive::Angle::ToXYVector2f ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the x-axis towards the y-axis. 0 ==> ( 1, 0 ) pi/2 ==> ( 0, 1 ) pi ==> (-1, 0 ) 3pi/2 ==> ( 0, -1 )

mathfu::vec3 motive::Angle::ToXZVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the x-axis towards the z-axis. 0 ==> ( 1, 0, 0) pi/2 ==> ( 0, 0, 1) pi ==> (-1, 0, 0) 3pi/2 ==> ( 0, 0, -1)

mathfu::vec3 motive::Angle::ToYXVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the y-axis towards the x-axis. 0 ==> ( 0, 1, 0) pi/2 ==> ( 1, 0, 0) pi ==> ( 0, -1, 0) 3pi/2 ==> (-1, 0, 0)

mathfu::vec2 motive::Angle::ToYXVector2f ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the y-axis towards the x-axis. 0 ==> ( 0, 1 ) pi/2 ==> ( 1, 0 ) pi ==> ( 0, -1 ) 3pi/2 ==> (-1, 0 )

mathfu::vec3 motive::Angle::ToYZVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the y-axis towards the z-axis. 0 ==> (0, 1, 0) pi/2 ==> (0, 0, 1) pi ==> (0, -1, 0) 3pi/2 ==> (0, 0, -1)

mathfu::vec3 motive::Angle::ToZXVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the z-axis towards the x-axis. 0 ==> ( 0, 0, 1) pi/2 ==> ( 1, 0, 0) pi ==> ( 0, 0, -1) 3pi/2 ==> (-1, 0, 0)

mathfu::vec3 motive::Angle::ToZYVector ( ) const

inline

Returns a point on unit circle corresponding to a sweep of angle degrees from the z-axis towards the y-axis. 0 ==> (0, 0, 1) pi/2 ==> (0, 1, 0) pi ==> (0, 0, -1) 3pi/2 ==> (0, -1, 0)

static float motive::Angle::WrapAngle ( float angle )

inlinestatic

Wraps an angle to the range (-pi, pi]. This function is slow because it has a division. When possible, use FromWithinThreePi instead.

The documentation for this class was generated from the following file:

angle.h

Detailed Description

Why use instead of Quaternions?

Public Member Functions

Static Public Member Functions

Friends

Constructor & Destructor Documentation

Member Function Documentation