scmp::geom Namespace Reference

Geometry-related code. More...

Classes
class	Point2D
	Point2D is a cartesian (X,Y) pairing. More...
class	Polar2D
	Polar2D is a pairing of a radius r and angle θ from some reference point; in this library, it is assumed to be the Cartesian origin (0, 0). More...
class	Quaternion
	Quaternions provide a representation of Orientation and rotations in three dimensions. More...
class	Vector
	Vectors represent a direction and Magnitude. More...

Typedefs
typedef Quaternion< float >	Quaternionf
	Type alias for a float Quaternion.
typedef Quaternion< double >	Quaterniond
	Type alias for a double Quaternion.
typedef Vector< float, 2 >	Vector2F
	Type alias for a two-dimensional float vector.
typedef Vector< float, 3 >	Vector3F
	Type alias for a three-dimensional float vector.
typedef Vector< float, 4 >	Vector4F
	Type alias for a four-dimensional float vector.
typedef Vector< double, 2 >	Vector2D
	Type alias for a two-dimensional double vector.
typedef Vector< double, 3 >	Vector3D
	Type alias for a three-dimensional double vector.
typedef Vector< double, 4 >	Vector4D
	Type alias for a four-dimensional double vector.

Functions
float	Heading2F (Vector2F vec)
	Compass heading for a Vector2F.
double	Heading2D (Vector2D vec)
	Compass heading for a Vector2D.
float	Heading3F (Vector3F vec)
	Compass heading for a Vector2F.
double	Heading3D (Vector3D vec)
Quaternionf	MakeQuaternion (Vector3F axis, float angle)
	Convenience Quaternion construction function.
Quaterniond	MakeQuaternion (Vector3D axis, double angle)
	Convience Quaternion construction function.
template<typename T >
Quaternion< T >	MakeQuaternion (Vector< T, 3 > axis, T angle)
	Convience Quaternion construction function.
Quaternionf	FloatQuaternionFromEuler (Vector3F euler)
	COnstruct a Quaternion from Euler angles.
Quaterniond	DoubleQuaternionFromEuler (Vector3D euler)
	COnstruct a Quaternion from Euler angles.
template<typename T >
Quaternion< T >	LERP (Quaternion< T > p, Quaternion< T > q, T t)
	Linear interpolation for two Quaternions.
template<typename T >
Quaternion< T >	ShortestSLERP (Quaternion< T > p, Quaternion< T > q, T t)
	Shortest distance spherical linear interpolation.
void	QuaternionSelfTest ()
	Internal consistency check.

Variables
constexpr uint8_t	BasisX = 0
	Convenience constant for the x index.
constexpr uint8_t	BasisY = 1
	Convenience constant for the y index.
constexpr uint8_t	BasisZ = 2
	Convenience constant for the z index.

Detailed Description

Geometry-related code.

Function Documentation

DoubleQuaternionFromEuler()

Quaterniond DoubleQuaternionFromEuler

(

Vector3D

euler

)

COnstruct a Quaternion from Euler angles.

Given a vector of Euler angles in ZYX sequence (e.g. yaw, pitch, roll), return a Quaternion.

Parameters

euler

A vector Euler Angle in ZYX sequence.

Returns

A Quaternion representation of the Orientation represented by the Euler angles.

FloatQuaternionFromEuler()

Quaternionf FloatQuaternionFromEuler

(

Vector3F

euler

)

COnstruct a Quaternion from Euler angles.

Given a vector of Euler angles in ZYX sequence (e.g. yaw, pitch, roll), return a Quaternion.

Parameters

euler

A vector Euler Angle in ZYX sequence.

Returns

A Quaternion representation of the Orientation represented by the Euler angles.

Heading2D()

double scmp::geom::Heading2D

(

Vector2D

vec

)

Compass heading for a Vector2D.

Parameters

vec	A vector Orientation.

Returns

The compass heading of the vector in radians.

Heading2F()

float scmp::geom::Heading2F

(

Vector2F

vec

)

Compass heading for a Vector2F.

Parameters

vec	A vector Orientation.

Returns

The compass heading of the vector in radians.

Heading3D()

double scmp::geom::Heading3D

(

Vector3D

vec

)

Heading3D returns a compass heading for a Vector2F.

Parameters

vec	A vector Orientation.

Returns

The compass heading of the vector in radians.

Heading3F()

float scmp::geom::Heading3F

(

Vector3F

vec

)

Compass heading for a Vector2F.

Parameters

vec	A vector Orientation.

Returns

The compass heading of the vector in radians.

LERP()

template<typename T >

Quaternion< T > scmp::geom::LERP	(	Quaternion< T >	p,
		Quaternion< T >	q,
		T	t
	)

Linear interpolation for two Quaternions.

LERP computes the linear interpolation of two quaternions At some fraction of the distance between them.

Template Parameters

T

Parameters

p	The starting Quaternion.
q	The ending Quaternion.
t	The fraction of the distance between the two quaternions to interpolate.

Returns

A Quaternion representing the linear interpolation of the two quaternions.

MakeQuaternion() [1/3]

Quaterniond MakeQuaternion	(	Vector3D	axis,
		double	angle
	)

Convience Quaternion construction function.

Return a double Quaternion scaled appropriately from a vector and Angle, e.g. Angle = cos(Angle / 2), Axis.UnitVector() * sin(Angle / 2).

Parameters

axis	The Axis of rotation.
angle	The Angle of rotation.

Returns

A Quaternion.

MakeQuaternion() [2/3]

Quaternionf MakeQuaternion	(	Vector3F	axis,
		float	angle
	)

Convenience Quaternion construction function.

Return a float Quaternion scaled appropriately from a vector and Angle, e.g. angle = cos(Angle / 2), Axis.UnitVector() * sin(Angle / 2).

Parameters

axis	The Axis of rotation.
angle	The Angle of rotation.

Returns

A Quaternion.

MakeQuaternion() [3/3]

template<typename T >

Quaternion< T > MakeQuaternion	(	Vector< T, 3 >	axis,
		T	angle
	)

Convience Quaternion construction function.

Return a double Quaternion scaled appropriately from a vector and Angle, e.g. Angle = cos(Angle / 2), Axis.UnitVector() * sin(Angle / 2).

Parameters

axis	The Axis of rotation.
angle	The Angle of rotation.

Returns

A Quaternion.

QuaternionSelfTest()

void scmp::geom::QuaternionSelfTest

(

)

Internal consistency check.

Run a quick self test to exercise basic functionality of the Quaternion class to verify correct operation. Note that if #NDEBUG is defined, the self test is disabled.

ShortestSLERP()

template<typename T >

Quaternion< T > scmp::geom::ShortestSLERP	(	Quaternion< T >	p,
		Quaternion< T >	q,
		T	t
	)

Shortest distance spherical linear interpolation.

ShortestSLERP computes the shortest distance spherical linear interpolation between two unit quaternions At some fraction of the distance between them.

Template Parameters

T

Parameters

p	The starting Quaternion.
q	The ending Quaternion.
t	The fraction of the distance between the two quaternions to interpolate.

Returns

A Quaternion representing the shortest path between two quaternions.