Passer::LinearAlgebra::Vector3 Struct Reference

A 3-dimensional vector. More...

#include <Vector3.h>

Inheritance diagram for Passer::LinearAlgebra::Vector3:

Public Member Functions
	Vector3 ()
	A new 3-dimensional zero vector.
	Vector3 (float right, float up, float forward)
	A new 3-dimensional vector.
	Vector3 (Vector2 v)
	Convert a 2-dimenstional vector to a 3-dimensional vector.
	Vector3 (Spherical v)
	Convert vector in spherical coordinates to 3d carthesian coordinates.
	~Vector3 ()
	Vector3 destructor.
float	Forward () const
float	Up () const
float	Right () const
bool	operator== (const Vector3 &v)
	Check if this vector to the given vector.
float	magnitude () const
	The vector length.
float	sqrMagnitude () const
	The squared vector length.
Vector3	normalized () const
	Convert the vector to a length of 1.
Vector3	operator- () const
	Negate te vector such that it points in the opposite direction.
Vector3	operator- (const Vector3 &v) const
	Subtract a vector from this vector.
Vector3	operator-= (const Vector3 &v)
Vector3	operator+ (const Vector3 &v) const
	Add a vector to this vector.
Vector3	operator+= (const Vector3 &v)
Vector3	operator*= (float f)
Vector3	operator/= (float f)

Static Public Member Functions
static float	Magnitude (const Vector3 &v)
	The vector length.
static float	SqrMagnitude (const Vector3 &v)
	The squared vector length.
static Vector3	Normalize (const Vector3 &v)
	Convert the vector to a length of 1.
static Vector3	Scale (const Vector3 &v1, const Vector3 &v2)
	Scale the vector using another vector.
static float	Distance (const Vector3 &v1, const Vector3 &v2)
	The distance between two vectors.
static float	Dot (const Vector3 &v1, const Vector3 &v2)
	The dot product of two vectors.
static Vector3	Cross (const Vector3 &v1, const Vector3 &v2)
	The cross product of two vectors.
static Vector3	Project (const Vector3 &v, const Vector3 &n)
	Project the vector on another vector.
static Vector3	ProjectOnPlane (const Vector3 &v, const Vector3 &n)
	Project the vector on a plane defined by a normal orthogonal to the plane.
static float	Angle (const Vector3 &v1, const Vector3 &v2)
	The angle between two vectors.
static float	SignedAngle (const Vector3 &v1, const Vector3 &v2, const Vector3 &axis)
	The signed angle between two vectors.
static Vector3	Lerp (const Vector3 &v1, const Vector3 &v2, float f)
	Lerp (linear interpolation) between two vectors.

Static Public Attributes
static const Vector3	zero = Vector3(0, 0, 0)
	A vector with zero for all axis.
static const Vector3	one = Vector3(1, 1, 1)
	A vector with one for all axis.
static const Vector3	forward = Vector3(0, 0, 1)
	A normalized forward-oriented vector.
static const Vector3	back = Vector3(0, 0, -1)
	A normalized back-oriented vector.
static const Vector3	right = Vector3(1, 0, 0)
	A normalized right-oriented vector.
static const Vector3	left = Vector3(-1, 0, 0)
	A normalized left-oriented vector.
static const Vector3	up = Vector3(0, 1, 0)
	A normalized up-oriented vector.
static const Vector3	down = Vector3(0, -1, 0)
	A normalized down-oriented vector.

Protected Attributes
float	x
	The right axis of the vector.
float	y
	The upward axis of the vector.
float	z
	The forward axis of the vector.

Friends
struct	Vec3
	3-dimensional Vector representation
Vector3	operator* (const Vector3 &v, float f)
	Scale the vector uniformly up.
Vector3	operator* (float f, const Vector3 &v)
Vector3	operator/ (const Vector3 &v, float f)
	Scale the vector uniformly down.
Vector3	operator/ (float f, const Vector3 &v)

Detailed Description

A 3-dimensional vector.

Remarks

This uses a right-handed carthesian coordinate system.

Note

This implementation intentionally avoids the use of x, y and z values.

Constructor & Destructor Documentation

Vector3() [1/4]

Vector3::Vector3

(

)

A new 3-dimensional zero vector.

Vector3() [2/4]

Vector3::Vector3	(	float	right,
		float	up,
		float	forward
	)

A new 3-dimensional vector.

Parameters

right	The distance in the right direction in meters
up	The distance in the upward direction in meters
forward	The distance in the forward direction in meters

Vector3() [3/4]

Vector3::Vector3

(

Vector2

v

)

Convert a 2-dimenstional vector to a 3-dimensional vector.

Parameters

v	The vector to convert

Vector3() [4/4]

Passer::LinearAlgebra::Vector3::Vector3

(

Spherical

v

)

Convert vector in spherical coordinates to 3d carthesian coordinates.

Parameters

v	The vector to convert

~Vector3()

Vector3::~Vector3

(

)

Vector3 destructor.

Member Function Documentation

Forward()

float Passer::LinearAlgebra::Vector3::Forward ( ) const

inline

Up()

float Passer::LinearAlgebra::Vector3::Up ( ) const

inline

Right()

float Passer::LinearAlgebra::Vector3::Right ( ) const

inline

operator==()

bool Vector3::operator==

(

const Vector3 &

v

)

Check if this vector to the given vector.

Parameters

v	The vector to check against

Returns

true if it is identical to the given vector

Note

This uses float comparison to check equality which may have strange effects. Equality on floats should be avoided.

Magnitude()

float Vector3::Magnitude ( const Vector3 &  v )

static

The vector length.

Parameters

v	The vector for which you need the length

Returns

The vector length

magnitude()

float Vector3::magnitude

(

)

const

The vector length.

Returns

The vector length

SqrMagnitude()

float Vector3::SqrMagnitude ( const Vector3 &  v )

static

The squared vector length.

Parameters

v	The vector for which you need the length

Returns

The squared vector length

Remarks

The squared length is computationally simpler than the real length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the calculation of the squared root of C.

sqrMagnitude()

float Vector3::sqrMagnitude

(

)

const

The squared vector length.

Returns

The squared vector length

Remarks

The squared length is computationally simpler than the real length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the calculation of the squared root of C.

Normalize()

Vector3 Vector3::Normalize ( const Vector3 &  v )

static

Convert the vector to a length of 1.

Parameters

v	The vector to convert

Returns

The vector normalized to a length of 1

normalized()

Vector3 Vector3::normalized

(

)

const

Convert the vector to a length of 1.

Returns

The vector normalized to a length of 1

operator-() [1/2]

Vector3 Vector3::operator-

(

)

const

Negate te vector such that it points in the opposite direction.

Returns

The negated vector

operator-() [2/2]

Vector3 Vector3::operator-

(

const Vector3 &

v

)

const

Subtract a vector from this vector.

Parameters

v	The vector to subtract from this vector

Returns

The result of this subtraction

operator-=()

Vector3 Vector3::operator-=

(

const Vector3 &

v

)

operator+()

Vector3 Vector3::operator+

(

const Vector3 &

v

)

const

Add a vector to this vector.

Parameters

v	The vector to add to this vector

Returns

The result of the addition

operator+=()

Vector3 Vector3::operator+=

(

const Vector3 &

v

)

Scale()

Vector3 Vector3::Scale ( const Vector3 &  v1, const Vector3 &  v2  )

static

Scale the vector using another vector.

Parameters

v1	The vector to scale
v2	A vector with the scaling factors

Returns

The scaled vector

Remarks

Each component of the vector v1 will be multiplied with the matching component from the scaling vector v2.

operator*=()

Vector3 Vector3::operator*=

(

float

f

)

operator/=()

Vector3 Vector3::operator/=

(

float

f

)

Distance()

float Vector3::Distance ( const Vector3 &  v1, const Vector3 &  v2  )

static

The distance between two vectors.

Parameters

v1	The first vector
v2	The second vector

Returns

The distance between the two vectors

Dot()

float Vector3::Dot ( const Vector3 &  v1, const Vector3 &  v2  )

static

The dot product of two vectors.

Parameters

v1	The first vector
v2	The second vector

Returns

The dot product of the two vectors

Cross()

Vector3 Vector3::Cross ( const Vector3 &  v1, const Vector3 &  v2  )

static

The cross product of two vectors.

Parameters

v1	The first vector
v2	The second vector

Returns

The cross product of the two vectors

Project()

Vector3 Vector3::Project ( const Vector3 &  v, const Vector3 &  n  )

static

Project the vector on another vector.

Parameters

v	The vector to project
n	The normal vecto to project on

Returns

The projected vector

ProjectOnPlane()

Vector3 Vector3::ProjectOnPlane ( const Vector3 &  v, const Vector3 &  n  )

static

Project the vector on a plane defined by a normal orthogonal to the plane.

Parameters

v	The vector to project
n	The normal of the plane to project on

Returns

Teh projected vector

Angle()

float Vector3::Angle ( const Vector3 &  v1, const Vector3 &  v2  )

static

The angle between two vectors.

Parameters

v1	The first vector
v2	The second vector

Returns

The angle between the two vectors

Remarks

This reterns an unsigned angle which is the shortest distance between the two vectors. Use Vector3::SignedAngle if a signed angle is needed.

SignedAngle()

float Vector3::SignedAngle ( const Vector3 &  v1, const Vector3 &  v2, const Vector3 &  axis  )

static

The signed angle between two vectors.

Parameters

v1	The starting vector
v2	The ending vector
axis	The axis to rotate around

Returns

The signed angle between the two vectors

Lerp()

Vector3 Vector3::Lerp ( const Vector3 &  v1, const Vector3 &  v2, float  f  )

static

Lerp (linear interpolation) between two vectors.

Parameters

v1	The starting vector
v2	The ending vector
f	The interpolation distance

Returns

The lerped vector

Remarks

The factor f is unclamped. Value 0 matches the vector v1, Value 1 matches vector v2. Value -1 is vector v1 minus the difference between v1 and v2 etc.

Friends And Related Symbol Documentation

Vec3

friend struct Vec3

friend

3-dimensional Vector representation

This is a C-style implementation This uses the right-handed coordinate system.

operator* [1/2]

Vector3 operator* ( const Vector3 &  v, float  f  )

friend

Scale the vector uniformly up.

Parameters

f	The scaling factor

Returns

The scaled vector

Remarks

Each component of the vector will be multipled with the same factor f.

operator* [2/2]

Vector3 operator* ( float  f, const Vector3 &  v  )

friend

operator/ [1/2]

Vector3 operator/ ( const Vector3 &  v, float  f  )

friend

Scale the vector uniformly down.

Parameters

f	The scaling factor

Returns

The scaled vector

Remarks

Each componet of the vector will be divided by the same factor.

operator/ [2/2]

Vector3 operator/ ( float  f, const Vector3 &  v  )

friend

Member Data Documentation

zero

const Vector3 Vector3::zero = Vector3(0, 0, 0)

static

A vector with zero for all axis.

one

const Vector3 Vector3::one = Vector3(1, 1, 1)

static

A vector with one for all axis.

forward

const Vector3 Vector3::forward = Vector3(0, 0, 1)

static

A normalized forward-oriented vector.

back

const Vector3 Vector3::back = Vector3(0, 0, -1)

static

A normalized back-oriented vector.

right

const Vector3 Vector3::right = Vector3(1, 0, 0)

static

A normalized right-oriented vector.

left

const Vector3 Vector3::left = Vector3(-1, 0, 0)

static

A normalized left-oriented vector.

up

const Vector3 Vector3::up = Vector3(0, 1, 0)

static

A normalized up-oriented vector.

down

const Vector3 Vector3::down = Vector3(0, -1, 0)

static

A normalized down-oriented vector.

x

float Passer::LinearAlgebra::Vec3::x

protectedinherited

The right axis of the vector.

y

float Passer::LinearAlgebra::Vec3::y

protectedinherited

The upward axis of the vector.

z

float Passer::LinearAlgebra::Vec3::z

protectedinherited

The forward axis of the vector.

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The documentation for this struct was generated from the following files:

• d:/PlatformIO/RoboidControl/LinearAlgebra/Vector3.h
• d:/PlatformIO/RoboidControl/LinearAlgebra/Vector3.cpp