Vector Struct Reference

The Vector struct represents a three-component mathematical vector or point such as a direction or position in three-dimensional space. More...

Inherits IEquatable< Vector >.

Public Member Functions
float	AngleTo (Vector other)
	The angle between this vector and the specified vector in radians. More...
Vector	Cross (Vector other)
	The cross product of this vector and the specified vector. More...
float	DistanceTo (Vector other)
	The distance between the point represented by this Vector object and a point represented by the specified Vector object. More...
float	Dot (Vector other)
	The dot product of this vector with another vector. More...
bool	Equals (Vector v)
	Compare Vector equality component-wise. More...
bool	IsValid ()
	Returns true if all of the vector's components are finite. More...
float[]	ToFloatArray ()
	Convert this vector to an array of three float values: [x,y,z]. More...
override string	ToString ()
	Returns a string containing this vector in a human readable format: (x, y, z). More...
	Vector (float x, float y, float z)
	Creates a new Vector with the specified component values. More...
	Vector (Vector vector)
	Copies the specified Vector. More...

Static Public Member Functions
static bool	operator!= (Vector v1, Vector v2)
	Compare two vectors for equality. More...
static Vector	operator* (Vector v1, float scalar)
	Multiply vector by a scalar. More...
static Vector	operator* (float scalar, Vector v1)
	Multiply vector by a scalar on the left-hand side. More...
static Vector	operator+ (Vector v1, Vector v2)
	Add vectors component-wise. More...
static Vector	operator- (Vector v1, Vector v2)
	Subtract vectors component-wise. More...
static Vector	operator- (Vector v1)
	Negate a vector. More...
static Vector	operator/ (Vector v1, float scalar)
	Divide vector by a scalar. More...
static bool	operator== (Vector v1, Vector v2)
	Compare two vectors for equality. More...

Public Attributes
float	x
	The horizontal component. More...
float	y
	The vertical component. More...
float	z
	The depth component. More...

Static Public Attributes
static readonly Vector	Backward = new Vector(0, 0, 1)
	The unit vector pointing backward along the positive z-axis: (0, 0, 1) More...
static readonly Vector	Down = new Vector(0, -1, 0)
	The unit vector pointing down along the negative y-axis: (0, -1, 0) More...
static readonly Vector	Forward = new Vector(0, 0, -1)
	The unit vector pointing forward along the negative z-axis: (0, 0, -1) More...
static readonly Vector	Left = new Vector(-1, 0, 0)
	The unit vector pointing left along the negative x-axis: (-1, 0, 0) More...
static readonly Vector	Ones = new Vector(1, 1, 1)
	The ones vector: (1, 1, 1) More...
static readonly Vector	Right = new Vector(1, 0, 0)
	The unit vector pointing right along the positive x-axis: (1, 0, 0) More...
static readonly Vector	Up = new Vector(0, 1, 0)
	The unit vector pointing up along the positive y-axis: (0, 1, 0) More...
static readonly Vector	XAxis = new Vector(1, 0, 0)
	The x-axis unit vector: (1, 0, 0) More...
static readonly Vector	YAxis = new Vector(0, 1, 0)
	The y-axis unit vector: (0, 1, 0) More...
static readonly Vector	ZAxis = new Vector(0, 0, 1)
	The z-axis unit vector: (0, 0, 1) More...
static readonly Vector	Zero = new Vector(0, 0, 0)
	The zero vector: (0, 0, 0) More...

Properties
float	Magnitude [get]
	The magnitude, or length, of this vector. More...
float	MagnitudeSquared [get]
	The square of the magnitude, or length, of this vector. More...
Vector	Normalized [get]
	A normalized copy of this vector. More...
float	Pitch [get]
	The pitch angle in radians. More...
float	Roll [get]
	The roll angle in radians. More...
float	Yaw [get]
	The yaw angle in radians. More...

Detailed Description

The Vector struct represents a three-component mathematical vector or point such as a direction or position in three-dimensional space.

The Leap Motion software employs a right-handed Cartesian coordinate system. Values given are in units of real-world millimeters. The origin is centered at the center of the Leap Motion Controller. The x- and z-axes lie in the horizontal plane, with the x-axis running parallel to the long edge of the device. The y-axis is vertical, with positive values increasing upwards (in contrast to the downward orientation of most computer graphics coordinate systems). The z-axis has positive values increasing away from the computer screen.

Since

1.0

Constructor & Destructor Documentation

Vector	(	float	x,
		float	y,
		float	z
	)

Creates a new Vector with the specified component values.

Vector newVector = new Vector (0.5f, 200.3f, 67f);

Since

1.0

Vector

(

Vector

vector

)

Copies the specified Vector.

Vector copiedVector = new Vector (otherVector);

Since

1.0

Member Function Documentation

float AngleTo

(

Vector

other

)

The angle between this vector and the specified vector in radians.

The angle is measured in the plane formed by the two vectors. The angle returned is always the smaller of the two conjugate angles. Thus A.angleTo(B) == B.angleTo(A) and is always a positive value less than or equal to pi radians (180 degrees).

If either vector has zero length, then this function returns zero.

float angleInRadians = Vector.ZAxis.AngleTo (Vector.YAxis);
// angleInRadians = PI/2 (90 degrees)

Parameters

other

A Vector object.

Returns

The angle between this vector and the specified vector in radians.

Since

1.0

Vector Cross

(

Vector

other

)

The cross product of this vector and the specified vector.

The cross product is a vector orthogonal to both original vectors. It has a magnitude equal to the area of a parallelogram having the two vectors as sides. The direction of the returned vector is determined by the right-hand rule. Thus A.cross(B) == -B.cross(A).

Vector crossProduct = thisVector.Cross (thatVector);

Parameters

other

A Vector object.

Returns

The cross product of this vector and the specified vector.

Since

1.0

float DistanceTo

(

Vector

other

)

The distance between the point represented by this Vector object and a point represented by the specified Vector object.

Vector aPoint = new Vector (10f, 0f, 0f);
Vector origin = Vector.Zero;
float distance = origin.DistanceTo (aPoint); // distance = 10

Parameters

other

A Vector object.

Returns

The distance from this point to the specified point.

Since

1.0

float Dot

(

Vector

other

)

The dot product of this vector with another vector.

The dot product is the magnitude of the projection of this vector onto the specified vector.

float dotProduct = thisVector.Dot (thatVector);

Parameters

other

A Vector object.

Returns

The dot product of this vector and the specified vector.

Since

1.0

bool Equals

(

Vector

v

)

Compare Vector equality component-wise.

bool vectorsAreEqual = thisVector == thatVector;

Since

1.0

bool IsValid

(

)

Returns true if all of the vector's components are finite.

If any component is NaN or infinite, then this returns false.

bool vectorIsValid = thisVector.IsValid ();

Since

1.0

static bool operator!= ( Vector  v1, Vector  v2  )

static

Compare two vectors for equality.

static Vector operator* ( Vector  v1, float  scalar  )

static

Multiply vector by a scalar.

static Vector operator* ( float  scalar, Vector  v1  )

static

Multiply vector by a scalar on the left-hand side.

static Vector operator+ ( Vector  v1, Vector  v2  )

static

Add vectors component-wise.

static Vector operator- ( Vector  v1, Vector  v2  )

static

Subtract vectors component-wise.

static Vector operator- ( Vector  v1 )

static

Negate a vector.

static Vector operator/ ( Vector  v1, float  scalar  )

static

Divide vector by a scalar.

static bool operator== ( Vector  v1, Vector  v2  )

static

Compare two vectors for equality.

float [] ToFloatArray

(

)

Convert this vector to an array of three float values: [x,y,z].

override string ToString

(

)

Returns a string containing this vector in a human readable format: (x, y, z).

Since

1.0

Member Data Documentation

readonly Vector Backward = new Vector(0, 0, 1)

static

The unit vector pointing backward along the positive z-axis: (0, 0, 1)

Vector backwardVector = Vector.Backward;

Since

1.0

readonly Vector Down = new Vector(0, -1, 0)

static

The unit vector pointing down along the negative y-axis: (0, -1, 0)

Vector downVector = Vector.Down;

Since

1.0

readonly Vector Forward = new Vector(0, 0, -1)

static

The unit vector pointing forward along the negative z-axis: (0, 0, -1)

Vector forwardVector = Vector.Forward;

Since

1.0

readonly Vector Left = new Vector(-1, 0, 0)

static

The unit vector pointing left along the negative x-axis: (-1, 0, 0)

Vector leftVector = Vector.Left;

Since

1.0

readonly Vector Ones = new Vector(1, 1, 1)

static

The ones vector: (1, 1, 1)

readonly Vector Right = new Vector(1, 0, 0)

static

The unit vector pointing right along the positive x-axis: (1, 0, 0)

Vector rightVector = Vector.Right;

Since

1.0

readonly Vector Up = new Vector(0, 1, 0)

static

The unit vector pointing up along the positive y-axis: (0, 1, 0)

Vector upVector = Vector.Up;

Since

1.0

float x

The horizontal component.

Since

1.0

readonly Vector XAxis = new Vector(1, 0, 0)

static

The x-axis unit vector: (1, 0, 0)

Vector xAxisVector = Vector.XAxis;

Since

1.0

float y

The vertical component.

Since

1.0

readonly Vector YAxis = new Vector(0, 1, 0)

static

The y-axis unit vector: (0, 1, 0)

Vector yAxisVector = Vector.YAxis;

Since

1.0

float z

The depth component.

Since

1.0

readonly Vector ZAxis = new Vector(0, 0, 1)

static

The z-axis unit vector: (0, 0, 1)

Vector zAxisVector = Vector.ZAxis;

Since

1.0

readonly Vector Zero = new Vector(0, 0, 0)

static

The zero vector: (0, 0, 0)

Vector zeroVector = Vector.Zero;

Since

1.0

Property Documentation

float Magnitude

get

The magnitude, or length, of this vector.

The magnitude is the L2 norm, or Euclidean distance between the origin and the point represented by the (x, y, z) components of this Vector object.

float length = thisVector.Magnitude;

Returns

The length of this vector.

Since

1.0

float MagnitudeSquared

get

The square of the magnitude, or length, of this vector.

float lengthSquared = thisVector.MagnitudeSquared;

Returns

The square of the length of this vector.

Since

1.0

Vector Normalized

get

A normalized copy of this vector.

A normalized vector has the same direction as the original vector, but with a length of one.

Vector normalizedVector = otherVector.Normalized;

Returns

A Vector object with a length of one, pointing in the same direction as this Vector object.

Since

1.0

float Pitch

get

The pitch angle in radians.

Pitch is the angle between the negative z-axis and the projection of the vector onto the y-z plane. In other words, pitch represents rotation around the x-axis. If the vector points upward, the returned angle is between 0 and pi radians (180 degrees); if it points downward, the angle is between 0 and -pi radians.

float pitchInRadians = thisVector.Pitch;

Returns

The angle of this vector above or below the horizon (x-z plane).

Since

1.0

float Roll

get

The roll angle in radians.

Roll is the angle between the y-axis and the projection of the vector onto the x-y plane. In other words, roll represents rotation around the z-axis. If the vector points to the left of the y-axis, then the returned angle is between 0 and pi radians (180 degrees); if it points to the right, the angle is between 0 and -pi radians.

Use this function to get roll angle of the plane to which this vector is a normal. For example, if this vector represents the normal to the palm, then this function returns the tilt or roll of the palm plane compared to the horizontal (x-z) plane.

float rollInRadians = thatVector.Roll;

Returns

The angle of this vector to the right or left of the y-axis.

Since

1.0

float Yaw

get

The yaw angle in radians.

Yaw is the angle between the negative z-axis and the projection of the vector onto the x-z plane. In other words, yaw represents rotation around the y-axis. If the vector points to the right of the negative z-axis, then the returned angle is between 0 and pi radians (180 degrees); if it points to the left, the angle is between 0 and -pi radians.

float yawInRadians = thisVector.Yaw;

Returns

The angle of this vector to the right or left of the negative z-axis.

Since

1.0