# Vector¶

Vector Class Reference

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

## 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...

Vector divide (float scalar)
Divide vector by a scalar. More...

float dot (Vector other)
The dot product of this vector with another vector. More...

boolean equals (Vector other)
Compare Vector equality component-wise. More...

float get (long index)
Index vector components numerically. More...

float getX ()
The horizontal component. More...

float getY ()
The vertical component. More...

float getZ ()
The depth component. More...

boolean isValid ()
Returns true if all of the vector's components are finite. More...

float magnitude ()
The magnitude, or length, of this vector. More...

float magnitudeSquared ()
The square of the magnitude, or length, of this vector. More...

Vector minus (Vector other)
Subtract vectors component-wise. More...

Vector normalized ()
A normalized copy of this vector. More...

Vector opposite ()
A copy of this vector pointing in the opposite direction. More...

float pitch ()
The pitch angle in radians. More...

Vector plus (Vector other)

float roll ()
The roll angle in radians. More...

void setX (float value)
The horizontal component. More...

void setY (float value)
The vertical component. More...

void setZ (float value)
The depth component. More...

Vector times (float scalar)
Multiply vector by a scalar. More...

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

Vector ()
Creates a new Vector with all components set to zero. 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...

float yaw ()
The yaw angle in radians. More...

## Static Public Member Functions

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

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

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

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

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

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

static Vector xAxis ()
The x-axis unit vector: (1, 0, 0) More...

static Vector yAxis ()
The y-axis unit vector: (0, 1, 0) More...

static Vector zAxis ()
The z-axis unit vector: (0, 0, 1) More...

static Vector zero ()
The zero vector: (0, 0, 0) 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 ( )

Creates a new Vector with all components set to zero.

Since
1.0
 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.

// 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
 static Vector backward ( )
static

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

Vector backwardVector = Vector.backward();
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
 Vector divide ( float scalar )

Divide vector by a scalar.

Vector quotient = thisVector.divide(2.5f);
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
 static Vector down ( )
static

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

Vector downVector = Vector.down();
Since
1.0
 boolean equals ( Vector other )

Compare Vector equality component-wise.

boolean vectorsAreEqual = thisVector == thatVector;
Since
1.0
 static Vector forward ( )
static

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

Vector forwardVector = Vector.forward();
Since
1.0
 float get ( long index )

Index vector components numerically.

Index 0 is x, index 1 is y, and index 2 is z.

Returns
The x, y, or z component of this Vector, if the specified index value is at least 0 and at most 2; otherwise, returns zero.
float x = thisVector.get(0);
float y = thisVector.get(1);
float z = thisVector.get(2);
Since
1.0
 float getX ( )

The horizontal component.

Since
1.0
 float getY ( )

The vertical component.

Since
1.0
 float getZ ( )

The depth component.

Since
1.0
 boolean isValid ( )

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

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

boolean vectorsIsValid = thisVector.isValid();
Since
1.0
 static Vector left ( )
static

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

Vector leftVector = Vector.left();
Since
1.0
 float magnitude ( )

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 ( )

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 minus ( Vector other )

Subtract vectors component-wise.

Vector difference = thisVector.minus(thatVector);
Since
1.0
 Vector normalized ( )

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
 Vector opposite ( )

A copy of this vector pointing in the opposite direction.

Vector negation = thisVector.opposite();
Returns
A Vector object with all components negated.
Since
1.0
 float pitch ( )

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.

Returns
The angle of this vector above or below the horizon (x-z plane).
Since
1.0
 Vector plus ( Vector other )

Vector sum = thisVector.plus(thatVector);
Since
1.0
 static Vector right ( )
static

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

Vector rightVector = Vector.right();
Since
1.0
 float roll ( )

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.

Returns
The angle of this vector to the right or left of the y-axis.
Since
1.0
 void setX ( float value )

The horizontal component.

Since
1.0
 void setY ( float value )

The vertical component.

Since
1.0
 void setZ ( float value )

The depth component.

Since
1.0
 Vector times ( float scalar )

Multiply vector by a scalar.

Vector product = thisVector.times(5.0f);
Since
1.0
 String toString ( )

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

Since
1.0
 static Vector up ( )
static

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

Vector upVector = Vector.up();
Since
1.0
 static Vector xAxis ( )
static

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

Vector xAxisVector = Vector.xAxis();
Since
1.0
 float yaw ( )

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.

Returns
The angle of this vector to the right or left of the negative z-axis.
Since
1.0
 static Vector yAxis ( )
static

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

Vector yAxisVector = Vector.yAxis();
Since
1.0
 static Vector zAxis ( )
static

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

Vector zAxisVector = Vector.zAxis();
Since
1.0
 static Vector zero ( )
static

The zero vector: (0, 0, 0)

Vector zeroVector = Vector.zero();
Since
1.0