# Vector¶

Properties:

Methods:

struct Leap::Vector

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

Public Functions

float angleTo(const 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::xAxis().angleTo(Vector::yAxis());
// angleInRadians is PI/2 (90 degrees) -- the angle between the x and y axes


Return
The angle between this vector and the specified vector in radians.
Since
1.0
Parameters

Vector cross(const 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);


Return
The cross product of this vector and the specified vector.
Since
1.0
Parameters

float distanceTo(const Vector & other)

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

Vector aPoint = Vector(10, 0, 0);
Vector origin = Vector::zero();
float distance = origin.distanceTo(aPoint); // distance = 10


Return
The distance from this point to the specified point.
Since
1.0
Parameters

float dot(const 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);


Return
The dot product of this vector and the specified vector.
Since
1.0
Parameters

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

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();


Return
The length of this vector.
Since
1.0

float magnitudeSquared()

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

float lengthSquared = thisVector.magnitudeSquared();


Return
The square of the length of this vector.
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();


Return
A Vector object with a length of one, pointing in the same direction as this Vector object.
Since
1.0

bool operator!=(const Vector & other)

Compare Vector inequality component-wise.

bool vectorsNotEqual = thisVector != thatVector;

Since
1.0

Vector operator*(float scalar)

Multiply vector by a scalar.

Vector product = thisVector * 5.0;

Since
1.0

Vector & operator*=(float scalar)

Multiply vector by a scalar and assign the product.

Since
1.0

Vector operator+(const Vector & other)

Vector sum = thisVector + thatVector;

Since
1.0

Vector & operator+=(const Vector & other)

Add vectors component-wise and assign the sum.

Since
1.0

Vector operator-()

A copy of this vector pointing in the opposite direction.

Vector negation = -thisVector;


Return
A Vector object with all components negated.
Since
1.0

Vector operator-(const Vector & other)

Subtract vectors component-wise.

Vector difference = thisVector - thatVector;

Since
1.0

Vector & operator-=(const Vector & other)

Subtract vectors component-wise and assign the difference.

Since
1.0

Vector operator/(float scalar)

Divide vector by a scalar.

Vector quotient = thisVector/2.5;

Since
1.0

Vector & operator/=(float scalar)

Divide vector by a scalar and assign the quotient.

Since
1.0

bool operator==(const Vector & other)

Compare Vector equality component-wise.

bool vectorsAreEqual = thisVector == thatVector;

Since
1.0

float operator[](unsigned int index)

Index vector components numerically.

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

float x = thisVector[0];
float y = thisVector[1];
float z = thisVector[2];

Return
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.
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.

float pitchInRadians = thisVector.pitch();


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

float rollInRadians = thatVector.roll();


Return
The angle of this vector to the right or left of the y-axis.
Since
1.0

const float * toFloatPointer()

Cast the vector to a float array.

const float *vectorData = thisVector.toFloatPointer();
float x = *vectorData;
float y = *(++vectorData);
float z = *(++vectorData);

Since
1.0

std::string toString()

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

Since
1.0

template < typename Vector3Type >
const Vector3Type toVector3()

Convert a Leap::Vector to another 3-component Vector type.

The specified type must define a constructor that takes the x, y, and z components as separate parameters.

Since
1.0

template < typename Vector4Type >
const Vector4Type toVector4(float w = 0.0f)

Convert a Leap::Vector to another 4-component Vector type.

The specified type must define a constructor that takes the x, y, z, and w components as separate parameters. (The homogeneous coordinate, w, is set to zero by default, but you should typically set it to one for vectors representing a position.)

Since
1.0

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 = Vector(0.5, 200.3, 67);

Since
1.0

Vector(const Vector & vector)

Copies the specified Vector.

Vector copiedVector = Vector(otherVector);

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.

float yawInRadians = thisVector.yaw();


Return
The angle of this vector to the right or left of the negative z-axis.
Since
1.0

Public Members

float x

The horizontal component.

Since
1.0

float y

The vertical component.

Since
1.0

float z

The depth component.

Since
1.0

Public Static Functions

const Vector & backward()

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

Vector backwardVector = Vector::backward();

Since
1.0

const Vector & down()

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

Vector downVector = Vector::down();

Since
1.0

const Vector & forward()

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

Vector forwardVector = Vector::forward();

Since
1.0

const Vector & left()

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

Vector leftVector = Vector::left();

Since
1.0

const Vector & right()

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

Vector rightVector = Vector::right();

Since
1.0

const Vector & up()

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

Vector upVector = Vector::up();

Since
1.0

const Vector & xAxis()

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

Vector xAxisVector = Vector::xAxis();

Since
1.0

const Vector & yAxis()

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

Vector yAxisVector = Vector::yAxis();

Since
1.0

const Vector & zAxis()

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

Vector zAxisVector = Vector::zAxis();

Since
1.0

const Vector & zero()

The zero vector: (0, 0, 0)

Vector zeroVector = Vector::zero();

Since
1.0