# LeapVector¶

Properties:

Methods:

class LeapVector

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

The Leap 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 device. 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 LeapVector *) vector

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

float angleInRadians = [[LeapVector xAxis] angleTo:[LeapVector yAxis]];
// angleInRadians = PI/2 (90 degrees)


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.

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

- (LeapVector *) cross:(const LeapVector *) vector

The cross product of this vector and the specified vector.

LeapVector *crossProduct = [thisVector cross:thatVector];


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 negate] cross:A].

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

- (float) distanceTo:(const LeapVector *) vector

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

LeapVector *aPoint = [[LeapVector alloc] initWithX:10 y:0 z:0];
LeapVector *origin = [LeapVector zero];
float distance = [origin distanceTo:aPoint]; // distance = 10


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

- (LeapVector *) divide:(float) scalar

Divide this vector by a number.

LeapVector *quotient = [thisVector divide:2.5];


Return
The dividend of this LeapVector divided by a scalar.
Since 1.0
Parameters
• scalar -

The scalar divisor;

- (float) dot:(const LeapVector *) vector

The dot product of this vector with another vector.

float dotProduct = [thisVector dot:thatVector];


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

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

- (BOOL) equals:(const LeapVector *) vector

Checks LeapVector equality.

bool vectorsAreEqual = [thisVector equals:thatVector];


Vectors are equal if each corresponding component is equal.

Return
YES, if the LeapVectors are equal.
Since 1.0
Parameters

- (id) initWithVector:(const LeapVector *) vector

Copies the specified LeapVector.

LeapVector *copiedVector = [[LeapVector alloc] initWithVector:otherVector];


Since 1.0
Parameters

- (id) initWithX:(float) x y:(float) y z:(float) z

Creates a new LeapVector with the specified component values.

LeapVector *newVector = [[LeapVector alloc] initWithX:0.5 y:200.3 z:67];


Since 1.0
Parameters
• x -

The horizontal component.

• y -

The vertical component.

• z -

The depth component.

- (LeapVector *) minus:(const LeapVector *) vector

Subtract a vector from this vector.

LeapVector *difference = [thisVector minus:thatVector];


Return
the difference between the two LeapVectors.
Since 1.0
Parameters

- (LeapVector *) negate

Negate this vector.

LeapVector *negation = thisVector.negate;


Return
The negation of this LeapVector.
Since 1.0

- (LeapVector *) plus:(const LeapVector *) vector

Adds two vectors.

LeapVector *sum = [thisVector plus:thatVector];


Return
The sum of the two LeapVectors.
Since 1.0
Parameters

- (LeapVector *) times:(float) scalar

Multiply this vector by a number.

LeapVector *product = [thisVector times:5.0];


Return
The product of this LeapVector and a scalar.
Since 1.0
Parameters
• scalar -

The scalar factor.

Property

- (float) magnitude
magnitude

The magnitude, or length, of this vector.

float length = thisVector.magnitude;


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

Return
The length of this vector.
Since 1.0

- (float) magnitudeSquared
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

- (LeapVector *) normalized
normalized

A normalized copy of this vector.

LeapVector *normalizedVector = otherVector.normalized;


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

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

- (float) pitch
pitch

The pitch angle in radians.

float pitchInRadians = thisVector.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.

Return
The angle of this vector above or below the horizon (x-z plane).
Since 1.0

- (float) roll
roll

The roll angle in radians.

float rollInRadians = thatVector.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.

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

- (NSMutableData *) toFloatPointer
toFloatPointer

Returns an NSMutableData object containing the vector components as consecutive floating point values.

NSData *vectorData = thisVector.toFloatPointer;
float x, y, z;
[vectorData getBytes:&x length:sizeof(float)];
[vectorData getBytes:&y length:sizeof(float)];
[vectorData getBytes:&z length:sizeof(float)];
//Or access as an array of float:
float array[3];
[vectorData getBytes:&array length:sizeof(float) * 3];
x = array[0];
y = array[1];
z = array[2];

Since 1.0

- (NSArray *) toNSArray
toNSArray

Returns an NSArray object containing the vector components in the order: x, y, z.

NSArray *vectorArray = thisVector.toNSArray;


Since 1.0

- (float) x
x

The horizontal component.

Since 1.0

- (float) y
y

The vertical component.

Since 1.0

- (float) yaw
yaw

The yaw angle in radians.

float yawInRadians = thisVector.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.

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

- (float) z
z

The depth component.

Since 1.0

Public Static Functions

+ (LeapVector *) backward

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

LeapVector *backwardVector = [LeapVector backward];

Since 1.0

+ (LeapVector *) down

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

LeapVector *downVector = [LeapVector down];

Since 1.0

+ (LeapVector *) forward

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

LeapVector *forwardVector = [LeapVector forward];

Since 1.0

+ (LeapVector *) left

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

LeapVector *leftVector = [LeapVector left];

Since 1.0

+ (LeapVector *) right

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

LeapVector *rightVector = [LeapVector right];

Since 1.0

+ (LeapVector *) up

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

LeapVector *upVector = [LeapVector up];

Since 1.0

+ (LeapVector *) xAxis

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

LeapVector *xAxisVector = [LeapVector xAxis];

Since 1.0

+ (LeapVector *) yAxis

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

LeapVector *yAxisVector = [LeapVector yAxis];

Since 1.0

+ (LeapVector *) zAxis

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

LeapVector *zAxisVector = [LeapVector zAxis];

Since 1.0

+ (LeapVector *) zero

The zero vector: (0, 0, 0)

LeapVector *zeroVector = [LeapVector zero];

Since 1.0