Oolite JavaScript Reference: Vector3D

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Prototype: Object
Subtypes: none

The Vector3D class represents a geometrical vector in three-dimensional space, in cartesian representation. It is used to represent positions, headings and velocities. Explaining vector geometry is beyond the scope of this document, but there are numerous tutorials on the web.

Vector Expressions

All Oolite-provided functions which take a vector as an argument may instead be passed an array of three numbers, or an Entity (in which case the entity’s position is used). In specifications, this is represented by arguments typed vectorExpression. For example, if a and b are vectors whose values are (0, 1, 0) and (1, 0, 0) respectively, the following are equivalent:

var c = a.add(b);
var d = a.add(Vector3D(1, 0, 0));
var e = a.add([1, 0, 0]);
// c, d and e are now all (1, 1, 0).

Properties

x

x : Number (read/write)

The x co-ordinate of the vector.

y

y : Number (read/write)

The y co-ordinate of the vector.

z

z : Number (read/write)

The z co-ordinate of the vector.

Methods

Constructor

new Vector3D([value : vectorExpression]) : Vector3D

Create a new vector with the specified value. If no value is provided, the vector is initialized to (0, 0, 0).

add

function add(v : vectorExpression) : Vector3D

Returns the vector sum of the target and v.

See Also: subtract()

angleTo

function angleTo(v : vectorExpression) : Number

Returns the angle (in radians) between the target and vectorExpression. This is always a positive value between 0 and π.

v.angleTo(u) is equivalent to Math.acos(v.direction().dot(u.direction())).

cross

function cross(v : vectorExpression) : Vector3D

Returns the cross product of the target and vectorExpression.

See Also: dot()

direction

function direction() : Vector3D

Returns the unit vector with the same direction as the target.

v.direction() is equivalent to v.multiply(1 / v.magnitude()).

See Also: magnitude()

distanceTo

function distanceTo(v : vectorExpression) : Number

Returns the distance between the target and v.

u.distanceTo(v) is equivalent to u.subtract(v).magnitude().

See Also: squaredDistanceTo()

dot

function dot(v : vectorExpression) : Number

Returns the dot product of the target and v.

The dot product of two vectors says something how well they are aligned to each other. The dot product of two identical vectors is 1 while two vectors pointing in opposite direction result in a -1 result. Also you can't reliably compare two vectors with each other to see if they are identical. To to check if vector1 == vector2 you need the dot product :

vector1.dot(vector2) > 0.999

See Also: cross()

fromCoordinateSystem

function fromCoordinateSystem(system : String) : Vector3D

Convert a vector from an abstract coordinate system to absolute coordinates. system must be a three-letter string specifying an abstract coordinate system.

Important: Vectors do not “know” which coordinate system they’re in. The script must keep track of that. If you add together vectors in different coordinate systems the result will be nonsense, just as if you added measurements in different units without appropriate conversions.

Example:

this.halfway = Vector3D(0, 0, 0.5).fromCoordinateSystem("wpu");
// Equivalent: Vector3D.interpolate([0, 0, 0], S.mainPlanet, 0.5)

See Also: toCoordinateSystem()

magnitude

function magnitude() : Number

Returns the magnitude (or length) of the vector.

See Also: squaredMagnitude(), direction()

multiply

function multiply(f : Number) : Vector3D

Returns the product of the target and f. This has the effect of scaling the vector by the factor f.

rotateBy

function rotateBy(q : quaternionExpression) : Vector3D

Apply the rotation specified by q to the target vector.

rotationTo

function rotationTo(v : vectorExpression [, maxArc : Number]) : Quaternion

Returns a quaternion corresponding to a rotation from the target vector to v. The optional parameter maxArc specifies a maximum rotation angle; if the angle between the target and v is greater than maxArc radians, a rotation of maxArc radians towards vectorExpression is generated instead.

Both the target and v must be normalized. The vectors must not be antiparallel (180° apart), since the axis of rotation is undefined in this case.

Example:

var orientation = myVector.rotationTo([0, 0, 1])

This will generate a quaternion were the forwardVector is pointing in the same direction as myVector. ([0, 0, 1] is equal to the forwardVector of the identity quaternion.)

squaredDistanceTo

function squaredDistanceTo(v: vectorExpression) : Number

Returns the square of the distance between the target and v.

u.squaredDistanceTo(v) is equivalent to u.distanceTo(v) * u.distanceTo(v), or u.subtract(v).squaredMagnitude().

squaredMagnitude

function squaredMagnitude() : Number

Returns the square of the magnitude of the vector.

v.squaredMagnitude() is equivalent to v.magnitude() * v.magnitude().

subtract

function subtract(v : vectorExpression) : Vector3D

Returns the vector difference between the target and v.

See Also: add()

toArray

function toArray() : Array

Returns an array of the vector’s components, in the order [x, y, z]. v.toArray() is equivalent to [v.x, v.y, v.z].

toCoordinateSystem

function toCoordinateSystem(system : String) : Vector3D

Convert a vector from absolute coordinates to an abstract coordinate system. system must be a three-letter string specifying an abstract coordinate system. The target of the method must be a vector in absolute coordinates. (To convert a vector from one abstract coordinate system to another, you must first call code>fromCoordinateSystem()</code>, then toCoordinateSystem().)

Important: Vectors do not “know” which coordinate system they’re in. The script must keep track of that. If you add together vectors in different coordinate systems the result will be nonsense, just as if you added measurements in different units without appropriate conversions.

Example:

Vector3D(0, 0, 226380).toCoordinateSystem("wpu")
// In Lave system, this returns (0, 0, 0.5).

See Also: fromCoordinateSystem()

tripleProduct

function tripleProduct(v : vectorExpression, w : vectorExpression) : Number

Returns the triple product of the target, v and w.

u.tripleProduct(v, w) is equivalent to u.dot(v.cross(w)).

Static methods

interpolate

function interpolate(u : vectorExpression, v : vectorExpression, where : Number) : Vector3D

Returns a point on the line between u and v. If where is 0, the result is u. If where is 1, the result is v. If where is 0.5, the result is half way between u and v. Values of where outside the range [0, 1] are valid; for instance, Vector3D.interpolate(u, v, -1) returns a point as far from u as v is, but in the opposite direction.

Vector3D.interpolate(u, v, where) is equivalent to u.add(v.subtract(u).multiply(where)), or u.multiply(1 - where).add(v. multiply(where)).

random

function random([maxLength : Number]) : Vector3D

Returns a vector of random length up to maxLength, in a random direction. If maxLength is not specified (or not a number), 1.0 is used. These vectors are uniformly distributed within the unit sphere, which has the effect that longer vectors are more common than shorter ones. Use Vector3D.randomDirectionAndLength() if an even length distribution is desired.

In the following image, the cloud on the left was made with the 2D equivalent of random(), and the image on the right was made with the 2D equivalent of randomDirectionAndLength().
Randomvectordistribution.png

See Also: randomDirection(), randomDirectionAndLength()

randomDirection

function randomDirection([scale : Number]) : Vector3D

Returns a vector of length scale, in a random direction. If scale is not specified (or not a number), 1.0 is used.

See Also: random(), randomDirectionAndLength()

randomDirectionAndLength

function randomDirectionAndLength([maxLength : Number]) : Vector3D

Returns a vector of random length up to maxLength, in a random direction. If maxLength is not specified (or not a number), 1.0 is used. These vectors have a uniform distribution of magnitude (all lengths are equally likely), but cluster towards the origin. Use Vector3D.random() if an even spacial distribution is desired.

See Also: random(), randomDirection()