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Class Vector

Direct Known Subclasses:
mathnetics.point2D, mathnetics.point3D
class Vector
The Vector class includes instance methods and static objects/methods. It has no dependencies but is automatically included with Matrix.js.
Defined in Vector.js

Variable Summary
Number[] components
the components of the Vector
public static Vector i
The unit vector [1,0,0]
public static Vector j
The unit vector [0,1,0]
public static Vector k
The unit vector [0,0,1]
int n
the dimension of the Vector (length of components array)

Constructor Summary
Vector (Number[] elements)
Vector (Vector vec)
Constructor function.

Function Summary
public Vector add (Vector vec)
Adds a vector to the supplied vector.
public Vector addElement (Number el)
Adds a new element to the vector and updates the dimension.
public Number angleBetween (Vector vec)
Finds and returns the angle between two vectors.
public Vector cross (Vector vec)
Computes the cross product of two 3-dimensional vectors.
public int dimension ([int n])
Sets and or returns the dimension of the vector: if no parameter supplied, returns dimension; if number given, sets dimension.
public Number distanceFrom (Object obj)
Returns the distance between the vector and an object, as if the vector were a point in its n-space.
public Number dot (Vector vec)
Returns the scalar dot product of this vector and the supplied vector.
public Number[] elements ([Number[] els])
Method for setting and getting the elements of a vector.
public boolean equalTo (Vector vec)
Tests to see if two vectors are equal to each other.
public Number get (int index)
Gets the component of the vector at index.
public Number getLength()
Returns the length of the vector by modulus definition: length = sqrt(this.dot(this))
public int indexOf (Number x)
Returns the first occurence of x in the vector.
public boolean isAntiParallel (Vector vec)
Tests if two vectors are antiparallel.
public boolean isParallel (Vector vec)
Tests if two vectors are parallel.
public boolean isPerpendicular (Vector vec)
Tests if two vectors are perpendicular.
public boolean linearlyDependent (Vector vec)
Tests to see if 2 vectors are linearly dependent.
public boolean linearlyIndependent (Vector vec)
Tests to see if 2 vectors are linearly independent from each other.
public Vector make3D()
Makes a copy of the given vector in 3 dimensions.
public Vector map (Function func)
Maps the vector to a new vector by the supplied function.
public Number max()
Finds and returns the element with the largest absolute value.
public Vector multiplyBy (Number k)
Multiplies a vector by a scalar k.
public Vector negative()
Returns a negative copy of the Vector (or point).
public Vector normalize()
Normalizes the vector and returns the new unit vector.
public static Vector random (int n, [Number max])
Creates and returns a new vector with n random elements less than or equal to max.
public Vector reflectionIn (Object obj)
Reflects the Vector or mathnetics.point2D/3D in the given point, line, or plane
public Vector resolute (Vector vec)
Projects one Vector onto another.
public Vector round()
Rounds all the elements of the vector and returns the copy.
public Vector snapTo (Number val)
Sets all values within range of mathnetics.zero (set in mathnetics.js) to val.
public Vector subtract (Vector vec)
Subtracts a vector to the supplied vector.
public Matrix toColumnMatrix()
Converts a Vector into a 1-column matrix.
public void toEach (Function func)
Performs a supplied function on every element of the vector.
public Object toPoint()
Converts a Vector to a point object of appropriate dimension in homogeneous coordinates.
public Matrix toRowMatrix()
Converts a Vector into a 1-row matrix.
public String toString()
Returns a string representation of the vector.
public static Vector zero (int n)
Creates and returns a new vector of dimension n with all 0 components.

Variable Details

variable Number[] components

the components of the Vector

variable public static Vector i

The unit vector [1,0,0]

variable public static Vector j

The unit vector [0,1,0]

variable public static Vector k

The unit vector [0,0,1]

variable int n

the dimension of the Vector (length of components array)

Constructor Details

constructor Vector

Vector(Number[] elements)
Vector(Vector vec)
Constructor function. Takes an Array or a Vector and creates a Vector object.
Parameters:
fromArray
elements - Array to become the components of the Vector
clone
vec - the vector to clone

Function Details

function add

public Vector add(Vector vec)
Adds a vector to the supplied vector.
Parameters:
vec - the vector to be added.
Returns:
a new vector that is the sum of the original and supplied.

function addElement

public Vector addElement(Number el)
Adds a new element to the vector and updates the dimension.
Parameters:
el - the number to add to the vector
Returns:
this vector, updated

function angleBetween

public Number angleBetween(Vector vec)
Finds and returns the angle between two vectors.
Parameters:
vec - the vector from which to find the angle
Returns:
the angle (in radians) between the two vectors

function cross

public Vector cross(Vector vec)
Computes the cross product of two 3-dimensional vectors.
Parameters:
vec - the vector with which to take the cross product
Returns:
a new vector that is the cross product; null if either of the vectors is not 3-dimensional

function dimension

public int dimension([int n])
Sets and or returns the dimension of the vector: if no parameter supplied, returns dimension; if number given, sets dimension.
Parameters:
[n] - the dimension to set the array. If n > current dimension, 0s added as all new components; if n < current dimension, all components greater than that dimension are deleted.
Returns:
the dimension of the vector.

function distanceFrom

public Number distanceFrom(Object obj)
Returns the distance between the vector and an object, as if the vector were a point in its n-space.
Parameters:
obj - the object (Vector, Line, Plane, etc) from which to get the distance
Returns:
the distance between the vector and the object

function dot

public Number dot(Vector vec)
Returns the scalar dot product of this vector and the supplied vector.
Parameters:
vec - the vector with which to compute the dot product
Returns:
null if vector is not a vector or is a different dimension, the dot product of the two vectors otherwise.

function elements

public Number[] elements([Number[] els])
Method for setting and getting the elements of a vector.
Parameters:
[els] - if supplied, will set the vector's elements to els.
Returns:
the elements of the vector as an array

function equalTo

public boolean equalTo(Vector vec)
Tests to see if two vectors are equal to each other.
Parameters:
vec - the vector to compare to
Returns:
true iff vectors are equal (all components are equal and have same dimension), false otherwise

function get

public Number get(int index)
Gets the component of the vector at index.
Parameters:
index - the index for which you want the component
Returns:
{Number} the (index)'th component of the vector

function getLength

public Number getLength()
Returns the length of the vector by modulus definition: length = sqrt(this.dot(this))
Returns:
the length of the vector

function indexOf

public int indexOf(Number x)
Returns the first occurence of x in the vector.
Parameters:
x - the element to search for
Returns:
the index of the first occurence of element x; null if never occurs

function isAntiParallel

public boolean isAntiParallel(Vector vec)
Tests if two vectors are antiparallel.
Parameters:
vec - the vector to compare
Returns:
true iff vectors are antiparallel, false or null otherwise

function isParallel

public boolean isParallel(Vector vec)
Tests if two vectors are parallel.
Parameters:
vec - the vector to compare
Returns:
true iff vectors are parallel, false or null otherwise

function isPerpendicular

public boolean isPerpendicular(Vector vec)
Tests if two vectors are perpendicular.
Parameters:
vec - the vector to compare
Returns:
true iff vectors are perpendicular, false or null otherwise

function linearlyDependent

public boolean linearlyDependent(Vector vec)
Tests to see if 2 vectors are linearly dependent.
Parameters:
vec - the vector to compare with
Returns:
true iff vectors are dependent, false otherwise

function linearlyIndependent

public boolean linearlyIndependent(Vector vec)
Tests to see if 2 vectors are linearly independent from each other.
Parameters:
vec - the vector to test for independence
Returns:
true iff vectors are independent, false otherwise (null if vectors not of same size)

function make3D

public Vector make3D()
Makes a copy of the given vector in 3 dimensions.
Returns:
a new vector that is 3-D, with components decided according to the dimension() method (i.e. 0 if n<3, removed if n > 3)
See also:
dimension

function map

public Vector map(Function func)
Maps the vector to a new vector by the supplied function.
Parameters:
func - the mapping function
Returns:
{Vector} the new vector generated by the map

function max

public Number max()
Finds and returns the element with the largest absolute value.
Returns:
the absolute largest element

function multiplyBy

public Vector multiplyBy(Number k)
Multiplies a vector by a scalar k.
Parameters:
k - the scalar by which to multiply the vector
Returns:
a new vector that is the scalar multiplication

function negative

public Vector negative()
Returns a negative copy of the Vector (or point).
Returns:
a new, negative copy of the original Vector or mathnetics.point2D/3D

function normalize

public Vector normalize()
Normalizes the vector and returns the new unit vector.
Returns:
a new vector that is the normalized version of the original vector

function random

public static Vector random(int n, [Number max])
Creates and returns a new vector with n random elements less than or equal to max.
Parameters:
n - the number of components the vector should be
[max] - the maximum value the elements can be; if not specified, values will be in rand [0,1)
Returns:
a new vector with random components

function reflectionIn

public Vector reflectionIn(Object obj)
Reflects the Vector or mathnetics.point2D/3D in the given point, line, or plane
Parameters:
obj - the Line, Plane, or Vector/mathnetics.point2D/3D in which to reflect this
Returns:
a new Vector or mathnetics.point3D (depends on which calls this function) that is reflected

function resolute

public Vector resolute(Vector vec)
Projects one Vector onto another. Gives the component of this Vector in the supplied Vector's direction.
Parameters:
vec - (or mathnetics.point2D/3D object) the vector onto which to project this vector
Returns:
a new Vector (or mathnetics.point2D/3D object), the original projected onto vec

function round

public Vector round()
Rounds all the elements of the vector and returns the copy.
Returns:
a copy of the original vector, but rounded

function snapTo

public Vector snapTo(Number val)
Sets all values within range of mathnetics.zero (set in mathnetics.js) to val.
Parameters:
val - the number to snap the vector to
Returns:
this Vector snapped to the given value

function subtract

public Vector subtract(Vector vec)
Subtracts a vector to the supplied vector.
Parameters:
vec - the vector to be subtracted.
Returns:
a new vector that is the result of the subtraction.

function toColumnMatrix

public Matrix toColumnMatrix()
Converts a Vector into a 1-column matrix.
Returns:
the column Matrix representation of the Vector

function toEach

public void toEach(Function func)
Performs a supplied function on every element of the vector. Used by map.
Parameters:
func the function to perform on each element

function toPoint

public Object toPoint()
Converts a Vector to a point object of appropriate dimension in homogeneous coordinates. If called from a mathnetics.point2D or mathnetics.point3D object, acts as another way to clone the point.
Returns:
either a mathnetics.point2D or mathnetics.point3D object, depending on size of Vector, with same coordinates as the Vector's components

function toRowMatrix

public Matrix toRowMatrix()
Converts a Vector into a 1-row matrix.
Returns:
the row Matrix representation of the Vector

function toString

public String toString()
Returns a string representation of the vector.
Returns:
the string representation of the vector.

function zero

public static Vector zero(int n)
Creates and returns a new vector of dimension n with all 0 components.
Parameters:
n - the dimension of the new zero vector
Returns:
a new zero vector of dimension n