hump.vector
===========

::

    vector = require "hump.vector"

A handy 2D vector class providing most of the things you do with vectors.

You can access the individual coordinates by ``vec.x`` and ``vec.y``.

.. note::

    The vectors are stored as tables. Most operations create new vectors and
    thus new tables, which *may* put the garbage collector under stress.
    If you experience slowdowns that are caused by hump.vector, try the
    table-less version :doc:`hump.vector-light <vector-light>`.

**Example**::

    function player:update(dt)
        local delta = vector(0,0)
        if love.keyboard.isDown('left') then
            delta.x = -1
        elseif love.keyboard.isDown('right') then
            delta.x =  1
        end
        if love.keyboard.isDown('up') then
            delta.y = -1
        elseif love.keyboard.isDown('down') then
            delta.y =  1
        end
        delta:normalizeInplace()

        player.velocity = player.velocity + delta * player.acceleration * dt

        if player.velocity:len() > player.max_velocity then
            player.velocity = player.velocity:normalized() * player.max_velocity
        end

        player.position = player.position + player.velocity * dt
    end

List of Functions
-----------------

* :func:`vector.new(x,y) <vector.new>`
* :func:`vector.fromPolar(angle, radius) <vector.fromPolar>`
* :func:`vector.randomDirection(len_min, len_max) <vector.randomDirection>`
* :func:`vector.isvector(v) <vector.isvector>`
* :func:`vector:clone() <vector:clone>`
* :func:`vector:unpack() <vector:unpack>`
* :func:`vector:permul(other) <vector:permul>`
* :func:`vector:len() <vector:len>`
* :func:`vector:toPolar() <vector:toPolar>`
* :func:`vector:len2() <vector:len2>`
* :func:`vector:dist(other) <vector:dist>`
* :func:`vector:dist2(other) <vector:dist2>`
* :func:`vector:normalized() <vector:normalized>`
* :func:`vector:normalizeInplace() <vector:normalizeInplace>`
* :func:`vector:rotated(angle) <vector:rotated>`
* :func:`vector:rotateInplace(angle) <vector:rotateInplace>`
* :func:`vector:perpendicular() <vector:perpendicular>`
* :func:`vector:projectOn(v) <vector:projectOn>`
* :func:`vector:mirrorOn(v) <vector:mirrorOn>`
* :func:`vector:cross(other) <vector:cross>`
* :func:`vector:angleTo(other) <vector:angleTo>`
* :func:`vector:trimmed(max_length) <vector:trimmed>`
* :func:`vector:trimInplace(max_length) <vector:trimInplace>`


Vector arithmetic
-----------------

**hump** provides vector arithmetic by implement the corresponding metamethods
(``__add``, ``__mul``, etc.). Here are the semantics:

``vector + vector = vector``
    Component wise sum: \\((a,b) + (x,y) = (a+x, b+y)\\)
``vector - vector = vector``
    Component wise difference: \\((a,b) - (x,y) = (a-x, b-y)\\)
``vector * vector = number``
    Dot product: \\((a,b) \\cdot  (x,y) = a\\cdot x + b\\cdot y\\)
``number * vector = vector``
    Scalar multiplication/scaling: \\((a,b) \\cdot  s = (s\\cdot a, s\\cdot b)\\)
``vector * number = vector``
    Scalar multiplication/scaling: \\(s \\cdot  (x,y) = (s\\cdot x, s\\cdot y)\\)
``vector / number = vector``
    Scalar multiplication/scaling: \\((a,b) / s = (a/s, b/s)\\).

Common relations are also defined:

``a == b``
    Same as ``a.x == b.x and a.y == b.y``.
``a <= b``
    Same as ``a.x <= b.x and a.y <= b.y``.
``a < b``
    Lexicographical order: ``a.x < b.x or (a.x == b.x and a.y < b.y)``.

**Example**::

    -- acceleration, player.velocity and player.position are vectors
    acceleration = vector(0,-9)
    player.velocity = player.velocity + acceleration * dt
    player.position = player.position + player.velocity * dt


Function Reference
------------------

.. function:: vector.new(x,y)

   :param numbers x,y: Coordinates.
   :returns: The vector.


Create a new vector.

**Examples**::

    a = vector.new(10,10)

::

    -- as a shortcut, you can call the module like a function:
    vector = require "hump.vector"
    a = vector(10,10)


.. function:: vector.fromPolar(angle, radius)

   :param number angle: Angle of the vector in radians.
   :param number radius: Length of the vector (optional, default = 1).
   :returns: The vector in cartesian coordinates.


Create a new vector from polar coordinates.
The ``angle`` is measured against the vector (1,0), i.e., the x axis.

**Examples**::

    a = vector.polar(math.pi,10)

.. function:: vector.randomDirection(len_min, len_max)

   :param number len_min: Minimum length of the vector (optional, default = 1).
   :param number len_max: Maximum length of the vector (optional, default = ``len_min``).
   :returns: A vector pointing in a random direction with a random length between ``len_min`` and ``len_max``.

**Examples**::

    rnd = vector.randomDirection()    -- length is 1
    rnd = vector.randomDirection(100) -- length is 100
    rnd = vector.randomDirection(1,5) -- length is a random value between 1 and 5

Sample a vector with random direction and (optional) length.

.. function:: vector.isvector(v)

   :param mixed v:  The variable to test.
   :returns: ``true`` if ``v`` is a vector, ``false`` otherwise.

Test whether a variable is a vector.

**Example**::

    if not vector.isvector(v) then
        v = vector(v,0)
    end


.. function:: vector:clone()

   :returns: Copy of the vector.

Copy a vector.  Assigning a vector to a variable will create a *reference*, so
when modifying the vector referenced by the new variable would also change the
old one::

    a = vector(1,1) -- create vector
    b = a           -- b references a
    c = a:clone()   -- c is a copy of a
    b.x = 0         -- changes a,b and c
    print(a,b,c)    -- prints '(1,0), (1,0), (1,1)'

**Example**::

    copy = original:clone()


.. function:: vector:unpack()

   :returns: The coordinates ``x,y``.


Extract coordinates.

**Examples**::

    x,y = pos:unpack()

::

    love.graphics.draw(self.image, self.pos:unpack())


.. function:: vector:permul(other)

   :param vector other: The second source vector.
   :returns: Vector whose components are products of the source vectors.


Multiplies vectors coordinate wise, i.e. ``result = vector(a.x * b.x, a.y *
b.y)``.

Does not change either argument vectors, but creates a new one.

**Example**::

    -- scale with different magnitudes
    scaled = original:permul(vector(1,1.5))


.. function:: vector:len()

   :returns: Length of the vector.


Get length of the vector, i.e. ``math.sqrt(vec.x * vec.x + vec.y * vec.y)``.

**Example**::

    distance = (a - b):len()


.. function:: vector:toPolar()

   :returns: The vector in polar coordinates (angle, radius).

Convert the vector to polar coordinates, i.e., the angle and the radius/lenth.

**Example**::

   -- complex multiplication
   p, q = a:toPolar(), b:toPolar()
   c = vector(p.x+q.x, p.y*q.y)


.. function:: vector:len2()

   :returns: Squared length of the vector.


Get squared length of the vector, i.e. ``vec.x * vec.x + vec.y * vec.y``.

**Example**::

    -- get closest vertex to a given vector
    closest, dsq = vertices[1], (pos - vertices[1]):len2()
    for i = 2,#vertices do
        local temp = (pos - vertices[i]):len2()
        if temp < dsq then
            closest, dsq = vertices[i], temp
        end
    end


.. function:: vector:dist(other)

   :param vector other: Other vector to measure the distance to.
   :returns: The distance of the vectors.


Get distance of two vectors. The same as ``(a - b):len()``.

**Example**::

    -- get closest vertex to a given vector
    -- slightly slower than the example using len2()
    closest, dist = vertices[1], pos:dist(vertices[1])
    for i = 2,#vertices do
        local temp = pos:dist(vertices[i])
        if temp < dist then
            closest, dist = vertices[i], temp
        end
    end


.. function:: vector:dist2(other)

   :param vector other: Other vector to measure the distance to.
   :returns: The squared distance of the vectors.


Get squared distance of two vectors. The same as ``(a - b):len2()``.

**Example**::

    -- get closest vertex to a given vector
    -- slightly faster than the example using len2()
    closest, dsq = vertices[1], pos:dist2(vertices[1])
    for i = 2,#vertices do
        local temp = pos:dist2(vertices[i])
        if temp < dsq then
            closest, dsq = vertices[i], temp
        end
    end


.. function:: vector:normalized()

   :returns: Vector with same direction as the input vector, but length 1.


Get normalized vector: a vector with the same direction as the input vector,
but with length 1.

Does not change the input vector, but creates a new vector.

**Example**::

    direction = velocity:normalized()


.. function:: vector:normalizeInplace()

   :returns: Itself -- the normalized vector


Normalize a vector, i.e. make the vector to have length 1. Great to use on
intermediate results.

.. warning::
    This modifies the vector. If in doubt, use :func:`vector:normalized()`.

**Example**::

    normal = (b - a):perpendicular():normalizeInplace()


.. function:: vector:rotated(angle)

   :param number angle:  Rotation angle in radians.
   :returns:  The rotated vector


Get a vector with same length, but rotated by ``angle``:

.. image:: _static/vector-rotated.png
   :alt: Sketch of rotated vector.

Does not change the input vector, but creates a new vector.

**Example**::

    -- approximate a circle
    circle = {}
    for i = 1,30 do
        local phi = 2 * math.pi * i / 30
        circle[#circle+1] = vector(0,1):rotated(phi)
    end

.. function:: vector:rotateInplace(angle)

   :param number angle: Rotation angle in radians.
   :returns: Itself -- the rotated vector


Rotate a vector in-place. Great to use on intermediate results.

.. warning::
    This modifies the vector. If in doubt, use :func:`vector:rotated()`.

**Example**::

    -- ongoing rotation
    spawner.direction:rotateInplace(dt)


.. function:: vector:perpendicular()

   :returns: A vector perpendicular to the input vector

Quick rotation by 90°. Creates a new vector. The same (but faster) as
``vec:rotate(math.pi/2)``:

.. image:: _static/vector-perpendicular.png
   :alt: Sketch of two perpendicular vectors

**Example**::

    normal = (b - a):perpendicular():normalizeInplace()



.. function:: vector:projectOn(v)

   :param vector v:  The vector to project on.
   :returns: ``vector``  The projected vector.


Project vector onto another vector:

.. image:: _static/vector-projectOn.png
   :alt: Sketch of vector projection.

**Example**::

    velocity_component = velocity:projectOn(axis)



.. function:: vector:mirrorOn(v)

   :param vector v: The vector to mirror on.
   :returns: The mirrored vector.


Mirrors vector on the axis defined by the other vector:

.. image: _static/vector-mirrorOn.png
   :alt: Sketch of a vector mirrored on another vector

**Example**::

    deflected_velocity = ball.velocity:mirrorOn(surface_normal)


.. function:: vector:cross(other)

   :param vector other:  Vector to compute the cross product with.
   :returns: ``number``  Cross product of both vectors.


Get cross product of two vectors. Equals the area of the parallelogram spanned
by both vectors.

**Example**::

    parallelogram_area = a:cross(b)


.. function:: vector:angleTo(other)

   :param vector other:  Vector to measure the angle to (optional).
   :returns: Angle in radians.


Measures the angle between two vectors. If ``other`` is omitted it defaults
to the vector ``(0,0)``, i.e. the function returns the angle to the coordinate
system.

**Example**::

    lean = self.upvector:angleTo(vector(0,1))
    if lean > .1 then self:fallOver() end

.. function:: vector:trimmed(max_length)

   :param number max_length: Maximum allowed length of the vector.
   :returns: A trimmed vector.

Trim the vector to ``max_length``, i.e. return a vector that points in the same
direction as the source vector, but has a magnitude smaller or equal to
``max_length``.

Does not change the input vector, but creates a new vector.

**Example**::

    ship.velocity = ship.force * ship.mass * dt
    ship.velocity = ship.velocity:trimmed(299792458)


.. function:: vector:trimInplace(max_length)

   :param number max_length: Maximum allowed length of the vector.
   :returns: Itself -- the trimmed vector.

Trim the vector to ``max_length``, i.e. return a vector that points in the same
direction as the source vector, but has a magnitude smaller or equal to
``max_length``.

.. warning::
    This modifies the vector. If in doubt, use :func:`vector:trimmed()`.


**Example**::

    ship.velocity = (ship.velocity + ship.force * ship.mass * dt):trimInplace(299792458)