# Vectors

This is a guide about the different built-in math objects: vectors, matrices, and quaternions. All of these will be referred to as "vector objects" or just "vectors". Vectors are useful because they can represent a multidimensional quantity (like a 3D position) using just a single value.

``````-- Without vectors
function object:update(dt)
object.x = object.x + object.vx * dt
object.y = object.y + object.vy * dt
object.z = object.z + object.vz * dt
end

-- With vectors
function object:update(dt)
end
``````

The following vector types are supported:

• `vec2`
• `vec3`
• `vec4`
• `quat`, a quaternion.
• `mat4`, a 4D matrix.

Most LÖVR functions that accept positions, orientations, transforms, velocities, etc. also accept vector objects, so they can be used interchangeably with numbers:

``````function lovr.draw()
-- position and size are vec3's, rotation is a quat
lovr.graphics.box('fill', position, size, rotation)
end
``````

## Temporary vs. Permanent

Vectors can be created in two different ways: permanent and temporary.

Permanent vectors behave like normal LÖVR objects. They are individual objects that are garbage collected when no longer needed. They're created using the usual `lovr.math.new<Type>` syntax:

``````self.position = lovr.math.newVec3(x, y, z)
``````

Temporary vectors are created from a shared pool of vector objects. This makes them faster because they use temporary memory and do not need to be garbage collected. To make a temporary vector, leave off the `new` prefix:

``````local position = lovr.math.vec3(x, y, z)
``````

As a further shorthand, these vector constructors are placed on the global scope. If you prefer to keep the global scope clean, this can be configured using the `t.math.globals` flag in `lovr.conf`.

``````local position = vec3(x1, y1, z1) + vec3(x2, y2, z2)
``````

Temporary vectors, with all their speed, come with an important restriction: they can only be used during the frame in which they were created. Saving them into variables and using them later on will throw an error:

``````local position = vec3(1, 2, 3)

function lovr.update(dt)
-- Reusing a temporary vector across frames will error:
end
``````

It's possible to overflow the temporary vector pool. If that happens, `lovr.math.drain` can be used to periodically drain the pool, invalidating any existing temporary vectors.

## Metamethods

Vectors have metamethods, allowing them to be used using the normal math operators like `+`, `-`, `*`, `/`, etc.

``````print(vec3(2, 4, 6) * .5 + vec3(10, 20, 30))
``````

These metamethods will create new temporary vectors.

## Components and Swizzles

The raw components of a vector can be accessed like normal fields:

``````print(vec3(1, 2, 3).z) --> 3
print(mat4()) --> 1
``````

Also, multiple fields can be accessed and combined into a new (temporary) vector, called swizzling:

``````local position = vec3(10, 5, 1)
print(position.xy) --> vec2(10, 5)
print(position.xyy) --> vec3(10, 5, 5)
print(position.zyxz) --> vec4(1, 5, 10, 1)
``````

The following fields are supported for vectors:

• `x`, `y`, `z`, `w`
• `r`, `g`, `b`, `a`
• `s`, `t`, `p`, `q`

Quaternions support `x`, `y`, `z`, and `w`.

Matrices use numbers for accessing individual components in "column-major" order.

All fields can also be assigned to.

``````-- Swap the components of a 2D vector
v.xy = v.yx
``````

The `unpack` function can be used (on any vector type) to access all of the individual components of a vector object. For quaternions you can choose whether you want to unpack the angle/axis representation or the raw quaternion components. Similarly, matrices support raw unpacking as well as decomposition into translation/scale/rotation values.

See `lovr.math` for the detailed API reference pages for the different vector types.