Start a Vectors guide;

guides/Vectors.md

@@ -0,0 +1,136 @@
+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)
+  object.position:add(object.velocity * 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:
+  position:add(vec3(dt))
+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()[16]) --> 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.

guides/init.lua

@@ -2,6 +2,7 @@ return {
   'Getting_Started',
   'Getting_Started_(Android)',
   'Callbacks_and_Modules',
+  'Vectors',
   'Libraries',
   'Distribution',
   'Compiling',