A Lua library for easy, intuitive 2D and 3D vectors.
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README.md

Vectorial

A Lua library for easy, intuitive 2D and 3D vectors. vectorial2.lua and vectorial3.lua, respecitvely, serve as definitions for instantiation of and operations on 2D and 3D vector quantities.

WARNING: Behavior of this library is not entirely stable. Pick a release and use it.

Current stable release is: 0.2

Usage

To use a vector library, simply require "vectorial2" or require "vectorial3" into a variable, i.e., v2d = require "vectorial2".

You can now create vectors with, for example, a = v2d.Vector2D(2, 3) will create the 2D vector (2,3), and c = v3d.Vector3D(2, 3, 4) will create the 3D vector (2,3,4).

You can retrieve the values of vector components with, for example, a:getX() (which, in our example, would return 2). You can set values in a similar way: for example, a:setX(3) will make a equal to (3,3). A construction like a:setX(a:getX() + 2) would add 2 to a's x component.

Operations on vectors are fairly intuitive. For example, if a and b are the 2D vectors (1,1) and (2,3), then a + b is equal to (3,4), a - b is equal to (-1,-2), and a / b is equal to (0.5, 0.333...). The unary minus works as well; -b equals (-2,-3).

Comparisons work intuitively as well. a == b will return false, but if we had c = Vector2D(1,1) then a == c will return true. a > b is false, as is a > c (since they are equal). a < b will return true, as will a <= c (again, since they are equal).

There are two exceptions. The modulo operator (%) is defined as caluclating vector distance; so a % b is equal to (1,2). The concatenation operator (..) is defined as linear distance, so a .. b is equal to 1.

Using tostring() works as well, so tostring(a) would return [(X:2),(Y:3)].

All of these work similarly for 3D vectors.

Angles can be obtained with :getAngle(). v2d:getAngle() returns the angle of the vector in radians. v3d:getAngle() returns TWO values: "heading" and "carom". Heading is the angle of the X and Y components, while carom is the angle of the Z component to the X/Y plane.

Length (distance from the origin) can be obtained with v2d:getLength(). It works identically for 2D vectors and 3D vectors.

Averaging is implemented, as well - this is especially useful for finding the center of a large number of points. Simply pass v2d.average() or v3d.average() an array of vectors, and you'll get one vector back.

Advanced Usage

(Almost) all operations on Vectorial vectors return Vectorial vectors. So, for example, to get the angle between two Vector2Ds a and b, one could simply use d = (a - b):getAngle().

Roadmap

We are planning to add

  • Arbitrary precision support (this may end up being a fork for various reasons)
  • Transformations (translate, stretch, shrink, rotate)
  • Tables of vectors with their own methods for retrieving, reordering, transforming, and operating on all or some subset of the vectors they contain.
  • N-dimensional vectors

though probably not in that order.