* Collision

A library for generating and working with polygons, particularly for detecting and resolving collisions between them.

** Implements the [[][separating axis theorem]] for polygon collision detection in 2D space.
Using regular polygons with an arbitrary number of sides and of an artbitrary size, can detect collisions and calculate the minimum translation vector to resolve collision.

* Current functionality:
** Detailed documentation available at [[][hexdocs]] 
** Functions
- Generate polygons
  - =Polygon.from_vertices/1= - Create a polygon from a list of vertices, expected to be in counter-clockwise order. Polygons can be convex or concave. Currently, if a polygon is concave then a convex hull is used in collision checks.
  - =Polygon.gen_regular_polygon/4= - Create a regular[fn:1] polygon from a number of sides, radius, rotation angle, and midpoint.
- Find out information about the polygon
  - =Polygon.convex?/1= - Determine whether a polygon is [[][convex]] 
  - =Polygon.centroid/1= - Find a polygon's midpoint
- Manipulate a polygon
  - =Polygon.translate/2= - Translate a polygon in Cartesian space
  - =Polygon.rotate/3= - Rotate a polygon by a measure in radians around a point.
  - =Polygon.rotate_degrees/3= - As above but with degrees.
- Determine and handle collisions 
  - =Collidable.collision?/2= - Check for collision between two polygons
  - =Collidable.resolution/2= - Get the minimum translation vector and magnitude to move two polygons out of collision.
  - =Collidable.resolve_collision/2= - Given two polygons, move them out of collision and returns the translated polygons.
- Work with polygon edges
  - =Edge.from_vertex_pair/1= - Construct an edge from a pair of vertices
  - =Edge.calculate_length/1= - Find the length of an edge
  - =Edge.calculate_angle/2= - Calculate the angle made by two edges meeting at a vertex.
- Work with vertices
  - =Vertex.from_tuple/1= - Construct a vertex from a tuple of numbers
  - =Vertex.to_tuple/1= - Revert a vertex to a tuple
  - =Vertex.graham_scan/1= - Construct a convex hull that bounds a list of vertices describing a polygon
  - =Vertex.round_vertices/1= - Round the components of a vertex

* Roadmap
- [ ] Additional means of collision detection
  - [ ] Detect impending collisions
- [ ] More accurately detect collisions when polygons are concave (via triangulation)
- [ ] 3D collision detection
  - [ ] 3D objects via polygon meshes
- [ ] Optimization 

* Installation

Add =collision= to your list of dependencies in =mix.exs=:

   #+BEGIN_SRC elixir
     def deps do
       [{:collision, "~> 0.3.1"}]

* Footnotes

[fn:1] A polygon with n equal sides and n equal angles.