Efficient Collision detection in Elm
This package implements the Gilbert-Johnson-Keerthi (GJK) collision detection algorithm for 2D convex objects. It is quite efficient, usually converging within one or two iterations.
import Collision exposing (..) -- Example polySupport function dot : Pt -> Pt -> Float dot (x1,y1) (x2,y2) = (x1*x2) + (y1*y2) polySupport : List Pt -> Pt -> Maybe Pt polySupport list d = let dotList = List.map (dot d) list decorated = (List.map2 (,)) dotList list max = List.maximum decorated in case max of Just (m, p) -> Just p _ -> Nothing poly1 = [(-15,-10),(0,15),(12,-5)] poly2 = [(-9,13),(6,13),(-2,22)] collision 10 (poly1, polySupport) (poly2, polySupport) == Just True
Note: the first parameter to collision is max recursion depth. It can easily be elided by defining an auxiliary helper
myCollision = collision 100. Control over recursion depth can be useful when defining your own support
type alias Pt = (Float, Float) type alias Mink a = (a, (a -> Pt -> Maybe Pt)) collision : Int -> Mink a -> Mink b -> Maybe Bool
Mink b is a pair of: a boundary object of type
b, and a suppport function of type
f: b -> Pt -> Maybe Pt which given a boundary object, and a direction vector (given by a Pt), produces
a point on the boundary furthest in the direction of the vector.
polySupport [(-15,-10),(0,15),(12,5)] (1,0) == Just (12,5) polySupport [(-15,-10),(0,15),(12,5)] (0,-1) == Just (-15,10)
You can define your own boundary objects and corresponding support functions, perhaps to handle circles. Look in GJK.elm in bakkemo/umwelt for just such an example. It doesn't make sense for this library to prescribe a boundary representation (for circles, or any OTHER object type).
Determining if a point is inside an object is just a special case of this: (pt, (\a b -> a)) : Mink Pt is a perfectly valid Minkowski object.