Safe Haskell	Safe-Inferred
Language	Haskell2010

Geometry.Processes.Billard

Synopsis

billard :: [Line] -> Line -> [Vec2]

Documentation

billard Source #

Arguments

:: [Line]	Geometry; typically involves the edges of a bounding polygon.
-> Line	Initial velocity vector of the ball. Only start and direction, not length, are relevant for the algorithm.
-> [Vec2]	List of collision points. Finite iff the ball escapes the geometry.

Shoot a billard ball, and record its trajectory as it is reflected off the edges of a provided geometry.

(image code)

Expand

>>> :{
haddockRender "Geometry/Processes/Billard/billard.svg" 330 360 $ \_ -> do
    let lambda = transform (translate (Vec2 10 350) <> mirrorYCoords) . Polygon $
            [ Vec2 0.387   340.156
            , Vec2 113.773 170.078
            , Vec2 0.387   0
            , Vec2 85.426  0
            , Vec2 312.195 340.156
            , Vec2 227.156 340.156
            , Vec2 156.293 233.859
            , Vec2 85.426  340.156
            , Vec2 0.387   340.156 ]
        startPoint = Vec2 100 100
        startAngle = deg (-25)
        numReflections = 128
        startVec = angledLine startPoint startAngle 100
        billardPoints = startPoint : take numReflections (billard (polygonEdges lambda) startVec)
    cairoScope $ do
        setColor (mma 0)
        C.setDash [2,4] 0
        sketch lambda
        C.stroke
    cairoScope $ do
        setColor (mma 0)
        for_ billardPoints $ \point -> sketch (Circle point 3) >> C.stroke
    cairoScope $ do
        setColor (mma 1)
        let billardArrows = zipWith Line billardPoints (tail billardPoints)
        for_ billardArrows $ \arr -> sketch arr >> C.stroke
:}
Generated file: size 80KB, crc32: 0xd6e508bf