module Geometry where


data Point = Pt {
  pointX :: Double,
  pointY :: Double
} deriving Show

data Vector = Vec {
  vectorX :: Double,
  vectorY :: Double
} deriving Show

data SourcedVector = SVec {
  vectorSource :: Point,
  vectorDirection :: Vector
} deriving Show

data PlaneVector = PVec {
  planeFrom :: Point,
  planeTo :: Point
} deriving Show


sourcedToPlane :: SourcedVector -> PlaneVector
sourcedToPlane (SVec (Pt fx fy) (Vec dx dy)) =
      (PVec (Pt fx fy) (Pt (fx + dx) (fy + dy)))

planeToSourced :: PlaneVector -> SourcedVector
planeToSourced (PVec (Pt fx fy) (Pt tx ty)) =
      (SVec (Pt fx fy) (Vec (tx - fx) (ty - fy)))

makeSourced :: Point -> Point -> SourcedVector
makeSourced f t = planeToSourced (PVec f t)


dest :: SourcedVector -> Point
dest (SVec (Pt fx fy) (Vec dx dy)) = Pt (fx + dx) (fy + dy)

dist :: Point -> Point -> Double
dist (Pt a b) (Pt c d) = sqrt ((a - c) * (a - c) + (b - d) * (b - d))

mult :: SourcedVector -> Double -> SourcedVector
mult (SVec s (Vec dx dy)) a = (SVec s newDirection)
    where newDirection = Vec (a*dx) (a*dy)

alpha :: SourcedVector -> Point -> Double
alpha (SVec (Pt x _) (Vec dx _)) (Pt a _) = (a - x) / dx

scp :: Vector -> Vector -> Double
scp (Vec fx fy) (Vec sx sy) = fx * sx + fy * sy

vcp :: Vector -> Vector -> Double
vcp (Vec x y) (Vec a b) = x * b - y * a



a = (Pt 2.0 2.0)
b = (Pt 6.0 10.0)

c = (Pt 7.0 4.0)
d = (Pt 4.0 6.0)


u = makeSourced a b
v = makeSourced c d

e = (Pt 3 (-1))
f = (Pt 7 2)


g = Pt 14 4
h = Pt 16 10
i = Pt 20 6