-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Copyright 2016, Julia Longtin (julial@turinglace.com)
-- Released under the GNU AGPLV3+, see LICENSE

module Graphics.Implicit.ObjectUtil.GetBox2 (getBox2, getBox2R) where

import Prelude(Bool, Fractional, Eq, (==), (||), unzip, minimum, maximum, ($), filter, not, (.), (/), fmap, (-), (+), (*), cos, sin, sqrt, min, max, head, (<), (<>), pi, atan2, (==), (>), show, (&&), otherwise, error)

import Graphics.Implicit.Definitions (ℝ, ℝ2, Box2, (⋯*),
                                      SymbolicObj2(Shell2, Outset2, Circle, Translate2, Rotate2, UnionR2, Scale2, RectR,
                                                   PolygonR, Complement2, DifferenceR2, IntersectR2, EmbedBoxedObj2), minℝ)

import Data.VectorSpace ((^-^), (^+^))

import Data.Fixed (mod')

-- | An empty box.
emptyBox :: Box2
emptyBox = ((0, 0), (0, 0))

-- | Is a Box2 empty?
-- | Really, this checks if it is one dimensional, which is good enough.
isEmpty :: Box2 -> Bool
isEmpty ((a, b), (c, d)) = a==c || b==d

-- | Define a Box2 around all of the given points.
pointsBox :: [ℝ2] -> Box2
pointsBox points =
    let
        (xs, ys) = unzip points
    in
        ((minimum xs, minimum ys), (maximum xs, maximum ys))

-- | Decompose a box into it's four corners.
boxPoints :: Box2 -> [ℝ2]
boxPoints ((x1,y1),(x2,y2)) = [(x1,y1), (x1,y2), (x2,y1), (x2,y2)]

-- | Define a Box2 around all of the given boxes.
unionBoxes :: [Box2] -> Box2
unionBoxes boxes =
    let
        (leftbot, topright) = unzip $ filter (not.isEmpty) boxes
        (lefts, bots) = unzip leftbot
        (rights, tops) = unzip topright
    in
        ((minimum lefts, minimum bots), (maximum rights, maximum tops))

-- | Define a Box2 that is the intersection of all of the given Box2s.
intersectBoxes :: [Box2] -> Box2
intersectBoxes [] = emptyBox
intersectBoxes [x] = x
intersectBoxes (x:xs) = if nmaxx > nminx && nmaxy > nminy
                        then ((nminx, nminy), (nmaxx, nmaxy))
                        else emptyBox
  where
    ((nminx, nminy), (nmaxx, nmaxy)) = ((max xmin1 xmin2, max ymin1 ymin2), (min xmax1 xmax2, min ymax1 ymax2)) 
    ((xmin1, ymin1), (xmax1, ymax1)) = x
    ((xmin2, ymin2), (xmax2, ymax2)) = intersectBoxes xs

-- | Increase a boxes size by a rounding value.
outsetBox :: ℝ -> Box2 -> Box2
outsetBox r (a,b) =
        (a ^-^ (r,r), b ^+^ (r,r))

-- Get a Box2 around the given object.
getBox2 :: SymbolicObj2 -> Box2
-- Primitives
getBox2 (RectR _ a b) = (a,b)
getBox2 (Circle r) = ((-r, -r), (r,r))
getBox2 (PolygonR _ points) = pointsBox points
-- (Rounded) CSG
getBox2 (Complement2 _) =
    ((-infty, -infty), (infty, infty))
        where
          infty :: (Fractional t) => t
          infty = 1/0
getBox2 (UnionR2 r symbObjs) =
  outsetBox r $ unionBoxes (fmap getBox2 symbObjs)
getBox2 (DifferenceR2 _ symbObjs) = getBox2 $ head symbObjs
getBox2 (IntersectR2 r symbObjs) =
  outsetBox r $ intersectBoxes $ filter (not.isEmpty) $ fmap getBox2 symbObjs
-- Simple transforms
getBox2 (Translate2 v symbObj) =
    let
        (a,b) = getBox2 symbObj
    in
        if isEmpty (a,b)
        then emptyBox
        else (a^+^v, b^+^v)
getBox2 (Scale2 s symbObj) =
    let
        (a,b) = getBox2 symbObj
        (sax, say) = s ⋯* a
        (sbx, sby) = s ⋯* b
    in
        ((min sax sbx, min say sby), (max sax sbx, max say sby))
getBox2 (Rotate2 θ symbObj) =
    let
        ((x1,y1), (x2,y2)) = getBox2 symbObj
        rotate (x,y) = (x*cos θ - y*sin θ, x*sin θ + y*cos θ)
    in
        pointsBox [ rotate (x1, y1)
                  , rotate (x1, y2)
                  , rotate (x2, y1)
                  , rotate (x2, y2)
                  ]
-- Boundary mods
getBox2 (Shell2 w symbObj) =
    outsetBox (w/2) $ getBox2 symbObj
getBox2 (Outset2 d symbObj) =
    outsetBox d $ getBox2 symbObj
-- Misc
getBox2 (EmbedBoxedObj2 (_,box)) = box

-- | Define a Box2 around the given object, and the space it occupies while rotating about the center point.
--   Note: No implementations for RectR, Translate2, or Scale2 as they would be identical to the fallthrough.
getBox2R :: SymbolicObj2 -> ℝ -> Box2
getBox2R (Circle r) _ = getBox2 $ Circle r
getBox2R (PolygonR _ points) deg =
  let
    pointRBoxes = [ pointRBox point deg | point <- points ]
    (pointValsMin, pointValsMax) = unzip pointRBoxes
    (pointValsX, pointValsY) = unzip (pointValsMin <> pointValsMax)
  in
    ((minimum pointValsX, minimum pointValsY), (maximum pointValsX, maximum pointValsY))
getBox2R (Complement2 symObj) _ = getBox2 $ Complement2 symObj
getBox2R (UnionR2 r symObjs) deg =
  let
    boxes = [ getBox2R obj deg| obj <- symObjs ]
  in
    outsetBox r $ unionBoxes boxes
getBox2R (DifferenceR2 _ symObjs) deg = getBox2R (head symObjs) deg
getBox2R (IntersectR2 r symObjs) deg =
  let
    boxes = [ getBox2R obj deg| obj <- symObjs ]
  in
    outsetBox r $ intersectBoxes boxes
-- FIXME: implement Rotate2.
-- Fallthrough: rotate the points of the containing box. no rounding.
getBox2R symObj deg =
  let
    origBox = getBox2 symObj
    points  = boxPoints origBox
  in
    getBox2R (PolygonR 0 points) deg

data Quadrant  = UpperRight | UpperLeft | LowerRight | LowerLeft
  deriving Eq
data Axis      = PosX | PosY | NegX | NegY
  deriving Eq
data Position  = OnAxis Axis | InQuadrant Quadrant | CenterPoint
data HasRotation = Rotation Direction | None
  deriving Eq
data Direction = Clockwise | CounterClockwise
  deriving Eq

-- | put a box around a point, and all of the locations it will be at during an x degree arc around (0,0).
pointRBox :: ℝ2 -> ℝ -> Box2
pointRBox (xStart, yStart) travel =
  let
    k :: ℝ
    k = pi/180
    -- distance betwen (0,0) and our target.
    distance = sqrt $ xStart*xStart + yStart*yStart
    -- radian starting position.
    θstart = atan2 yStart xStart
    -- logical starting position
    startPosition = positionOf distance $ absrad θstart
    -- how far we should rotate our point.
    rotationAmount = travel * k
    -- what direction are we rotating.
    rotationDirection = case travel of
      polarity | polarity > 0  -> Rotation CounterClockwise
               | polarity == 0 -> None
      _                        -> Rotation Clockwise
    -- stopping position of our point.
    θstop = absrad $ θstart + rotationAmount
    stopPosition = positionOf distance θstop
    (xStop, yStop) =
      case positionOf distance θstop of
        CenterPoint -> (0,0)
        OnAxis PosX -> (distance,0)
        OnAxis PosY -> (0,distance)
        OnAxis NegX -> (-distance,0)
        OnAxis NegY -> (0,-distance)
        InQuadrant _ -> ( distance*cos θstop, distance*sin θstop)
    (minX, minY, maxX, maxY) = (min xStart xStop, min yStart yStop, max xStart xStop, max yStart yStop)
    positionOf :: ℝ -> ℝ -> Position
    positionOf d θpos
      | d < minℝ                      = CenterPoint
      | θpos == 0 || θpos == 360*k    = OnAxis PosX
      | θpos == 90*k                  = OnAxis PosY
      | θpos == 180*k || θpos == -0   = OnAxis NegX
      | θpos == 270*k                 = OnAxis NegY
      | θpos > 0 && θpos < 90*k       = InQuadrant UpperRight
      | θpos > 90*k && θpos < 180*k   = InQuadrant UpperLeft
      | θpos > 180*k && θpos < 270*k  = InQuadrant LowerLeft
      | θpos > 270*k && θpos < 360*k  = InQuadrant LowerRight
      | otherwise                     = error $ "illegal position in positionOf: " <> show (θpos*k) <> " pos: " <> show θpos <> " d: " <> show d
    -- returns position around a circle in radians, from 0 to 2pi.
    absrad :: ℝ -> ℝ
    absrad rad
      | rad > (360*k) = rad `mod'` (360*k)
      | rad < 0       = absrad (360*k)+rad
      | otherwise     = rad
    noAxis :: Quadrant -> Quadrant -> Direction -> ℝ -> Box2
    noAxis q1 q2 dir amount
      | q1 == q2 && amount < 90*k && amount > -90*k = ((minX, minY), (maxX, maxY))
      | dir == Clockwise && q1 == UpperLeft  = oneAxis PosY q2 dir amount
      | dir == Clockwise && q1 == LowerRight = oneAxis PosX q2 dir amount
      | dir == Clockwise && q1 == LowerLeft  = oneAxis NegY q2 dir amount
      | dir == Clockwise && q1 == UpperRight = oneAxis NegX q2 dir amount
      | dir == CounterClockwise && q1 == UpperRight = oneAxis PosX q2 dir amount
      | dir == CounterClockwise && q1 == UpperLeft  = oneAxis PosY q2 dir amount
      | dir == CounterClockwise && q1 == LowerLeft  = oneAxis NegX q2 dir amount
      | dir == CounterClockwise && q1 == LowerRight = oneAxis NegY q2 dir amount
    noAxis _ _ _ _ = ((-distance, -distance), (distance, distance))
    oneAxis :: Axis -> Quadrant -> Direction -> ℝ -> Box2
    oneAxis axis quadrant dir amount
      | dir == Clockwise &&
        amount < 90*k && amount > -90*k &&
        ((axis == PosX && quadrant == LowerRight) ||
         (axis == NegY && quadrant == LowerLeft)  ||
         (axis == NegX && quadrant == UpperLeft)  ||
         (axis == PosY && quadrant == UpperRight))  = ((minX, minY), (maxX, maxY))
      | dir == CounterClockwise &&
        amount < 90*k && amount > -90*k &&
        ((axis == PosX && quadrant == UpperRight) ||
         (axis == PosY && quadrant == UpperLeft)  ||
         (axis == NegX && quadrant == LowerLeft)  ||
         (axis == NegY && quadrant == LowerRight))  = ((minX, minY), (maxX, maxY))
      | dir == Clockwise &&
        ((axis == PosX && quadrant == LowerLeft)  ||
         (axis == NegY && quadrant == UpperLeft)  ||
         (axis == NegX && quadrant == UpperRight) ||
         (axis == PosY && quadrant == LowerRight))  = crossOne axis dir
      | dir == CounterClockwise &&
        ((axis == PosX && quadrant == UpperLeft)  ||
         (axis == PosY && quadrant == LowerLeft)  ||
         (axis == NegX && quadrant == LowerRight) ||
         (axis == NegY && quadrant == UpperRight))  = crossOne axis dir
      | dir == Clockwise &&
        ((axis == PosX && quadrant == UpperLeft)  ||
         (axis == PosY && quadrant == LowerLeft)  ||
         (axis == NegX && quadrant == LowerRight) ||
         (axis == NegY && quadrant == UpperRight))  = crossTwo axis dir
      | dir == CounterClockwise &&
        ((axis == PosX && quadrant == LowerLeft)  ||
         (axis == NegY && quadrant == UpperLeft)  ||
         (axis == NegX && quadrant == UpperRight) ||
         (axis == PosY && quadrant == LowerRight))  = crossTwo axis dir
      | dir == Clockwise &&
        ((axis == PosX && quadrant == UpperRight) ||
         (axis == PosY && quadrant == UpperLeft)  ||
         (axis == NegX && quadrant == LowerLeft)  ||
         (axis == NegY && quadrant == LowerRight))  = crossThree axis
      | dir == CounterClockwise &&
        ((axis == PosX && quadrant == LowerRight) ||
         (axis == NegY && quadrant == LowerLeft)  ||
         (axis == NegX && quadrant == UpperLeft)  ||
         (axis == PosY && quadrant == UpperRight))  = crossThree axis
      | otherwise = ((-distance, -distance), (distance, distance))
    twoAxis :: Axis -> Axis -> Direction -> Box2
    twoAxis start stop dir
      | (start == PosX && stop == NegX) ||
        (start == PosY && stop == NegY) || 
        (start == NegX && stop == PosX) ||
        (start == NegY && stop == PosY)  = crossOne start dir
    twoAxis start stop dir
      | (start == PosX && stop == NegY) ||
        (start == NegY && stop == NegX) ||
        (start == NegX && stop == PosY) ||
        (start == PosY && stop == PosX)  = if dir == Clockwise
                                           then ((minX, minY), (maxX, maxY))
                                           else crossTwo start dir
      | (start == PosX && stop == PosY) ||
        (start == PosY && stop == NegX) ||
        (start == NegX && stop == NegY) ||
        (start == NegY && stop == PosX)  = if dir == CounterClockwise
                                           then ((minX, minY), (maxX, maxY))
                                           else crossTwo start dir
    twoAxis _ _ _ = ((-distance, -distance), (distance, distance))
    crossOne :: Axis -> Direction -> Box2
    crossOne start dir
      | (start == PosX && dir == Clockwise)        ||
        (start == NegX && dir == CounterClockwise)  = mixWith [(0,-distance)]
      | (start == NegY && dir == Clockwise)        ||
        (start == PosY && dir == CounterClockwise)  = mixWith [(-distance, 0)]
      | (start == NegX && dir == Clockwise)        ||
        (start == PosX && dir == CounterClockwise)  = mixWith [(0, distance)]
      | (start == PosY && dir == Clockwise)        ||
        (start == NegY && dir == CounterClockwise)  = mixWith [( distance, 0)]
      | otherwise = ((-distance, -distance), (distance, distance))
    crossTwo :: Axis -> Direction -> Box2
    crossTwo start dir
      | (start == PosX && dir == Clockwise)        ||
        (start == PosY && dir == CounterClockwise)  = mixWith [(-distance, 0), ( 0,-distance)]
      | (start == PosY && dir == Clockwise)        ||
        (start == NegX && dir == CounterClockwise)  = mixWith [( distance, 0), ( 0,-distance)]
      | (start == NegX && dir == Clockwise)        ||
        (start == NegY && dir == CounterClockwise)  = mixWith [( distance, 0), ( 0, distance)]
      | (start == NegY && dir == Clockwise)        ||
        (start == PosX && dir == CounterClockwise)  = mixWith [(-distance, 0), ( 0, distance)]
      | otherwise = ((-distance, -distance), (distance, distance))
    crossThree :: Axis -> Box2
    crossThree PosX = mixWith [( 0, distance), (-distance, 0), ( 0,-distance)]
    crossThree PosY = mixWith [(-distance, 0), ( 0,-distance), ( distance, 0)]
    crossThree NegX = mixWith [( 0,-distance), ( distance, 0), ( 0, distance)]
    crossThree NegY = mixWith [( distance, 0), ( 0, distance), (-distance, 0)]
    mixWith :: [ℝ2] -> Box2
    mixWith points = ((minimum xPoints, minimum yPoints), (maximum xPoints, maximum yPoints))
                     where
                       (xPoints, yPoints) = unzip $ points <> [(xStart, yStart), (xStop, yStop)] 
    invertRotation :: Direction -> Direction
    invertRotation Clockwise = CounterClockwise
    invertRotation CounterClockwise = Clockwise
  in
    case rotationDirection of
      None -> ((xStart, yStart),(xStart, yStart))
      Rotation dir -> case rotationAmount of
                 amount | amount < 360*k && amount > -360*k ->
                          case startPosition of
                            CenterPoint -> emptyBox
                            OnAxis axis -> case stopPosition of
                                             OnAxis stopaxis         -> twoAxis axis stopaxis dir
                                             InQuadrant stopquadrant -> oneAxis axis stopquadrant dir amount
                                             CenterPoint -> emptyBox
                            InQuadrant quadrant -> case stopPosition of
                                             OnAxis stopaxis         -> oneAxis stopaxis quadrant (invertRotation dir) (-amount)
                                             InQuadrant stopquadrant -> noAxis quadrant stopquadrant dir travel
                                             CenterPoint -> emptyBox
                 _                         ->
                            ((-distance, -distance), (distance, distance))