-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Copyright 2014 2015 2016, Julia Longtin (julial@turinglace.com)
-- Copyright 2015 2016, Mike MacHenry (mike.machenry@gmail.com)
-- Released under the GNU AGPLV3+, see LICENSE

module Graphics.Implicit.ObjectUtil.GetBox3 (getBox3) where

import Prelude(Eq, Bool(False), Fractional, Either (Left, Right), (==), (||), max, (/), (-), (+), fmap, unzip, ($), filter, not, (.), unzip3, minimum, maximum, min, (>), (&&), head, (*), (<), abs, either, error, const, otherwise, take, fst, snd)

import Graphics.Implicit.Definitions (ℝ, Fastℕ, Box3, SymbolicObj3 (Rect3R, Sphere, Cylinder, Complement3, UnionR3, IntersectR3, DifferenceR3, Translate3, Scale3, Rotate3, Rotate3V, Shell3, Outset3, EmbedBoxedObj3, ExtrudeR, ExtrudeOnEdgeOf, ExtrudeRM, RotateExtrude, ExtrudeRotateR), SymbolicObj2 (Rotate2, RectR), (⋯*), fromFastℕtoℝ, fromFastℕ)

import Graphics.Implicit.ObjectUtil.GetBox2 (getBox2, getBox2R)

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

-- FIXME: many variables are being ignored here. no rounding for intersect, or difference.. etc.

-- | An empty box.
emptyBox :: Box3
emptyBox = ((0,0,0), (0,0,0))

-- | Is a Box3 empty?
-- | Really, this checks if it is one dimensional, which is good enough.
isEmpty :: (Eq a2, Eq a1, Eq a) =>
           ((a, a1, a2), (a, a1, a2)) -> Bool
isEmpty ((a,b,c),(d,e,f)) = a==d || b==e || c==f

-- | Increase a boxes size by a rounding value.
outsetBox :: ℝ -> Box3 -> Box3
outsetBox r (a,b) =
    (a ^-^ (r,r,r), b ^+^ (r,r,r))

-- Get a Box3 around the given object.
getBox3 :: SymbolicObj3 -> Box3
-- Primitives
getBox3 (Rect3R _ a b) = (a,b)
getBox3 (Sphere r) = ((-r, -r, -r), (r,r,r))
getBox3 (Cylinder h r1 r2) = ( (-r,-r,0), (r,r,h) ) where r = max r1 r2
-- (Rounded) CSG
getBox3 (Complement3 _) =
    ((-infty, -infty, -infty), (infty, infty, infty))
        where
          infty :: (Fractional t) => t
          infty = 1/0
getBox3 (UnionR3 r symbObjs) = outsetBox r ((left,bot,inward), (right,top,out))
    where
        boxes = fmap getBox3 symbObjs
        (leftbot, topright) = unzip $ filter (not.isEmpty) boxes
        (lefts, bots, ins) = unzip3 leftbot
        (rights, tops, outs) = unzip3 topright
        left = minimum lefts
        bot = minimum bots
        inward = minimum ins
        right = maximum rights
        top = maximum tops
        out = maximum outs
getBox3 (DifferenceR3 _ symbObjs)  = getBox3 $ head symbObjs
getBox3 (IntersectR3 _ symbObjs) =
    let
        boxes = fmap getBox3 symbObjs
        (leftbot, topright) = unzip boxes
        (lefts, bots, ins) = unzip3 leftbot
        (rights, tops, outs) = unzip3 topright
        left = maximum lefts
        bot = maximum bots
        inward = maximum ins
        right = minimum rights
        top = minimum tops
        out = minimum outs
    in
        if   top   > bot
          && right > left
          && out   > inward
        then ((left,bot,inward),(right,top,out))
        else emptyBox
-- Simple transforms
getBox3 (Translate3 v symbObj) =
    let
        (a,b) = getBox3 symbObj
    in
        (a^+^v, b^+^v)
getBox3 (Scale3 s symbObj) =
    let
        (a,b) = getBox3 symbObj
        (sax,say,saz) = s ⋯* a
        (sbx,sby,sbz) = s ⋯* b
    in
        ((min sax sbx, min say sby, min saz sbz), (max sax sbx, max say sby, max saz sbz))
getBox3 (Rotate3 (a, b, c) symbObj) =
    let
        ((x1, y1, z1), (x2, y2, z2)) = getBox3 symbObj
        rotate v1 w1 v2 w2 angle = getBox2(Rotate2 angle $ RectR 0 (v1, w1) (v2, w2))
        ((y1', z1'), (y2', z2')) = rotate y1 z1 y2 z2 a
        ((z1'', x1'), (z2'', x2')) = rotate z1' x1 z2' x2 b
        ((x1'', y1''), (x2'', y2'')) = rotate x1' y1' x2' y2' c
        (xs, ys, zs) = ([x1'', x2''], [y1'', y2''], [z1'', z2''])
    in
        ((minimum xs, minimum ys, minimum zs), (maximum xs, maximum ys, maximum zs))

getBox3 (Rotate3V _ v symbObj) = getBox3 (Rotate3 v symbObj)
-- Boundary mods
getBox3 (Shell3 w symbObj) =
    outsetBox (w/2) $ getBox3 symbObj
getBox3 (Outset3 d symbObj) =
    outsetBox d $ getBox3 symbObj
-- Misc
getBox3 (EmbedBoxedObj3 (_,box)) = box
-- 2D Based
getBox3 (ExtrudeR _ symbObj h) = ((x1,y1,0),(x2,y2,h))
    where
        ((x1,y1),(x2,y2)) = getBox2 symbObj
getBox3 (ExtrudeOnEdgeOf symbObj1 symbObj2) =
    let
        ((ax1,ay1),(ax2,ay2)) = getBox2 symbObj1
        ((bx1,by1),(bx2,by2)) = getBox2 symbObj2
    in
        ((bx1+ax1, by1+ax1, ay1), (bx2+ax2, by2+ax2, ay2))
-- FIXME: magic numbers: 0.2 and 11.
-- FIXME: this may use an approximation, based on sampling functions. generate a warning if the approximation part of this function is used.
-- FIXME: re-implement the expression system, so this can recieve a function, and determine class (constant, linear)... and implement better forms of this function.
getBox3 (ExtrudeRM _ twist scale translate symbObj height) =
    let
        ((x1,y1),(x2,y2)) = getBox2 symbObj
        (dx,dy) = (x2 - x1, y2 - y1)

        samples :: Fastℕ
        samples = 11
        range :: [Fastℕ]
        range = [0, 1 .. (samples-1)]
        (xrange, yrange) = ( fmap ((\s -> x1+s*dx/fromFastℕtoℝ (samples-1)) . fromFastℕtoℝ) range, fmap ((\s -> y1+s*dy/fromFastℕtoℝ (samples-1)) . fromFastℕtoℝ) range)

        hfuzz :: ℝ
        hfuzz = 0.2
        h = case height of
              Left hval -> hval
              Right hfun -> hmax + hfuzz*(hmax-hmin)
                where
                    hs = [hfun (x,y) | x <- xrange, y <- yrange]
                    (hmin, hmax) = (minimum hs, maximum hs)
        hrange = fmap ((/ fromFastℕtoℝ (samples-1)) . (h*) . fromFastℕtoℝ) range

        (twistXmin, twistYmin, twistXmax, twistYmax) =
          let
            scale' = case scale of
                       Left  sval -> sval
                       Right sfun -> maximum $ fmap (abs . sfun) hrange
            smin v = min v (scale' * v)
            smax v = max v (scale' * v)
            -- FIXME: assumes minimums are negative, and maximums are positive.
            scaleVal d = scale' * d
            scaleEach ((d1, d2),(d3, d4)) = (scaleVal d1, scaleVal d2, scaleVal d3, scaleVal d4) 
          in case twist of
            Left twval -> if twval == 0
                          then (smin x1, smin y1, smax x2, smax y2)
                          else scaleEach $ getBox2R symbObj twval
            Right _  -> scaleEach $ getBox2R symbObj 360 -- we can't range functions yet, so assume a full circle.

        (tminx, tmaxx, tminy, tmaxy) =
          let
            tvalsx :: (ℝ -> (ℝ, ℝ)) -> [ℝ]
            tvalsx tfun = fmap (fst . tfun) hrange
            tvalsy :: (ℝ -> (ℝ, ℝ)) -> [ℝ]
            tvalsy tfun = fmap (snd . tfun) hrange
          in case translate of
            Left  (tvalx, tvaly) -> (tvalx, tvalx, tvaly, tvaly)
            Right tfun -> (minimum $ tvalsx tfun, maximum $ tvalsx tfun, minimum $ tvalsy tfun, maximum $ tvalsy tfun)
    in
        ((twistXmin + tminx, twistYmin + tminy, 0),(twistXmax + tmaxx, twistYmax + tmaxy, h))
-- Note: Assumes x2 is always greater than x1.
-- FIXME: Insert the above assumption as an assertion in the type system?
getBox3 (RotateExtrude _ _ (Left (xshift,yshift)) _ symbObj) =
    let
        ((_,y1),(x2,y2)) = getBox2 symbObj
        r = max x2 (x2 + xshift)
    in
        ((-r, -r, min y1 (y1 + yshift)),(r, r, max y2 (y2 + yshift)))
-- FIXME: magic numbers: 0.1, 1.1, and 11.
-- FIXME: this may use an approximation, based on sampling functions. generate a warning if the approximation part of this function is used.
-- FIXME: re-implement the expression system, so this can recieve a function, and determine class (constant, linear)... and implement better forms of this function.
getBox3 (RotateExtrude rot _ (Right f) rotate symbObj) =
    let
        samples :: Fastℕ
        samples = 11
        xfuzz :: ℝ
        xfuzz = 1.1
        yfuzz :: ℝ
        yfuzz=0.1
        range :: [Fastℕ]
        range = [0, 1 .. (samples-1)]
        step = rot/fromFastℕtoℝ (samples-1)
        ((x1,y1),(x2,y2)) = getBox2 symbObj
        (xrange, yrange) = unzip $ take (fromFastℕ samples) $ fmap (f . (step*) . fromFastℕtoℝ) range
        xmax = maximum xrange
        ymax = maximum yrange
        ymin = minimum yrange
        xmax' | xmax > 0 = xmax * xfuzz
              | xmax < - x1 = 0
              | otherwise = xmax
        ymax' = ymax + yfuzz * (ymax - ymin)
        ymin' = ymin - yfuzz * (ymax - ymin)
        (r, _, _) = if either (==0) (const False) rotate
            then let
                s = maximum $ fmap abs [x2, y1, y2]
            in (s + xmax', s + ymin', y2 + ymax')
            else (x2 + xmax', y1 + ymin', y2 + ymax')
    in
        ((-r, -r, y1 + ymin'),(r, r, y2 + ymax'))
-- FIXME: add case for ExtrudeRotateR!
getBox3 ExtrudeRotateR{} = error "ExtrudeRotateR implementation incomplete!"