-- 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

-- FIXME: required. why?
{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts, TypeSynonymInstances, UndecidableInstances #-}

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

import Prelude(Eq, Bool(False), Fractional, Either (Left, Right), Maybe(Nothing, Just), (==), (||), max, (/), (-), (+), map, unzip, ($), filter, not, (.), unzip3, minimum, maximum, min, sqrt, (>), (&&), head, (*), (<), abs, either, error, const, otherwise)

import Graphics.Implicit.Definitions (ℝ, Box3, SymbolicObj3 (Rect3R, Sphere, Cylinder, Complement3, UnionR3, IntersectR3, DifferenceR3, Translate3, Scale3, Rotate3, Rotate3V, Shell3, Outset3, EmbedBoxedObj3, ExtrudeR, ExtrudeOnEdgeOf, ExtrudeRM, RotateExtrude, ExtrudeRotateR), (⋯*))
import Graphics.Implicit.ObjectUtil.GetBox2 (getBox2, getDist2)

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

-- test to see whether a Box3 has area.
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

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) = ((left-r,bot-r,inward-r), (right+r,top+r,out+r))
    where
        boxes = map 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 (IntersectR3 _ symbObjs) =
    let
        boxes = map 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 ((0,0,0),(0,0,0))
getBox3 (DifferenceR3 _ symbObjs)  = getBox3 $ head symbObjs
-- 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 _ symbObj) = ( (-d, -d, -d), (d, d, d) )
    where
        ((x1,y1, z1), (x2,y2, z2)) = getBox3 symbObj
        d = (sqrt 3 *) . maximum $ map abs [x1, x2, y1, y2, z1, z2]
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 in range.
getBox3 (ExtrudeRM _ twist scale translate symbObj eitherh) =
    let
        range :: [ℝ]
        range = [0, 0.1 .. 1.0]
        ((x1,y1),(x2,y2)) = getBox2 symbObj
        (dx,dy) = (x2 - x1, y2 - y1)
        (xrange, yrange) = (map (\s -> x1+s*dx) range, map (\s -> y1+s*dy) range )

        h = case eitherh of
              Left h' -> h'
              Right hf -> hmax + 0.2*(hmax-hmin)
                where
                    hs = [hf (x,y) | x <- xrange, y <- yrange]
                    (hmin, hmax) = (minimum hs, maximum hs)
        hrange = map (h*) range
        sval = case scale of
            Nothing -> 1
            Just scale' -> maximum $ map (abs . scale') hrange
        (twistXmin, twistYmin, twistXmax, twistYmax) = case twist of
            Nothing -> (smin x1, smin y1, smax x2, smax y2)
                where
                    smin y = min y (sval * y)
                    smax y = max y (sval * y)
            Just _  -> (-d, -d, d, d)
                where d = sval * getDist2 (0,0) symbObj
        translate' = fromMaybe (const (0,0)) translate
        (tvalsx, tvalsy) = unzip . map (translate' . (h*)) $ hrange
        (tminx, tminy) = (minimum tvalsx, minimum tvalsy)
        (tmaxx, tmaxy) = (maximum tvalsx, maximum tvalsy)
    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 language structure?
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
getBox3 (RotateExtrude rot _ (Right f) rotate symbObj) =
    let
        ((x1,y1),(x2,y2)) = getBox2 symbObj
        (xshifts, yshifts) = unzip [f θ | θ <- [0 , rot / 10 .. rot] ]
        xmax = maximum xshifts
        ymax = maximum yshifts
        ymin = minimum yshifts
        xmax' | xmax > 0 = xmax * 1.1
              | xmax < - x1 = 0
              | otherwise = xmax
        ymax' = ymax + 0.1 * (ymax - ymin)
        ymin' = ymin - 0.1 * (ymax - ymin)
        (r, _, _) = if either (==0) (const False) rotate
            then let
                s = maximum $ map 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!"