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 ((^-^), (^+^))
emptyBox :: Box3
emptyBox = ((0,0,0), (0,0,0))
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))
getBox3 :: SymbolicObj3 -> Box3
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
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
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)
getBox3 (Shell3 w symbObj) =
outsetBox (w/2) $ getBox3 symbObj
getBox3 (Outset3 d symbObj) =
outsetBox d $ getBox3 symbObj
getBox3 (EmbedBoxedObj3 (_,box)) = box
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))
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)
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
(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))
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)))
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'))
getBox3 ExtrudeRotateR{} = error "ExtrudeRotateR implementation incomplete!"