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-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Released under the GNU GPL, see LICENSE
{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, FlexibleContexts, TypeSynonymInstances, UndecidableInstances #-}
module Graphics.Implicit.ObjectUtil.GetImplicit2 (getImplicit2) where
import Graphics.Implicit.Definitions
import qualified Graphics.Implicit.MathUtil as MathUtil
import Data.VectorSpace
import Data.List (nub)
getImplicit2 :: SymbolicObj2 -> Obj2
-- Primitives
getImplicit2 (RectR r (x1,y1) (x2,y2)) = \(x,y) -> MathUtil.rmaximum r
[abs (x-dx/2-x1) - dx/2, abs (y-dy/2-y1) - dy/2]
where (dx, dy) = (x2-x1, y2-y1)
getImplicit2 (Circle r ) =
\(x,y) -> sqrt (x**2 + y**2) - r
getImplicit2 (PolygonR r points) =
\p -> let
pair :: Int -> (ℝ2,ℝ2)
pair n = (points !! n, points !! (mod (n + 1) (length points) ) )
pairs = [ pair n | n <- [0 .. (length points) - 1] ]
relativePairs = map (\(a,b) -> (a ^-^ p, b ^-^ p) ) pairs
crossing_points =
[x2 ^-^ y2*(x2-x1)/(y2-y1) | ((x1,y1), (x2,y2)) <-relativePairs,
( (y2 <= 0) && (y1 >= 0) ) || ( (y2 >= 0) && (y1 <= 0) ) ]
seemsInRight = odd $ length $ filter (>0) $ nub crossing_points
seemsInLeft = odd $ length $ filter (<0) $ nub crossing_points
isIn = seemsInRight && seemsInLeft
dists = map (MathUtil.distFromLineSeg p) pairs :: [ℝ]
in
minimum dists * if isIn then -1 else 1
-- (Rounded) CSG
getImplicit2 (Complement2 symbObj) =
let
obj = getImplicit2 symbObj
in
\p -> - obj p
getImplicit2 (UnionR2 r symbObjs) =
let
objs = map getImplicit2 symbObjs
in
if r == 0
then \p -> minimum $ map ($p) objs
else \p -> MathUtil.rminimum r $ map ($p) objs
getImplicit2 (DifferenceR2 r symbObjs) =
let
obj:objs = map getImplicit2 symbObjs
complement obj = \p -> - obj p
in
if r == 0
then \p -> maximum $ map ($p) $ obj:(map complement objs)
else \p -> MathUtil.rmaximum r $ map ($p) $ obj:(map complement objs)
getImplicit2 (IntersectR2 r symbObjs) =
let
objs = map getImplicit2 symbObjs
in
if r == 0
then \p -> maximum $ map ($p) objs
else \p -> MathUtil.rmaximum r $ map ($p) objs
-- Simple transforms
getImplicit2 (Translate2 v symbObj) =
let
obj = getImplicit2 symbObj
in
\p -> obj (p ^-^ v)
getImplicit2 (Mirror2 a symbObj) =
let
obj = getImplicit2 symbObj
in
\p ->
let
c = 2 * (p a) / (a a)
in obj $ c *^ a ^-^ p
getImplicit2 (Scale2 s@(sx,sy) symbObj) =
let
obj = getImplicit2 symbObj
in
\p -> (max sx sy) * obj (p ⋯/ s)
getImplicit2 (Rotate2 θ symbObj) =
let
obj = getImplicit2 symbObj
in
\(x,y) -> obj ( cos(θ)*x + sin(θ)*y, cos(θ)*y - sin(θ)*x)
-- Boundary mods
getImplicit2 (Shell2 w symbObj) =
let
obj = getImplicit2 symbObj
in
\p -> abs (obj p) - w/2
getImplicit2 (Outset2 d symbObj) =
let
obj = getImplicit2 symbObj
in
\p -> obj p - d
-- Misc
getImplicit2 (EmbedBoxedObj2 (obj,box)) = obj
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