-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A math-inspired programmatic 2D & 3D CAD system.
--   
--   An OpenSCAD execution engine for generating models in STL and many
--   other formats.
@package implicit
@version 0.4.1.0

module Graphics.Implicit.Export.OutputFormat

-- | A type serving to enumerate our output formats.
data OutputFormat
SVG :: OutputFormat
SCAD :: OutputFormat
PNG :: OutputFormat
GCode :: OutputFormat
ASCIISTL :: OutputFormat
STL :: OutputFormat
THREEJS :: OutputFormat
OBJ :: OutputFormat
DXF :: OutputFormat

-- | Lookup an output format for a given output file. Throw an error if one
--   cannot be found.
guessOutputFormat :: FilePath -> OutputFormat

-- | A list mapping file extensions to output formats.
formatExtensions :: [(String, OutputFormat)]

-- | Get filename extension for <a>OutputFormat</a>
formatExtension :: OutputFormat -> String

-- | All supported 2D formats
formats2D :: [OutputFormat]

-- | True for 2D capable <a>OutputFormat</a>s
formatIs2D :: OutputFormat -> Bool

-- | Default 2D output format
def2D :: OutputFormat

-- | All supported 3D formats
formats3D :: [OutputFormat]

-- | True for 3D capable <a>OutputFormat</a>s
formatIs3D :: OutputFormat -> Bool

-- | Default 3D output format
def3D :: OutputFormat
instance GHC.Classes.Eq Graphics.Implicit.Export.OutputFormat.OutputFormat
instance GHC.Show.Show Graphics.Implicit.Export.OutputFormat.OutputFormat
instance Data.Default.Class.Default Graphics.Implicit.Export.OutputFormat.OutputFormat
instance GHC.Read.Read Graphics.Implicit.Export.OutputFormat.OutputFormat

module Graphics.Implicit.Export.Render.GetLoops

-- | The goal of getLoops is to extract loops from a list of segments. The
--   input is a list of segments. The output a list of loops, where each
--   loop is a list of segments, which each piece representing a "side".
--   
--   For example: Given points [[1,2],[5,1],[2,3,4,5], ... ] notice that
--   there is a loop 1,2,3,4,5... <a>repeat</a> But we give the output [ [
--   [1,2], [2,3,4,5], [5,1] ], ... ] so that we have the loop, and also
--   knowledge of how the list is built (the "sides" of it).
getLoops :: Eq a => [[a]] -> Maybe [[[a]]]

module Graphics.Implicit.Definitions
newtype Fastℕ
Fastℕ :: Int -> Fastℕ
fromFastℕ :: FastN n => Fastℕ -> n
toFastℕ :: FastN n => n -> Fastℕ
data ℕ
fromℕ :: N n => ℕ -> n
toℕ :: N n => n -> ℕ

-- | A type synonym for <a>Double</a>. When used in the context of
--   positions or sizes, measured in units of millimeters. When used as in
--   the context of a rotation, measured in radians.
type ℝ = Double

-- | A pair of two <a>Double</a>s. When used as an area or position vector,
--   measured in millimeters squared.
type ℝ2 = V2 ℝ

-- | A triple of <a>Double</a>s. When used as a volume or position vector,
--   measured in millimeters cubed. When used as a rotation, interpreted as
--   Euler angles measured in radians.
type ℝ3 = V3 ℝ
newtype ℝ3'
ℝ3' :: V3 ℝ -> ℝ3'

-- | A give up point for dividing ℝs, and for the maximum difference
--   between abs(n) and abs(-n).
minℝ :: ℝ

-- | Add multiply and divide operators for two ℝ2s or ℝ3s.
class ComponentWiseMultable a
(⋯*) :: ComponentWiseMultable a => a -> a -> a
(⋯/) :: ComponentWiseMultable a => a -> a -> a

-- | A chain of line segments, as in SVG or DXF. eg. [(0,0), (0.5,1),
--   (1,0)] ---&gt; / FIXME: May not be empty. expose to type system.
newtype Polyline
Polyline :: [ℝ2] -> Polyline
[getSegments] :: Polyline -> [ℝ2]

-- | A triangle in 2D space (a,b,c).
newtype Polytri
Polytri :: (ℝ2, ℝ2, ℝ2) -> Polytri

-- | A triangle in 3D space (a,b,c) = a triangle with vertices a, b and c
newtype Triangle
Triangle :: (ℝ3, ℝ3, ℝ3) -> Triangle

-- | A triangle ((v1,n1),(v2,n2),(v3,n3)) has vertices v1, v2, v3 with
--   corresponding normals n1, n2, and n3
newtype NormedTriangle
NormedTriangle :: ((ℝ3, ℝ3), (ℝ3, ℝ3), (ℝ3, ℝ3)) -> NormedTriangle

-- | A triangle mesh is a bunch of triangles, attempting to be a surface.
newtype TriangleMesh
TriangleMesh :: [Triangle] -> TriangleMesh
[getTriangles] :: TriangleMesh -> [Triangle]

-- | A normed triangle mesh is a mesh of normed triangles.
newtype NormedTriangleMesh
NormedTriangleMesh :: [NormedTriangle] -> NormedTriangleMesh
[getNormedTriangles] :: NormedTriangleMesh -> [NormedTriangle]

-- | A 2D object.
type Obj2 = (ℝ2 -> ℝ)

-- | A 3D object.
type Obj3 = (ℝ3 -> ℝ)

-- | A 2D box.
type Box2 = (ℝ2, ℝ2)

-- | A 3D box.
type Box3 = (ℝ3, ℝ3)

-- | A Box containing a 2D object.
type Boxed2 a = (a, Box2)

-- | A Box containing a 3D object.
type Boxed3 a = (a, Box3)

-- | A Boxed 2D object
type BoxedObj2 = Boxed2 Obj2

-- | A Boxed 3D object
type BoxedObj3 = Boxed3 Obj3

-- | Means of constructing symbolic objects that are common between the 2D
--   and 3D case. This type is parameterized on <tt>obj</tt> and
--   <tt>vec</tt> so that <a>SymbolicObj2</a> and <a>SymbolicObj3</a> can
--   instantiate it for their own purposes.
data SharedObj obj f a

-- | The empty object
Empty :: SharedObj obj f a

-- | The entirely full object
Full :: SharedObj obj f a
Complement :: obj -> SharedObj obj f a
UnionR :: ℝ -> [obj] -> SharedObj obj f a
DifferenceR :: ℝ -> obj -> [obj] -> SharedObj obj f a
IntersectR :: ℝ -> [obj] -> SharedObj obj f a
Translate :: f a -> obj -> SharedObj obj f a
Scale :: f a -> obj -> SharedObj obj f a

-- | Mirror across the line whose normal is defined by the vector
Mirror :: f a -> obj -> SharedObj obj f a
Outset :: ℝ -> obj -> SharedObj obj f a
Shell :: ℝ -> obj -> SharedObj obj f a
EmbedBoxedObj :: (f a -> a, (f a, f a)) -> SharedObj obj f a
WithRounding :: ℝ -> obj -> SharedObj obj f a

-- | A 2-dimensional vector
--   
--   <pre>
--   &gt;&gt;&gt; pure 1 :: V2 Int
--   V2 1 1
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; V2 1 2 + V2 3 4
--   V2 4 6
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; V2 1 2 * V2 3 4
--   V2 3 8
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum (V2 1 2)
--   3
--   </pre>
data V2 a
V2 :: !a -> !a -> V2 a

-- | A 3-dimensional vector
data V3 a
V3 :: !a -> !a -> !a -> V3 a

-- | A symbolic 2D object format. We want to have symbolic objects so that
--   we can accelerate rendering &amp; give ideal meshes for simple cases.
data SymbolicObj2
Square :: ℝ2 -> SymbolicObj2
Circle :: ℝ -> SymbolicObj2
Polygon :: [ℝ2] -> SymbolicObj2
Rotate2 :: ℝ -> SymbolicObj2 -> SymbolicObj2
Transform2 :: M33 ℝ -> SymbolicObj2 -> SymbolicObj2
Shared2 :: SharedObj SymbolicObj2 V2 ℝ -> SymbolicObj2

-- | A symbolic 3D format!
data SymbolicObj3
Cube :: ℝ3 -> SymbolicObj3
Sphere :: ℝ -> SymbolicObj3
Cylinder :: ℝ -> ℝ -> ℝ -> SymbolicObj3
Rotate3 :: Quaternion ℝ -> SymbolicObj3 -> SymbolicObj3
Transform3 :: M44 ℝ -> SymbolicObj3 -> SymbolicObj3
Extrude :: SymbolicObj2 -> ℝ -> SymbolicObj3
ExtrudeM :: Either ℝ (ℝ -> ℝ) -> ExtrudeMScale -> Either ℝ2 (ℝ -> ℝ2) -> SymbolicObj2 -> Either ℝ (ℝ2 -> ℝ) -> SymbolicObj3
RotateExtrude :: ℝ -> Either ℝ2 (ℝ -> ℝ2) -> Either ℝ (ℝ -> ℝ) -> SymbolicObj2 -> SymbolicObj3
ExtrudeOnEdgeOf :: SymbolicObj2 -> SymbolicObj2 -> SymbolicObj3
Shared3 :: SharedObj SymbolicObj3 V3 ℝ -> SymbolicObj3
data ExtrudeMScale
C1 :: ℝ -> ExtrudeMScale
C2 :: ℝ2 -> ExtrudeMScale
Fn :: (ℝ -> Either ℝ ℝ2) -> ExtrudeMScale
newtype ObjectContext
ObjectContext :: ℝ -> ObjectContext
[objectRounding] :: ObjectContext -> ℝ
defaultObjectContext :: ObjectContext

-- | Convert from our Integral to our Rational.
fromℕtoℝ :: ℕ -> ℝ

-- | Convert from our Fast Integer (int32) to ℝ.
fromFastℕtoℝ :: Fastℕ -> ℝ

-- | Convert from our rational to a float, for output to a file.
fromℝtoFloat :: ℝ -> Float
toScaleFn :: ExtrudeMScale -> ℝ -> ℝ2
isScaleID :: ExtrudeMScale -> Bool

-- | Convert a <a>Quaternion</a> to its constituent euler angles.
--   
--   From
--   <a>https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles#Source_code_2</a>
quaternionToEuler :: RealFloat a => Quaternion a -> V3 a

-- | Returns True if any component of a foldable functor is zero
hasZeroComponent :: (Foldable f, Num a, Eq a) => f a -> Bool
instance GHC.Generics.Generic (Graphics.Implicit.Definitions.SharedObj obj f a)
instance GHC.Show.Show Graphics.Implicit.Definitions.ObjectContext
instance GHC.Classes.Ord Graphics.Implicit.Definitions.ObjectContext
instance GHC.Classes.Eq Graphics.Implicit.Definitions.ObjectContext
instance GHC.Generics.Generic Graphics.Implicit.Definitions.SymbolicObj2
instance GHC.Generics.Generic Graphics.Implicit.Definitions.ExtrudeMScale
instance GHC.Generics.Generic Graphics.Implicit.Definitions.SymbolicObj3
instance GHC.Show.Show Graphics.Implicit.Definitions.SymbolicObj3
instance GHC.Base.Semigroup Graphics.Implicit.Definitions.SymbolicObj3
instance GHC.Base.Monoid Graphics.Implicit.Definitions.SymbolicObj3
instance GHC.Show.Show Graphics.Implicit.Definitions.ExtrudeMScale
instance GHC.Show.Show Graphics.Implicit.Definitions.SymbolicObj2
instance GHC.Base.Semigroup Graphics.Implicit.Definitions.SymbolicObj2
instance GHC.Base.Monoid Graphics.Implicit.Definitions.SymbolicObj2
instance (GHC.Show.Show obj, GHC.Show.Show (f a)) => GHC.Show.Show (Graphics.Implicit.Definitions.SharedObj obj f a)
instance GHC.Show.Show Graphics.Implicit.Definitions.Blackhole
instance Control.DeepSeq.NFData Graphics.Implicit.Definitions.TriangleMesh
instance Control.DeepSeq.NFData Graphics.Implicit.Definitions.NormedTriangle
instance Control.DeepSeq.NFData Graphics.Implicit.Definitions.Triangle
instance Control.DeepSeq.NFData Graphics.Implicit.Definitions.Polytri
instance Control.DeepSeq.NFData Graphics.Implicit.Definitions.Polyline
instance Graphics.Implicit.Definitions.ComponentWiseMultable Graphics.Implicit.Definitions.ℝ2
instance Graphics.Implicit.Definitions.ComponentWiseMultable Graphics.Implicit.Definitions.ℝ3
instance (Graphics.Implicit.Definitions.ℝ3' GHC.Types.~ t) => Control.Lens.Wrapped.Rewrapped Graphics.Implicit.Definitions.ℝ3' t
instance Control.Lens.Wrapped.Wrapped Graphics.Implicit.Definitions.ℝ3'
instance GHC.Classes.Eq Graphics.Implicit.Definitions.ℝ3'

module Graphics.Implicit.ExtOpenScad.Definitions

-- | Handles parsing arguments to built-in modules
data ArgParser a

-- | For actual argument entries: <tt>AP (argument name) (default) (doc)
--   (next Argparser...)</tt>
AP :: Symbol -> Maybe OVal -> Text -> (OVal -> ArgParser a) -> ArgParser a

-- | For returns: <tt>APTerminator (return value)</tt>
APTerminator :: a -> ArgParser a

-- | For failure: <tt>APFail (error message)</tt>
APFail :: Text -> ArgParser a

-- | An example, then next
APExample :: Text -> ArgParser a -> ArgParser a

-- | A string to run as a test, then invariants for the results, then next
APTest :: Text -> [TestInvariant] -> ArgParser a -> ArgParser a

-- | A branch where there are a number of possibilities for the parser
--   underneath
APBranch :: [ArgParser a] -> ArgParser a
newtype Symbol
Symbol :: Text -> Symbol
data Pattern
Name :: Symbol -> Pattern
ListP :: [Pattern] -> Pattern
Wild :: Pattern

-- | An expression.
data Expr
Var :: Symbol -> Expr
LitE :: OVal -> Expr
ListE :: [Expr] -> Expr
LamE :: [Pattern] -> Expr -> Expr
(:$) :: Expr -> [Expr] -> Expr

-- | A statement, along with the line, column number, and file it is found
--   at.
data StatementI
StatementI :: SourcePosition -> Statement StatementI -> StatementI
data Statement st
Include :: Text -> Bool -> Statement st
(:=) :: Pattern -> Expr -> Statement st
If :: Expr -> [st] -> [st] -> Statement st
NewModule :: Symbol -> [(Symbol, Maybe Expr)] -> [st] -> Statement st
ModuleCall :: Symbol -> [(Maybe Symbol, Expr)] -> [st] -> Statement st
DoNothing :: Statement st

-- | Objects for our OpenSCAD-like language
data OVal
OUndefined :: OVal
OError :: Text -> OVal
OBool :: Bool -> OVal
ONum :: ℝ -> OVal
OList :: [OVal] -> OVal
OString :: Text -> OVal
OFunc :: (OVal -> OVal) -> OVal
OIO :: IO OVal -> OVal
OUModule :: Symbol -> Maybe [(Symbol, Bool)] -> (VarLookup -> ArgParser (StateC [OVal])) -> OVal
ONModule :: Symbol -> (SourcePosition -> [OVal] -> ArgParser (StateC [OVal])) -> [([(Symbol, Bool)], Maybe Bool)] -> OVal
OVargsModule :: Symbol -> (Symbol -> SourcePosition -> [(Maybe Symbol, OVal)] -> [StatementI] -> ([StatementI] -> StateC ()) -> StateC ()) -> OVal
OObj3 :: SymbolicObj3 -> OVal
OObj2 :: SymbolicObj2 -> OVal
newtype TestInvariant
EulerCharacteristic :: ℕ -> TestInvariant

-- | In order to not propagate Parsec or other modules around, create our
--   own source position type for the AST.
data SourcePosition
SourcePosition :: Fastℕ -> Fastℕ -> FilePath -> SourcePosition
type StateC a = ImplicitCadM ScadOpts [Message] CompState IO a

-- | The state of computation.
data CompState
CompState :: VarLookup -> [OVal] -> FilePath -> CompState

-- | A hash of variables and functions.
[scadVars] :: CompState -> VarLookup

-- | The result of geometry generating functions.
[oVals] :: CompState -> [OVal]

-- | The path we are looking for includes in.
[sourceDir] :: CompState -> FilePath
newtype ImplicitCadM r w s m a
ImplicitCadM :: ReaderT r (WriterT w (StateT s m)) a -> ImplicitCadM r w s m a
[unImplicitCadM] :: ImplicitCadM r w s m a -> ReaderT r (WriterT w (StateT s m)) a
newtype VarLookup
VarLookup :: Map Symbol OVal -> VarLookup

-- | An individual message.
data Message
Message :: MessageType -> SourcePosition -> Text -> Message

-- | The types of messages the execution engine can send back to the
--   application.
data MessageType
TextOut :: MessageType
Warning :: MessageType
Error :: MessageType
SyntaxError :: MessageType
Compatibility :: MessageType
Unimplemented :: MessageType

-- | Options changing the behavior of the extended OpenScad engine.
data ScadOpts
ScadOpts :: Bool -> Bool -> ScadOpts
[openScadCompatibility] :: ScadOpts -> Bool
[importsAllowed] :: ScadOpts -> Bool

-- | For programs using this API to perform variable lookups, after
--   execution of an escad has completed.
lookupVarIn :: Text -> VarLookup -> Maybe OVal
varUnion :: VarLookup -> VarLookup -> VarLookup
runImplicitCadM :: Monad m => r -> s -> ImplicitCadM r w s m a -> m (a, w, s)
type CanCompState m = CanCompState' ScadOpts [Message] CompState m
type CanCompState' r w s m = (MonadReader r m, MonadWriter w m, MonadState s m, MonadIO m)
instance GHC.Base.Functor m => GHC.Base.Functor (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, GHC.Base.Monad m) => GHC.Base.Applicative (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, GHC.Base.Monad m) => GHC.Base.Monad (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, Control.Monad.IO.Class.MonadIO m) => Control.Monad.IO.Class.MonadIO (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, GHC.Base.Monad m) => Control.Monad.State.Class.MonadState s (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, GHC.Base.Monad m) => Control.Monad.Writer.Class.MonadWriter w (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance (GHC.Base.Monoid w, GHC.Base.Monad m) => Control.Monad.Reader.Class.MonadReader r (Graphics.Implicit.ExtOpenScad.Definitions.ImplicitCadM r w s m)
instance GHC.Classes.Ord Graphics.Implicit.ExtOpenScad.Definitions.Symbol
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.Symbol
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.Symbol
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.Pattern
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.Pattern
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.SourcePosition
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.MessageType
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.MessageType
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.Message
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.ScadOpts
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.ScadOpts
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.TestInvariant
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.CompState
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.VarLookup
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.VarLookup
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.Expr
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.Expr
instance GHC.Classes.Eq st => GHC.Classes.Eq (Graphics.Implicit.ExtOpenScad.Definitions.Statement st)
instance GHC.Show.Show st => GHC.Show.Show (Graphics.Implicit.ExtOpenScad.Definitions.Statement st)
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.StatementI
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.StatementI
instance GHC.Base.Functor Graphics.Implicit.ExtOpenScad.Definitions.ArgParser
instance GHC.Base.Applicative Graphics.Implicit.ExtOpenScad.Definitions.ArgParser
instance GHC.Base.Monad Graphics.Implicit.ExtOpenScad.Definitions.ArgParser
instance GHC.Base.MonadPlus Graphics.Implicit.ExtOpenScad.Definitions.ArgParser
instance GHC.Base.Alternative Graphics.Implicit.ExtOpenScad.Definitions.ArgParser
instance GHC.Classes.Eq Graphics.Implicit.ExtOpenScad.Definitions.OVal
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.OVal
instance Data.Default.Class.Default Graphics.Implicit.ExtOpenScad.Definitions.ScadOpts
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.Message
instance GHC.Show.Show Graphics.Implicit.ExtOpenScad.Definitions.SourcePosition

module Graphics.Implicit.ExtOpenScad.Parser.Expr
expr0 :: GenParser Char st Expr

module Graphics.Implicit.ExtOpenScad.Parser.Statement

-- | all of the token parsers are lexemes which consume all trailing spaces
--   nicely. | This leaves us to deal only with the first spaces in the
--   file.
parseProgram :: SourceName -> String -> Either ParseError [StatementI]

module Graphics.Implicit.Export.TriangleMeshFormats

-- | Generate an STL file is ASCII format.
stl :: TriangleMesh -> Text

-- | Generate an STL file in it's binary format.
binaryStl :: TriangleMesh -> ByteString
jsTHREE :: TriangleMesh -> Text

module Graphics.Implicit.Export.PolylineFormats
svg :: [Polyline] -> Text

-- | Gcode generation for the laser cutter in HackLab. Complies with
--   <a>https://ws680.nist.gov/publication/get_pdf.cfm?pub_id=823374</a>
--   FIXME: parameters would be nice.
hacklabLaserGCode :: [Polyline] -> Text

-- | DXF2 export in 2D. conforming to AutoCAD R12/13.
dxf2 :: [Polyline] -> Text

module Graphics.Implicit.Export.NormedTriangleMeshFormats

-- | Generate a .obj format file from a NormedTriangleMesh see:
--   <a>https://en.wikipedia.org/wiki/Wavefront_.obj_file</a>
obj :: NormedTriangleMesh -> Text

module Graphics.Implicit.MathUtil

-- | Rounded Maximum Consider max(x,y) = 0, the generated curve has a
--   square-like corner. We replace it with a quarter of a circle
--   
--   NOTE: rmax is not associative!
rmax :: ℝ -> ℝ -> ℝ -> ℝ

-- | Like rmax, but on a list instead of two. Just as maximum is. The
--   implementation is to take the maximum two and rmax those.
rmaximum :: ℝ -> [ℝ] -> ℝ

-- | Like rmin but on a list.
rminimum :: ℝ -> [ℝ] -> ℝ

-- | The distance a point p is from a line segment (a,b)
distFromLineSeg :: ℝ2 -> (ℝ2, ℝ2) -> ℝ

-- | Pack the given objects in a box the given size.
pack :: Box2 -> ℝ -> [(Box2, a)] -> ([(ℝ2, a)], [(Box2, a)])
box3sWithin :: ℝ -> (ℝ3, ℝ3) -> (ℝ3, ℝ3) -> Bool

-- | Reflect a vector across a hyperplane defined by its normal vector.
--   
--   From
--   <a>https://en.wikipedia.org/wiki/Reflection_(mathematics)#Reflection_through_a_hyperplane_in_n_dimensions</a>
reflect :: (Num (f a), Fractional a, Metric f) => f a -> f a -> f a

-- | Lift a function over <a>V3</a> into a function over <a>ℝ3</a>.
alaV3 :: (V3 a -> V3 a) -> (a, a, a) -> (a, a, a)
packV3 :: (a, a, a) -> V3 a
unpackV3 :: V3 a -> (a, a, a)

-- | Haskell's standard library doesn't make floating-point infinity
--   available in any convenient way, so we define it here.
infty :: Fractional t => t

module Graphics.Implicit.Primitives

-- | Translate an object by a vector of appropriate dimension.
translate :: Object obj f a => f a -> obj -> obj

-- | Mirror an object across the hyperplane whose normal is a given vector.
mirror :: Object obj f a => f a -> obj -> obj

-- | Scale an object
scale :: Object obj f a => f a -> obj -> obj

-- | Outset of an object.
outset :: Object obj f a => ℝ -> obj -> obj

-- | Complement an Object
complement :: Object obj f a => obj -> obj
union :: Object obj f a => [obj] -> obj
intersect :: Object obj f a => [obj] -> obj
difference :: Object obj f a => obj -> [obj] -> obj

-- | Rounded union
unionR :: Object obj f a => ℝ -> [obj] -> obj

-- | Rounded minimum
intersectR :: Object obj f a => ℝ -> [obj] -> obj

-- | Rounded difference
differenceR :: Object obj f a => ℝ -> obj -> [obj] -> obj

-- | Make a shell of an object.
shell :: Object obj f a => ℝ -> obj -> obj

-- | Get the bounding box an object
getBox :: Object obj f a => obj -> (f a, f a)

-- | Get the implicit function for an object
getImplicit :: Object obj f a => obj -> f a -> a

-- | Get the implicit function for an object
getImplicit' :: Object obj f a => ObjectContext -> obj -> f a -> a

-- | Extrude a 2d object upwards. The current object-rounding value set by
--   <a>withRounding</a> is used to round the caps, but is not used by the
--   2D object.
extrude :: SymbolicObj2 -> ℝ -> SymbolicObj3

-- | The current object-rounding value set by <a>withRounding</a> is used
--   to round the caps, but is not used by the 2D object.
extrudeM :: Either ℝ (ℝ -> ℝ) -> ExtrudeMScale -> Either ℝ2 (ℝ -> ℝ2) -> SymbolicObj2 -> Either ℝ (ℝ2 -> ℝ) -> SymbolicObj3
extrudeOnEdgeOf :: SymbolicObj2 -> SymbolicObj2 -> SymbolicObj3
sphere :: ℝ -> SymbolicObj3

-- | A cube
cube :: Bool -> ℝ3 -> SymbolicObj3

-- | A rectangular prism
rect3 :: ℝ3 -> ℝ3 -> SymbolicObj3
circle :: ℝ -> SymbolicObj2
cylinder :: ℝ -> ℝ -> SymbolicObj3

-- | A conical frustum --- ie. a cylinder with different radii at either
--   end.
cylinder2 :: ℝ -> ℝ -> ℝ -> SymbolicObj3
cone :: ℝ -> ℝ -> SymbolicObj3
torus :: ℝ -> ℝ -> SymbolicObj3
ellipsoid :: ℝ -> ℝ -> ℝ -> SymbolicObj3

-- | A square
square :: Bool -> ℝ2 -> SymbolicObj2

-- | A rectangle
rect :: ℝ2 -> ℝ2 -> SymbolicObj2

-- | A 2D polygon
polygon :: [ℝ2] -> SymbolicObj2
rotateExtrude :: ℝ -> Either ℝ2 (ℝ -> ℝ2) -> Either ℝ (ℝ -> ℝ) -> SymbolicObj2 -> SymbolicObj3

-- | Rotate a 3D object via an Euler angle, measured in radians, along the
--   world axis.
rotate3 :: ℝ3 -> SymbolicObj3 -> SymbolicObj3
rotateQ :: Quaternion ℝ -> SymbolicObj3 -> SymbolicObj3

-- | Rotate a 3D object along an arbitrary axis.
rotate3V :: ℝ -> ℝ3 -> SymbolicObj3 -> SymbolicObj3

-- | Transform a 3D object using a 4x4 matrix representing affine
--   transformation (OpenSCAD multmatrix)
transform3 :: M44 ℝ -> SymbolicObj3 -> SymbolicObj3

-- | Attempt to pack multiple 3D objects into a fixed area. The <tt>z</tt>
--   coordinate of each object is dropped, and the resulting packed objects
--   will all be on the same plane.
--   
--   FIXME: shouldn't this pack into a 3d area, or have a 3d equivalent?
pack3 :: ℝ2 -> ℝ -> [SymbolicObj3] -> Maybe SymbolicObj3
rotate :: ℝ -> SymbolicObj2 -> SymbolicObj2

-- | Transform a 2D object using a 3x3 matrix representing affine
--   transformation (OpenSCAD multmatrix)
transform :: M33 ℝ -> SymbolicObj2 -> SymbolicObj2

-- | Attempt to pack multiple 2D objects into a fixed area.
pack2 :: ℝ2 -> ℝ -> [SymbolicObj2] -> Maybe SymbolicObj2
implicit :: Object obj f a => (f a -> a) -> (f a, f a) -> obj

-- | The object that fills no space
emptySpace :: Object obj f a => obj

-- | The object that fills the entire space
fullSpace :: Object obj f a => obj

-- | Set the current object-rounding value for the given object. The
--   rounding value is measured in units of distance, and describes the
--   radius of rounded corners.
--   
--   This can be used to change the shape of more primitive forms, for
--   example, we can make a cube with rounded corners via <tt>withRounding
--   5 (<a>cube</a> True 20)</tt>.
--   
--   <tt><a>withRounding</a> r obj</tt> applies the rounding <tt>r</tt>
--   <i>all</i> primitives objects in <tt>obj</tt>, so long as they have
--   the same dimensionality. That is to say, the current object-rounding
--   value set in 3D will not apply to extruded 2D shapes.
withRounding :: Object obj f a => ℝ -> obj -> obj

-- | A <a>Prism'</a> for including <a>SharedObj</a>s in <tt>obj</tt>.
--   Prefer using <a>Shared</a> instead of this.
_Shared :: Object obj f a => Prism' obj (SharedObj obj f a)

-- | A pattern that abstracts over <a>Shared2</a> and <a>Shared3</a>.
pattern Shared :: Object obj f a => SharedObj obj f a -> obj

-- | Operations available on both 2D and 3D objects. The obvious omission
--   of rotation operations from this class are a technical limitation, and
--   are instead provided by <a>rotate</a> and <a>rotate3</a>.
--   
--   Library users shouldn't need to provide new instances of this class.
class (Applicative f, Eq a, Eq (f a), Foldable f, Num a, Num (f a)) => Object obj f a | obj -> f a where {
    
    -- | Type representing a space this object belongs to. V3 for 3D objects,
    --   V2 for 2D
    type Space obj :: Type -> Type;
}

-- | Canonicalization function used to rewrite / normalize abstract syntax
--   tree representing an object
canonicalize :: Object obj f a => obj -> obj
instance Graphics.Implicit.Primitives.Object Graphics.Implicit.Definitions.SymbolicObj2 Linear.V2.V2 Graphics.Implicit.Definitions.ℝ
instance Graphics.Implicit.Primitives.Object Graphics.Implicit.Definitions.SymbolicObj3 Linear.V3.V3 Graphics.Implicit.Definitions.ℝ

module Graphics.Implicit.ObjectUtil
getImplicit3 :: ObjectContext -> SymbolicObj3 -> Obj3
getImplicit2 :: ObjectContext -> SymbolicObj2 -> Obj2
getBox3 :: SymbolicObj3 -> Box3
getBox2 :: SymbolicObj2 -> Box2


-- | This module implements canonicalization pass that * eliminates
--   identities * merges consecutive transformations like transform .
--   transform into one * prevents invalid transformations like scaling by
--   zero that would otherwise result in NaNs down the pipe * turns
--   degenerate objects into empty space (i.e. circle 0, cube (pure 0))
module Graphics.Implicit.Canon

-- | Canonicalize <tt>SymbolicObj2</tt> tree
canonicalize2 :: SymbolicObj2 -> SymbolicObj2

-- | Canonicalize <tt>SymbolicObj3</tt> tree
canonicalize3 :: SymbolicObj3 -> SymbolicObj3

-- | Map over <tt>SymbolicObj2</tt> and its underlying shared objects
--   
--   This function is co-recursive with <tt>fmapSharedObj</tt> to achieve
--   deep mapping over objects nested in <tt>Shared2</tt> constructor
fmapObj2 :: (SymbolicObj2 -> SymbolicObj2) -> (SymbolicObj3 -> SymbolicObj3) -> (forall obj f a. Object obj f a => obj -> obj) -> SymbolicObj2 -> SymbolicObj2

-- | Map over <tt>SymbolicObj3</tt> and its underlying shared objects
--   
--   This function is co-recursive with <tt>fmapSharedObj</tt> to achieve
--   deep mapping over objects nested in <tt>Shared3</tt> constructor
fmapObj3 :: (SymbolicObj3 -> SymbolicObj3) -> (SymbolicObj2 -> SymbolicObj2) -> (forall obj f a. Object obj f a => obj -> obj) -> SymbolicObj3 -> SymbolicObj3

-- | Map over <tt>SharedObj</tt> and its underlying objects
--   
--   This resembles bimap from Bifunctor but the structure of SharedObj
--   doesn't allow us to define Bifunctor instance as we need to map over
--   the first type argument (obj) and not f and a.
fmapSharedObj :: forall obj f a. Object obj f a => (obj -> obj) -> (obj -> obj) -> obj -> obj

-- | Rewrite the object tree until it cannot be reduced further
rewriteUntilIrreducible :: (Object obj f a, EqObj obj) => (obj -> obj) -> obj -> obj

-- | We have to define our own variant of Eq which compares objects when
--   possible and returns True when we cannot compare things like functions
class EqObj a
(=^=) :: EqObj a => a -> a -> Bool
instance Graphics.Implicit.Canon.EqObj a => Graphics.Implicit.Canon.EqObj [a]
instance (Graphics.Implicit.Canon.EqObj obj, GHC.Classes.Eq (f a)) => Graphics.Implicit.Canon.EqObj (Graphics.Implicit.Definitions.SharedObj obj f a)
instance Graphics.Implicit.Canon.EqObj Graphics.Implicit.Definitions.ExtrudeMScale
instance Graphics.Implicit.Canon.EqObj Graphics.Implicit.Definitions.SymbolicObj2
instance Graphics.Implicit.Canon.EqObj Graphics.Implicit.Definitions.SymbolicObj3

module Graphics.Implicit.Export.SymbolicFormats
scad2 :: ℝ -> SymbolicObj2 -> Text
scad3 :: ℝ -> SymbolicObj3 -> Text
instance Graphics.Implicit.Export.SymbolicFormats.Build Graphics.Implicit.Definitions.SymbolicObj2
instance Graphics.Implicit.Export.SymbolicFormats.Build Graphics.Implicit.Definitions.SymbolicObj3

module Graphics.Implicit.ExtOpenScad.Primitives

-- | The only thing exported here. basically, a list of modules.
primitiveModules :: [(Symbol, OVal)]

module Graphics.Implicit.ExtOpenScad.Eval.Constant

-- | Define variables used during the extOpenScad run.
addConstants :: [String] -> Bool -> IO (VarLookup, [Message])

-- | Evaluate an expression.
runExpr :: String -> Bool -> (OVal, [Message])

module Graphics.Implicit.ExtOpenScad

-- | Small wrapper of our parser to handle parse errors, etc.
runOpenscad :: ScadOpts -> [String] -> String -> IO (VarLookup, [SymbolicObj2], [SymbolicObj3], [Message])

module Graphics.Implicit.Export.SymbolicObj3
symbolicGetMesh :: ℝ -> SymbolicObj3 -> TriangleMesh

module Graphics.Implicit.Export.SymbolicObj2
symbolicGetContour :: ℝ -> ObjectContext -> SymbolicObj2 -> [Polyline]


-- | A module for retrieving approximate represententations of objects.
module Graphics.Implicit.Export.DiscreteAproxable

-- | There is a discrete way to aproximate this object. eg. Aproximating a
--   3D object with a triangle mesh would be DiscreteApproxable Obj3
--   TriangleMesh
class DiscreteAproxable obj aprox
discreteAprox :: DiscreteAproxable obj aprox => ℝ -> obj -> aprox
instance Graphics.Implicit.Export.DiscreteAproxable.DiscreteAproxable Graphics.Implicit.Definitions.SymbolicObj3 Graphics.Implicit.Definitions.TriangleMesh
instance Graphics.Implicit.Export.DiscreteAproxable.DiscreteAproxable Graphics.Implicit.Definitions.SymbolicObj3 Graphics.Implicit.Definitions.NormedTriangleMesh
instance Graphics.Implicit.Export.DiscreteAproxable.DiscreteAproxable Graphics.Implicit.Definitions.SymbolicObj3 Codec.Picture.Types.DynamicImage
instance Graphics.Implicit.Export.DiscreteAproxable.DiscreteAproxable Graphics.Implicit.Definitions.SymbolicObj2 [Graphics.Implicit.Definitions.Polyline]
instance Graphics.Implicit.Export.DiscreteAproxable.DiscreteAproxable Graphics.Implicit.Definitions.SymbolicObj2 Codec.Picture.Types.DynamicImage

module Graphics.Implicit.Export

-- | Output a file containing a 2D object.
export2 :: OutputFormat -> ℝ -> FilePath -> SymbolicObj2 -> IO ()

-- | Output a file containing a 3D object.
export3 :: OutputFormat -> ℝ -> FilePath -> SymbolicObj3 -> IO ()

-- | A type serving to enumerate our output formats.
data OutputFormat
SVG :: OutputFormat
SCAD :: OutputFormat
PNG :: OutputFormat
GCode :: OutputFormat
ASCIISTL :: OutputFormat
STL :: OutputFormat
THREEJS :: OutputFormat
OBJ :: OutputFormat
DXF :: OutputFormat

-- | Write an object to a file with LazyText IO, using the given format
--   writer function.
writeObject :: DiscreteAproxable obj aprox => ℝ -> (aprox -> Text) -> FilePath -> obj -> IO ()

-- | Serialize an object using the given format writer. No file target is
--   implied.
formatObject :: DiscreteAproxable obj aprox => ℝ -> (aprox -> Text) -> obj -> Text
writeSVG :: DiscreteAproxable obj [Polyline] => ℝ -> FilePath -> obj -> IO ()
writeSTL :: DiscreteAproxable obj TriangleMesh => ℝ -> FilePath -> obj -> IO ()
writeBinSTL :: DiscreteAproxable obj TriangleMesh => ℝ -> FilePath -> obj -> IO ()
writeOBJ :: DiscreteAproxable obj NormedTriangleMesh => ℝ -> FilePath -> obj -> IO ()
writeTHREEJS :: DiscreteAproxable obj TriangleMesh => ℝ -> FilePath -> obj -> IO ()
writeGCodeHacklabLaser :: DiscreteAproxable obj [Polyline] => ℝ -> FilePath -> obj -> IO ()
writeDXF2 :: DiscreteAproxable obj [Polyline] => ℝ -> FilePath -> obj -> IO ()
writeSCAD2 :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writeSCAD3 :: ℝ -> FilePath -> SymbolicObj3 -> IO ()
writePNG :: DiscreteAproxable obj DynamicImage => ℝ -> FilePath -> obj -> IO ()

module Graphics.Implicit

-- | A type synonym for <a>Double</a>. When used in the context of
--   positions or sizes, measured in units of millimeters. When used as in
--   the context of a rotation, measured in radians.
type ℝ = Double

-- | A pair of two <a>Double</a>s. When used as an area or position vector,
--   measured in millimeters squared.
type ℝ2 = V2 ℝ

-- | A triple of <a>Double</a>s. When used as a volume or position vector,
--   measured in millimeters cubed. When used as a rotation, interpreted as
--   Euler angles measured in radians.
type ℝ3 = V3 ℝ

-- | A symbolic 2D object format. We want to have symbolic objects so that
--   we can accelerate rendering &amp; give ideal meshes for simple cases.
data SymbolicObj2

-- | A symbolic 3D format!
data SymbolicObj3
data ExtrudeMScale
C1 :: ℝ -> ExtrudeMScale
C2 :: ℝ2 -> ExtrudeMScale
Fn :: (ℝ -> Either ℝ ℝ2) -> ExtrudeMScale

-- | Operations available on both 2D and 3D objects. The obvious omission
--   of rotation operations from this class are a technical limitation, and
--   are instead provided by <a>rotate</a> and <a>rotate3</a>.
--   
--   Library users shouldn't need to provide new instances of this class.
class (Applicative f, Eq a, Eq (f a), Foldable f, Num a, Num (f a)) => Object obj f a | obj -> f a

-- | Translate an object by a vector of appropriate dimension.
translate :: Object obj f a => f a -> obj -> obj

-- | Scale an object
scale :: Object obj f a => f a -> obj -> obj

-- | Mirror an object across the hyperplane whose normal is a given vector.
mirror :: Object obj f a => f a -> obj -> obj

-- | Complement an Object
complement :: Object obj f a => obj -> obj
union :: Object obj f a => [obj] -> obj

-- | Rounded union
unionR :: Object obj f a => ℝ -> [obj] -> obj
intersect :: Object obj f a => [obj] -> obj

-- | Rounded minimum
intersectR :: Object obj f a => ℝ -> [obj] -> obj
difference :: Object obj f a => obj -> [obj] -> obj

-- | Rounded difference
differenceR :: Object obj f a => ℝ -> obj -> [obj] -> obj
implicit :: Object obj f a => (f a -> a) -> (f a, f a) -> obj

-- | Make a shell of an object.
shell :: Object obj f a => ℝ -> obj -> obj

-- | Outset of an object.
outset :: Object obj f a => ℝ -> obj -> obj

-- | The object that fills no space
emptySpace :: Object obj f a => obj

-- | The object that fills the entire space
fullSpace :: Object obj f a => obj

-- | Set the current object-rounding value for the given object. The
--   rounding value is measured in units of distance, and describes the
--   radius of rounded corners.
--   
--   This can be used to change the shape of more primitive forms, for
--   example, we can make a cube with rounded corners via <tt>withRounding
--   5 (<a>cube</a> True 20)</tt>.
--   
--   <tt><a>withRounding</a> r obj</tt> applies the rounding <tt>r</tt>
--   <i>all</i> primitives objects in <tt>obj</tt>, so long as they have
--   the same dimensionality. That is to say, the current object-rounding
--   value set in 3D will not apply to extruded 2D shapes.
withRounding :: Object obj f a => ℝ -> obj -> obj

-- | A square
square :: Bool -> ℝ2 -> SymbolicObj2

-- | A rectangle
rect :: ℝ2 -> ℝ2 -> SymbolicObj2
circle :: ℝ -> SymbolicObj2

-- | A 2D polygon
polygon :: [ℝ2] -> SymbolicObj2
rotate :: ℝ -> SymbolicObj2 -> SymbolicObj2

-- | Transform a 2D object using a 3x3 matrix representing affine
--   transformation (OpenSCAD multmatrix)
transform :: M33 ℝ -> SymbolicObj2 -> SymbolicObj2

-- | Attempt to pack multiple 2D objects into a fixed area.
pack2 :: ℝ2 -> ℝ -> [SymbolicObj2] -> Maybe SymbolicObj2

-- | A cube
cube :: Bool -> ℝ3 -> SymbolicObj3

-- | A rectangular prism
rect3 :: ℝ3 -> ℝ3 -> SymbolicObj3
sphere :: ℝ -> SymbolicObj3
cylinder :: ℝ -> ℝ -> SymbolicObj3

-- | A conical frustum --- ie. a cylinder with different radii at either
--   end.
cylinder2 :: ℝ -> ℝ -> ℝ -> SymbolicObj3

-- | Rotate a 3D object via an Euler angle, measured in radians, along the
--   world axis.
rotate3 :: ℝ3 -> SymbolicObj3 -> SymbolicObj3

-- | Rotate a 3D object along an arbitrary axis.
rotate3V :: ℝ -> ℝ3 -> SymbolicObj3 -> SymbolicObj3

-- | Attempt to pack multiple 3D objects into a fixed area. The <tt>z</tt>
--   coordinate of each object is dropped, and the resulting packed objects
--   will all be on the same plane.
--   
--   FIXME: shouldn't this pack into a 3d area, or have a 3d equivalent?
pack3 :: ℝ2 -> ℝ -> [SymbolicObj3] -> Maybe SymbolicObj3

-- | Transform a 3D object using a 4x4 matrix representing affine
--   transformation (OpenSCAD multmatrix)
transform3 :: M44 ℝ -> SymbolicObj3 -> SymbolicObj3

-- | Extrude a 2d object upwards. The current object-rounding value set by
--   <a>withRounding</a> is used to round the caps, but is not used by the
--   2D object.
extrude :: SymbolicObj2 -> ℝ -> SymbolicObj3

-- | The current object-rounding value set by <a>withRounding</a> is used
--   to round the caps, but is not used by the 2D object.
extrudeM :: Either ℝ (ℝ -> ℝ) -> ExtrudeMScale -> Either ℝ2 (ℝ -> ℝ2) -> SymbolicObj2 -> Either ℝ (ℝ2 -> ℝ) -> SymbolicObj3
extrudeOnEdgeOf :: SymbolicObj2 -> SymbolicObj2 -> SymbolicObj3
rotateExtrude :: ℝ -> Either ℝ2 (ℝ -> ℝ2) -> Either ℝ (ℝ -> ℝ) -> SymbolicObj2 -> SymbolicObj3

-- | Small wrapper of our parser to handle parse errors, etc.
runOpenscad :: ScadOpts -> [String] -> String -> IO (VarLookup, [SymbolicObj2], [SymbolicObj3], [Message])
writeSVG :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writePNG2 :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writeDXF2 :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writeSCAD2 :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writeGCodeHacklabLaser :: ℝ -> FilePath -> SymbolicObj2 -> IO ()
writeSTL :: ℝ -> FilePath -> SymbolicObj3 -> IO ()
writeBinSTL :: ℝ -> FilePath -> SymbolicObj3 -> IO ()
writeOBJ :: ℝ -> FilePath -> SymbolicObj3 -> IO ()
writeTHREEJS :: ℝ -> FilePath -> SymbolicObj3 -> IO ()
writeSCAD3 :: ℝ -> FilePath -> SymbolicObj3 -> IO ()

-- | Export a PNG of the <a>SymbolicObj3</a>. The projection is with a
--   front-facing camera, so the coordinate system is <tt>(left to right,
--   front to back, down to up)</tt>.
writePNG3 :: ℝ -> FilePath -> SymbolicObj3 -> IO ()

-- | A 2-dimensional vector
--   
--   <pre>
--   &gt;&gt;&gt; pure 1 :: V2 Int
--   V2 1 1
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; V2 1 2 + V2 3 4
--   V2 4 6
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; V2 1 2 * V2 3 4
--   V2 3 8
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; sum (V2 1 2)
--   3
--   </pre>
data V2 a
V2 :: !a -> !a -> V2 a

-- | A 3-dimensional vector
data V3 a
V3 :: !a -> !a -> !a -> V3 a

-- | Quaternions
data Quaternion a
Quaternion :: !a -> {-# UNPACK #-} !V3 a -> Quaternion a

module Graphics.Implicit.Export.Resolution

-- | Find the resolution to raytrace at.
estimateResolution :: (VarLookup, [SymbolicObj2], [SymbolicObj3], [Message]) -> ℝ