Diagrams.Core

The core library of primitives forming the basis of an embedded domain-specific language for describing and rendering diagrams. Normal users of the diagrams library should almost never need to import anything from this package directly; instead, import modules (especially Diagrams.Prelude) from the diagrams-lib package, which re-exports most things of value to users.

For most library code needing access to core internals, it should be sufficient to import this module, which simply re-exports useful functionality from other modules in the core library. Library writers needing finer-grained access or functionality may occasionally find it useful to directly import one of the constituent core modules.

The diagrams library relies heavily on custom types and classes. Many of the relevant definitions are in the Diagrams.Core.Types module. Indeed the definition of the diagram type QDiagram is contained in: QDiagram.

The best place to start when learning about diagrams' types is the user manual: http://projects.haskell.org/diagrams/doc/manual.html#type-reference The following list shows which types are contained in each module of Diagrams.Core.

• Diagrams.Core.Types

  • Annotation,
  • UpAnnots b v n m, DownAnnots v n,
  • QDiaLeaf b v n m, Measure n,
  • Subdiagram b v n m, SubMap b v n m,
  • Prim b v n, Backend b v n,
  • DNode b v n a, DTree b v n a,
  • RNode b v n a, RTree b v n a,
  • NullBackend, Renderable t b,
  • D v n.

• Diagrams.Core.Envelope

  • Envelope v n, Enveloped a,
  • OrderedField s.

• Diagrams.Core.Juxtapose

  • Juxtaposable a.

• Diagrams.Core.Names

  • AName, Name, IsName a,
  • Qualifiable q.

• Diagrams.Core.HasOrigin

  • HasOrigin t.

• Diagrams.Core.Query

  • Query v n m.

• Diagrams.Core.Style

  • AttributeClass a, Attribute v n,
  • Style v n, HasStyle.

• Diagrams.Core.Trace

  • SortedList a,
  • Trace v n, Traced a.

• Diagrams.Core.Transform

  • u :-: v, HasLinearMap, HasBasis
  • Transformation v n, Transformable t,
  • TransInv t.

• Diagrams.Core.V

  • V a,
  • N a,
  • Vn a,
  • InSpace v n a,
  • SameSpace a b.

Associated vector spaces

type family V a :: * -> *

Many sorts of objects have an associated vector space in which they "live". The type function V maps from object types to the associated vector space. The resulting vector space has kind * -> * which means it takes another value (a number) and returns a concrete vector. For example V2 has kind * -> * and V2 Double is a vector.

Instances

type V [a]

type V [a] = V a

type V (Option a)

type V (Option a) = V a

type V (Set a)

type V (Set a) = V a

type V (Split m)

type V (Split m) = V m

type V (Deletable m)

type V (Deletable m) = V m

type V (TransInv t)

type V (TransInv t) = V t

type V (a -> b)

type V (a -> b) = V b

type V (a, b)

type V (a, b) = V a

type V (Map k a)

type V (Map k a) = V a

type V (Point v n)

type V (Point v n) = v

type V ((:+:) m n)

type V ((:+:) m n) = V m

type V (Measured n a)

type V (Measured n a) = V a

type V (Transformation v n)

type V (Transformation v n) = v

type V (Style v n)

type V (Style v n) = v

type V (Attribute v n)

type V (Attribute v n) = v

type V (Trace v n)

type V (Trace v n) = v

type V (Envelope v n)

type V (Envelope v n) = v

type V (a, b, c)

type V (a, b, c) = V a

type V (Query v n m)

type V (Query v n m) = v

type V (Prim b v n)

type V (Prim b v n) = v

type V (SubMap b v n m)

type V (SubMap b v n m) = v

type V (Subdiagram b v n m)

type V (Subdiagram b v n m) = v

type V (QDiagram b v n m)

type V (QDiagram b v n m) = v

type family N a :: *

The numerical field for the object, the number type used for calculations.

Instances

type N [a]

type N [a] = N a

type N (Option a)

type N (Option a) = N a

type N (Set a)

type N (Set a) = N a

type N (Split m)

type N (Split m) = N m

type N (Deletable m)

type N (Deletable m) = N m

type N (TransInv t)

type N (TransInv t) = N t

type N (a -> b)

type N (a -> b) = N b

type N (a, b)

type N (a, b) = N a

type N (Map k a)

type N (Map k a) = N a

type N (Point v n)

type N (Point v n) = n

type N ((:+:) m n)

type N ((:+:) m n) = N m

type N (Measured n a)

type N (Measured n a) = N a

type N (Transformation v n)

type N (Transformation v n) = n

type N (Style v n)

type N (Style v n) = n

type N (Attribute v n)

type N (Attribute v n) = n

type N (Trace v n)

type N (Trace v n) = n

type N (Envelope v n)

type N (Envelope v n) = n

type N (a, b, c)

type N (a, b, c) = N a

type N (Query v n m)

type N (Query v n m) = n

type N (Prim b v n)

type N (Prim b v n) = n

type N (SubMap b v n m)

type N (SubMap b v n m) = n

type N (Subdiagram b v n m)

type N (Subdiagram b v n m) = n

type N (QDiagram b v n m)

type N (QDiagram b v n m) = n

type Vn a = V a (N a)

Conveient type alias to retrieve the vector type associated with an object's vector space. This is usually used as Vn a ~ v n where v is the vector space and n is the numerical field.

class (V a ~ v, N a ~ n, Additive v, Num n) => InSpace v n a

InSpace v n a means the type a belongs to the vector space v n, where v is Additive and n is a Num.

Instances

((~) (* -> *) (V a) v, (~) * (N a) n, Additive v, Num n) => InSpace v n a

class (V a ~ V b, N a ~ N b) => SameSpace a b

SameSpace a b means the types a and b belong to the same vector space v n.

Instances

((~) (* -> *) (V a) (V b), (~) * (N a) (N b)) => SameSpace a b

Points

data Point f a :: (* -> *) -> * -> *

A handy wrapper to help distinguish points from vectors at the type level

Instances

Unbox (f a) => Vector Vector (Point f a)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> m (Vector (Point f a))

basicUnsafeThaw :: PrimMonad m => Vector (Point f a) -> m (Mutable Vector (PrimState m) (Point f a))

basicLength :: Vector (Point f a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a)

basicUnsafeIndexM :: Monad m => Vector (Point f a) -> Int -> m (Point f a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> Vector (Point f a) -> m ()

elemseq :: Vector (Point f a) -> Point f a -> b -> b

Unbox (f a) => MVector MVector (Point f a)

Methods

basicLength :: MVector s (Point f a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Point f a) -> MVector s (Point f a)

basicOverlaps :: MVector s (Point f a) -> MVector s (Point f a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Point f a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Point f a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Point f a -> m (MVector (PrimState m) (Point f a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (Point f a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> Point f a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Point f a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Point f a) -> Point f a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (MVector (PrimState m) (Point f a))

Monad f => Monad (Point f)

Methods

(>>=) :: Point f a -> (a -> Point f b) -> Point f b

(>>) :: Point f a -> Point f b -> Point f b

return :: a -> Point f a

fail :: String -> Point f a

Functor f => Functor (Point f)

Methods

fmap :: (a -> b) -> Point f a -> Point f b

(<$) :: a -> Point f b -> Point f a

Applicative f => Applicative (Point f)

Methods

pure :: a -> Point f a

(<*>) :: Point f (a -> b) -> Point f a -> Point f b

(*>) :: Point f a -> Point f b -> Point f b

(<*) :: Point f a -> Point f b -> Point f a

Foldable f => Foldable (Point f)

Methods

fold :: Monoid m => Point f m -> m

foldMap :: Monoid m => (a -> m) -> Point f a -> m

foldr :: (a -> b -> b) -> b -> Point f a -> b

foldr' :: (a -> b -> b) -> b -> Point f a -> b

foldl :: (b -> a -> b) -> b -> Point f a -> b

foldl' :: (b -> a -> b) -> b -> Point f a -> b

foldr1 :: (a -> a -> a) -> Point f a -> a

foldl1 :: (a -> a -> a) -> Point f a -> a

toList :: Point f a -> [a]

null :: Point f a -> Bool

length :: Point f a -> Int

elem :: Eq a => a -> Point f a -> Bool

maximum :: Ord a => Point f a -> a

minimum :: Ord a => Point f a -> a

sum :: Num a => Point f a -> a

product :: Num a => Point f a -> a

Traversable f => Traversable (Point f)

Methods

traverse :: Applicative f => (a -> f b) -> Point f a -> f (Point f b)

sequenceA :: Applicative f => Point f (f a) -> f (Point f a)

mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b)

sequence :: Monad m => Point f (m a) -> m (Point f a)

Generic1 (Point f)

Associated Types

type Rep1 (Point f :: * -> *) :: * -> *

Methods

from1 :: Point f a -> Rep1 (Point f) a

to1 :: Rep1 (Point f) a -> Point f a

Distributive f => Distributive (Point f)

Methods

distribute :: Functor f => f (Point f a) -> Point f (f a)

collect :: Functor f => (a -> Point f b) -> f a -> Point f (f b)

distributeM :: Monad m => m (Point f a) -> Point f (m a)

collectM :: Monad m => (a -> Point f b) -> m a -> Point f (m b)

Representable f => Representable (Point f)

Associated Types

type Rep (Point f :: * -> *) :: *

Methods

tabulate :: (Rep (Point f) -> a) -> Point f a

index :: Point f a -> Rep (Point f) -> a

Eq1 f => Eq1 (Point f)

Methods

liftEq :: (a -> b -> Bool) -> Point f a -> Point f b -> Bool

Ord1 f => Ord1 (Point f)

Methods

liftCompare :: (a -> b -> Ordering) -> Point f a -> Point f b -> Ordering

Read1 f => Read1 (Point f)

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point f a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point f a]

Show1 f => Show1 (Point f)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point f a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point f a] -> ShowS

Serial1 f => Serial1 (Point f)

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Point f a -> m ()

deserializeWith :: MonadGet m => m a -> m (Point f a)

Additive f => Affine (Point f)

Associated Types

type Diff (Point f :: * -> *) :: * -> *

Methods

(.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a

(.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a

(.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a

R4 f => R4 (Point f)

Methods

_w :: Functor f => (a -> f a) -> Point f a -> f (Point f a)

_xyzw :: Functor f => (V4 a -> f (V4 a)) -> Point f a -> f (Point f a)

R3 f => R3 (Point f)

Methods

_z :: Functor f => (a -> f a) -> Point f a -> f (Point f a)

_xyz :: Functor f => (V3 a -> f (V3 a)) -> Point f a -> f (Point f a)

R2 f => R2 (Point f)

Methods

_y :: Functor f => (a -> f a) -> Point f a -> f (Point f a)

_xy :: Functor f => (V2 a -> f (V2 a)) -> Point f a -> f (Point f a)

R1 f => R1 (Point f)

Methods

_x :: Functor f => (a -> f a) -> Point f a -> f (Point f a)

Finite f => Finite (Point f)

Associated Types

type Size (Point f :: * -> *) :: Nat

Methods

toV :: Point f a -> V Nat (Size (Point f)) a

fromV :: V Nat (Size (Point f)) a -> Point f a

Metric f => Metric (Point f)

Methods

dot :: Num a => Point f a -> Point f a -> a

quadrance :: Num a => Point f a -> a

qd :: Num a => Point f a -> Point f a -> a

distance :: Floating a => Point f a -> Point f a -> a

norm :: Floating a => Point f a -> a

signorm :: Floating a => Point f a -> Point f a

Additive f => Additive (Point f)

Methods

zero :: Num a => Point f a

(^+^) :: Num a => Point f a -> Point f a -> Point f a

(^-^) :: Num a => Point f a -> Point f a -> Point f a

lerp :: Num a => a -> Point f a -> Point f a -> Point f a

liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a

liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c

Apply f => Apply (Point f)

Methods

(<.>) :: Point f (a -> b) -> Point f a -> Point f b

(.>) :: Point f a -> Point f b -> Point f b

(<.) :: Point f a -> Point f b -> Point f a

Bind f => Bind (Point f)

Methods

(>>-) :: Point f a -> (a -> Point f b) -> Point f b

join :: Point f (Point f a) -> Point f a

Functor v => Cosieve (Query v) (Point v)

Methods

cosieve :: Query v a b -> Point v a -> b

Eq (f a) => Eq (Point f a)

Methods

(==) :: Point f a -> Point f a -> Bool

(/=) :: Point f a -> Point f a -> Bool

Fractional (f a) => Fractional (Point f a)

Methods

(/) :: Point f a -> Point f a -> Point f a

recip :: Point f a -> Point f a

fromRational :: Rational -> Point f a

(Data (f a), Typeable * a, Typeable (* -> *) f) => Data (Point f a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point f a -> c (Point f a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point f a)

toConstr :: Point f a -> Constr

dataTypeOf :: Point f a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Point f a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Point f a))

gmapT :: (forall b. Data b => b -> b) -> Point f a -> Point f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r

gmapQ :: (forall d. Data d => d -> u) -> Point f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Point f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a)

Num (f a) => Num (Point f a)

Methods

(+) :: Point f a -> Point f a -> Point f a

(-) :: Point f a -> Point f a -> Point f a

(*) :: Point f a -> Point f a -> Point f a

negate :: Point f a -> Point f a

abs :: Point f a -> Point f a

signum :: Point f a -> Point f a

fromInteger :: Integer -> Point f a

Ord (f a) => Ord (Point f a)

Methods

compare :: Point f a -> Point f a -> Ordering

(<) :: Point f a -> Point f a -> Bool

(<=) :: Point f a -> Point f a -> Bool

(>) :: Point f a -> Point f a -> Bool

(>=) :: Point f a -> Point f a -> Bool

max :: Point f a -> Point f a -> Point f a

min :: Point f a -> Point f a -> Point f a

Read (f a) => Read (Point f a)

Methods

readsPrec :: Int -> ReadS (Point f a)

readList :: ReadS [Point f a]

readPrec :: ReadPrec (Point f a)

readListPrec :: ReadPrec [Point f a]

Show (f a) => Show (Point f a)

Methods

showsPrec :: Int -> Point f a -> ShowS

show :: Point f a -> String

showList :: [Point f a] -> ShowS

Ix (f a) => Ix (Point f a)

Methods

range :: (Point f a, Point f a) -> [Point f a]

index :: (Point f a, Point f a) -> Point f a -> Int

unsafeIndex :: (Point f a, Point f a) -> Point f a -> Int

inRange :: (Point f a, Point f a) -> Point f a -> Bool

rangeSize :: (Point f a, Point f a) -> Int

unsafeRangeSize :: (Point f a, Point f a) -> Int

Generic (Point f a)

Associated Types

type Rep (Point f a) :: * -> *

Methods

from :: Point f a -> Rep (Point f a) x

to :: Rep (Point f a) x -> Point f a

Storable (f a) => Storable (Point f a)

Methods

sizeOf :: Point f a -> Int

alignment :: Point f a -> Int

peekElemOff :: Ptr (Point f a) -> Int -> IO (Point f a)

pokeElemOff :: Ptr (Point f a) -> Int -> Point f a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Point f a)

pokeByteOff :: Ptr b -> Int -> Point f a -> IO ()

peek :: Ptr (Point f a) -> IO (Point f a)

poke :: Ptr (Point f a) -> Point f a -> IO ()

Binary (f a) => Binary (Point f a)

Methods

put :: Point f a -> Put

get :: Get (Point f a)

putList :: [Point f a] -> Put

Serial (f a) => Serial (Point f a)

Methods

serialize :: MonadPut m => Point f a -> m ()

deserialize :: MonadGet m => m (Point f a)

Serialize (f a) => Serialize (Point f a)

Methods

put :: Putter (Point f a)

get :: Get (Point f a)

NFData (f a) => NFData (Point f a)

Methods

rnf :: Point f a -> ()

Hashable (f a) => Hashable (Point f a)

Methods

hashWithSalt :: Int -> Point f a -> Int

hash :: Point f a -> Int

Unbox (f a) => Unbox (Point f a)

Ixed (f a) => Ixed (Point f a)

Methods

ix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a))

Wrapped (Point f a)

Associated Types

type Unwrapped (Point f a) :: *

Methods

_Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a))

Epsilon (f a) => Epsilon (Point f a)

Methods

nearZero :: Point f a -> Bool

(Additive v, Num n) => HasOrigin (Point v n)

Methods

moveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n

(Additive v, Num n) => Transformable (Point v n)

Methods

transform :: Transformation (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n

(Additive v, Ord n) => Traced (Point v n)

The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).

Methods

getTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n))

(OrderedField n, Metric v) => Enveloped (Point v n)

Methods

getEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n))

(~) * t (Point g b) => Rewrapped (Point f a) t

Traversable f => Each (Point f a) (Point f b) a b

Methods

each :: Traversal (Point f a) (Point f b) a b

data MVector s (Point f a)

data MVector s (Point f a) = MV_P (MVector s (f a))

type Rep1 (Point f)

type Rep1 (Point f) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.7-1RYm9pIRoWLF5idZRHcwlx" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))

type Rep (Point f)

type Rep (Point f) = Rep f

type Diff (Point f)

type Diff (Point f) = f

type Size (Point f)

type Size (Point f) = Size f

type Rep (Point f a)

type Rep (Point f a) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.7-1RYm9pIRoWLF5idZRHcwlx" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))

data Vector (Point f a)

data Vector (Point f a) = V_P (Vector (f a))

type Index (Point f a)

type Index (Point f a) = Index (f a)

type IxValue (Point f a)

type IxValue (Point f a) = IxValue (f a)

type Unwrapped (Point f a)

type Unwrapped (Point f a) = f a

type N (Point v n)

type N (Point v n) = n

type V (Point v n)

type V (Point v n) = v

origin :: (Additive f, Num a) => Point f a

Vector spaces have origins.

(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n

Scale a point by a scalar. Specialized version of '(*^)'.

relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)

An isomorphism between points and vectors, given a reference point.

Transformations

Utilities

basis :: (Additive t, Traversable t, Num a) => [t a]

Produce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see basisFor.

dimension :: forall a. (Additive (V a), Traversable (V a)) => a -> Int

Get the dimension of an object whose vector space is an instance of HasLinearMap, e.g. transformations, paths, diagrams, etc.

determinant :: (Additive v, Traversable v, Num n) => Transformation v n -> n

The determinant of (the linear part of) a Transformation.

isReflection :: (Additive v, Traversable v, Num n, Ord n) => Transformation v n -> Bool

Determine whether a Transformation includes a reflection component, that is, whether it reverses orientation.

Invertible linear transformations

data u :-: v infixr 7

(v1 :-: v2) is a linear map paired with its inverse.

Instances

Semigroup ((:-:) a a)

Methods

(<>) :: (a :-: a) -> (a :-: a) -> a :-: a

sconcat :: NonEmpty (a :-: a) -> a :-: a

stimes :: Integral b => b -> (a :-: a) -> a :-: a

Monoid ((:-:) v v)

Invertible linear maps from a vector space to itself form a monoid under composition.

Methods

mempty :: v :-: v

mappend :: (v :-: v) -> (v :-: v) -> v :-: v

mconcat :: [v :-: v] -> v :-: v

(<->) :: (u -> v) -> (v -> u) -> u :-: v

Create an invertible linear map from two functions which are assumed to be linear inverses.

linv :: (u :-: v) -> v :-: u

Invert a linear map.

lapp :: (u :-: v) -> u -> v

Apply a linear map to a vector.

General transformations

data Transformation v n

General (affine) transformations, represented by an invertible linear map, its transpose, and a vector representing a translation component.

By the transpose of a linear map we mean simply the linear map corresponding to the transpose of the map's matrix representation. For example, any scale is its own transpose, since scales are represented by matrices with zeros everywhere except the diagonal. The transpose of a rotation is the same as its inverse.

The reason we need to keep track of transposes is because it turns out that when transforming a shape according to some linear map L, the shape's normal vectors transform according to L's inverse transpose. (For a more detailed explanation and proof, see https://wiki.haskell.org/Diagrams/Dev/Transformations.) This is exactly what we need when transforming bounding functions, which are defined in terms of perpendicular (i.e. normal) hyperplanes.

For more general, non-invertible transformations, see Diagrams.Deform (in diagrams-lib).

Instances

(Additive v, Num n) => Semigroup (Transformation v n)

Transformations are closed under composition; t1 <> t2 is the transformation which performs first t2, then t1.

Methods

(<>) :: Transformation v n -> Transformation v n -> Transformation v n

sconcat :: NonEmpty (Transformation v n) -> Transformation v n

stimes :: Integral b => b -> Transformation v n -> Transformation v n

(Additive v, Num n) => Monoid (Transformation v n)

Methods

mempty :: Transformation v n

mappend :: Transformation v n -> Transformation v n -> Transformation v n

mconcat :: [Transformation v n] -> Transformation v n

(Additive v, Num n) => HasOrigin (Transformation v n)

Methods

moveOriginTo :: Point (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n

(Additive v, Num n) => Transformable (Transformation v n)

Methods

transform :: Transformation (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n

(Transformable a, (~) (* -> *) (V a) v, (~) * (N a) n) => Action (Transformation v n) a

Transformations can act on transformable things.

Methods

act :: Transformation v n -> a -> a

type N (Transformation v n)

type N (Transformation v n) = n

type V (Transformation v n)

type V (Transformation v n) = v

inv :: (Functor v, Num n) => Transformation v n -> Transformation v n

Invert a transformation.

transp :: Transformation v n -> v n :-: v n

Get the transpose of a transformation (ignoring the translation component).

transl :: Transformation v n -> v n

Get the translational component of a transformation.

dropTransl :: (Additive v, Num n) => Transformation v n -> Transformation v n

Drop the translational component of a transformation, leaving only the linear part.

apply :: Transformation v n -> v n -> v n

Apply a transformation to a vector. Note that any translational component of the transformation will not affect the vector, since vectors are invariant under translation.

papply :: (Additive v, Num n) => Transformation v n -> Point v n -> Point v n

Apply a transformation to a point.

fromLinear :: (Additive v, Num n) => (v n :-: v n) -> (v n :-: v n) -> Transformation v n

Create a general affine transformation from an invertible linear transformation and its transpose. The translational component is assumed to be zero.

Some specific transformations

translation :: v n -> Transformation v n

Create a translation.

translate :: Transformable t => Vn t -> t -> t

Translate by a vector.

moveTo :: (InSpace v n t, HasOrigin t) => Point v n -> t -> t

Translate the object by the translation that sends the origin to the given point. Note that this is dual to moveOriginTo, i.e. we should have

  moveTo (origin .^+ v) === moveOriginTo (origin .^- v)
  

For types which are also Transformable, this is essentially the same as translate, i.e.

  moveTo (origin .^+ v) === translate v
  

place :: (InSpace v n t, HasOrigin t) => t -> Point v n -> t

A flipped variant of moveTo, provided for convenience. Useful when writing a function which takes a point as an argument, such as when using withName and friends.

scaling :: (Additive v, Fractional n) => n -> Transformation v n

Create a uniform scaling transformation.

scale :: (InSpace v n a, Eq n, Fractional n, Transformable a) => n -> a -> a

Scale uniformly in every dimension by the given scalar.

avgScale :: (Additive v, Traversable v, Floating n) => Transformation v n -> n

Compute the "average" amount of scaling performed by a transformation. Satisfies the properties

  avgScale (scaling k) == k
  avgScale (t1 <> t2)  == avgScale t1 * avgScale t2
  

The Transformable class

class Transformable t where

Type class for things t which can be transformed.

Minimal complete definition

transform

Methods

transform :: Transformation (V t) (N t) -> t -> t

Apply a transformation to an object.

Instances

Transformable t => Transformable [t]

Methods

transform :: Transformation (V [t]) (N [t]) -> [t] -> [t]

(Transformable t, Ord t) => Transformable (Set t)

Methods

transform :: Transformation (V (Set t)) (N (Set t)) -> Set t -> Set t

Transformable m => Transformable (Deletable m)

Methods

transform :: Transformation (V (Deletable m)) (N (Deletable m)) -> Deletable m -> Deletable m

(Num (N t), Additive (V t), Transformable t) => Transformable (TransInv t)

Methods

transform :: Transformation (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t

((~) (* -> *) (V t) v, (~) * (N t) n, (~) (* -> *) (V t) (V s), (~) * (N t) (N s), Functor v, Num n, Transformable t, Transformable s) => Transformable (s -> t)

Methods

transform :: Transformation (V (s -> t)) (N (s -> t)) -> (s -> t) -> s -> t

(Transformable t, Transformable s, (~) (* -> *) (V t) (V s), (~) * (N t) (N s)) => Transformable (t, s)

Methods

transform :: Transformation (V (t, s)) (N (t, s)) -> (t, s) -> (t, s)

Transformable t => Transformable (Map k t)

Methods

transform :: Transformation (V (Map k t)) (N (Map k t)) -> Map k t -> Map k t

(Additive v, Num n) => Transformable (Point v n)

Methods

transform :: Transformation (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n

(InSpace v n t, Transformable t, HasLinearMap v, Floating n) => Transformable (Measured n t)

Methods

transform :: Transformation (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t

(Additive v, Num n) => Transformable (Transformation v n)

Methods

transform :: Transformation (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n

(Additive v, Traversable v, Floating n) => Transformable (Style v n)

Methods

transform :: Transformation (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n

(Additive v, Traversable v, Floating n) => Transformable (Attribute v n)

TAttributes are transformed directly, MAttributes have their local scale multiplied by the average scale of the transform. Plain Attributes are unaffected.

Methods

transform :: Transformation (V (Attribute v n)) (N (Attribute v n)) -> Attribute v n -> Attribute v n

(Additive v, Num n) => Transformable (Trace v n)

Methods

transform :: Transformation (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n

(Metric v, Floating n) => Transformable (Envelope v n)

Methods

transform :: Transformation (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n

(Transformable t, Transformable s, Transformable u, (~) (* -> *) (V s) (V t), (~) * (N s) (N t), (~) (* -> *) (V s) (V u), (~) * (N s) (N u)) => Transformable (t, s, u)

Methods

transform :: Transformation (V (t, s, u)) (N (t, s, u)) -> (t, s, u) -> (t, s, u)

(Additive v, Num n) => Transformable (Query v n m)

Methods

transform :: Transformation (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m

Transformable (Prim b v n)

The Transformable instance for Prim just pushes calls to transform down through the Prim constructor.

Methods

transform :: Transformation (V (Prim b v n)) (N (Prim b v n)) -> Prim b v n -> Prim b v n

Transformable (SubMap b v n m)

Methods

transform :: Transformation (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

Transformable (Subdiagram b v n m)

Methods

transform :: Transformation (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)

Diagrams can be transformed by transforming each of their components appropriately.

Methods

transform :: Transformation (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

Translational invariance

newtype TransInv t

TransInv is a wrapper which makes a transformable type translationally invariant; the translational component of transformations will no longer affect things wrapped in TransInv.

Constructors

TransInv t

Instances

Eq t => Eq (TransInv t)

Methods

(==) :: TransInv t -> TransInv t -> Bool

(/=) :: TransInv t -> TransInv t -> Bool

Ord t => Ord (TransInv t)

Methods

compare :: TransInv t -> TransInv t -> Ordering

(<) :: TransInv t -> TransInv t -> Bool

(<=) :: TransInv t -> TransInv t -> Bool

(>) :: TransInv t -> TransInv t -> Bool

(>=) :: TransInv t -> TransInv t -> Bool

max :: TransInv t -> TransInv t -> TransInv t

min :: TransInv t -> TransInv t -> TransInv t

Show t => Show (TransInv t)

Methods

showsPrec :: Int -> TransInv t -> ShowS

show :: TransInv t -> String

showList :: [TransInv t] -> ShowS

Semigroup t => Semigroup (TransInv t)

Methods

(<>) :: TransInv t -> TransInv t -> TransInv t

sconcat :: NonEmpty (TransInv t) -> TransInv t

stimes :: Integral b => b -> TransInv t -> TransInv t

Monoid t => Monoid (TransInv t)

Methods

mempty :: TransInv t

mappend :: TransInv t -> TransInv t -> TransInv t

mconcat :: [TransInv t] -> TransInv t

Wrapped (TransInv t)

Associated Types

type Unwrapped (TransInv t) :: *

Methods

_Wrapped' :: Iso' (TransInv t) (Unwrapped (TransInv t))

HasOrigin (TransInv t)

Methods

moveOriginTo :: Point (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t

(Num (N t), Additive (V t), Transformable t) => Transformable (TransInv t)

Methods

transform :: Transformation (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t

Qualifiable a => Qualifiable (TransInv a)

Methods

(.>>) :: IsName a => a -> TransInv a -> TransInv a

Traced t => Traced (TransInv t)

Methods

getTrace :: TransInv t -> Trace (V (TransInv t)) (N (TransInv t))

Enveloped t => Enveloped (TransInv t)

Methods

getEnvelope :: TransInv t -> Envelope (V (TransInv t)) (N (TransInv t))

Rewrapped (TransInv t) (TransInv t')

type Unwrapped (TransInv t)

type Unwrapped (TransInv t) = t

type N (TransInv t)

type N (TransInv t) = N t

type V (TransInv t)

type V (TransInv t) = V t

eye :: (HasBasis v, Num n) => v (v n)

Identity matrix.

Names

data AName

Atomic names. AName is just an existential wrapper around things which are Typeable, Ord and Show.

Instances

Eq AName

Methods

(==) :: AName -> AName -> Bool

(/=) :: AName -> AName -> Bool

Ord AName

Methods

compare :: AName -> AName -> Ordering

(<) :: AName -> AName -> Bool

(<=) :: AName -> AName -> Bool

(>) :: AName -> AName -> Bool

(>=) :: AName -> AName -> Bool

max :: AName -> AName -> AName

min :: AName -> AName -> AName

Show AName

Methods

showsPrec :: Int -> AName -> ShowS

show :: AName -> String

showList :: [AName] -> ShowS

IsName AName

Methods

toName :: AName -> Name

Each Name Name AName AName

Methods

each :: Traversal Name Name AName AName

data Name

A (qualified) name is a (possibly empty) sequence of atomic names.

Instances

Eq Name

Methods

(==) :: Name -> Name -> Bool

(/=) :: Name -> Name -> Bool

Ord Name

Methods

compare :: Name -> Name -> Ordering

(<) :: Name -> Name -> Bool

(<=) :: Name -> Name -> Bool

(>) :: Name -> Name -> Bool

(>=) :: Name -> Name -> Bool

max :: Name -> Name -> Name

min :: Name -> Name -> Name

Show Name

Methods

showsPrec :: Int -> Name -> ShowS

show :: Name -> String

showList :: [Name] -> ShowS

Semigroup Name

Methods

(<>) :: Name -> Name -> Name

sconcat :: NonEmpty Name -> Name

stimes :: Integral b => b -> Name -> Name

Monoid Name

Methods

mempty :: Name

mappend :: Name -> Name -> Name

mconcat :: [Name] -> Name

Wrapped Name

Associated Types

type Unwrapped Name :: *

Methods

_Wrapped' :: Iso' Name (Unwrapped Name)

Qualifiable Name

Of course, names can be qualified using (.>).

Methods

(.>>) :: IsName a => a -> Name -> Name

IsName Name

Methods

toName :: Name -> Name

Rewrapped Name Name

Each Name Name AName AName

Methods

each :: Traversal Name Name AName AName

Action Name (SubMap b v n m)

A name acts on a name map by qualifying every name in it.

Methods

act :: Name -> SubMap b v n m -> SubMap b v n m

type Unwrapped Name

type Unwrapped Name = [AName]

class (Typeable a, Ord a, Show a) => IsName a where

Class for those types which can be used as names. They must support Typeable (to facilitate extracting them from existential wrappers), Ord (for comparison and efficient storage) and Show.

To make an instance of IsName, you need not define any methods, just declare it.

WARNING: it is not recommended to use GeneralizedNewtypeDeriving in conjunction with IsName, since in that case the underlying type and the newtype will be considered equivalent when comparing names. For example:

    newtype WordN = WordN Int deriving (Show, Ord, Eq, Typeable, IsName)
  

is unlikely to work as intended, since (1 :: Int) and (WordN 1) will be considered equal as names. Instead, use

    newtype WordN = WordN Int deriving (Show, Ord, Eq, Typeable, IsName)
    instance IsName WordN
  

Methods

toName :: a -> Name

Instances

IsName Bool

Methods

toName :: Bool -> Name

IsName Char

Methods

toName :: Char -> Name

IsName Double

Methods

toName :: Double -> Name

IsName Float

Methods

toName :: Float -> Name

IsName Int

Methods

toName :: Int -> Name

IsName Integer

Methods

toName :: Integer -> Name

IsName ()

Methods

toName :: () -> Name

IsName Name

Methods

toName :: Name -> Name

IsName AName

Methods

toName :: AName -> Name

IsName a => IsName [a]

Methods

toName :: [a] -> Name

IsName a => IsName (Maybe a)

Methods

toName :: Maybe a -> Name

(IsName a, IsName b) => IsName (a, b)

Methods

toName :: (a, b) -> Name

(IsName a, IsName b, IsName c) => IsName (a, b, c)

Methods

toName :: (a, b, c) -> Name

class Qualifiable q where

Instances of Qualifiable are things which can be qualified by prefixing them with a name.

Minimal complete definition

(.>>)

Methods

(.>>) :: IsName a => a -> q -> q infixr 5

Qualify with the given name.

Instances

Qualifiable Name

Of course, names can be qualified using (.>).

Methods

(.>>) :: IsName a => a -> Name -> Name

Qualifiable a => Qualifiable [a]

Methods

(.>>) :: IsName a => a -> [a] -> [a]

(Ord a, Qualifiable a) => Qualifiable (Set a)

Methods

(.>>) :: IsName a => a -> Set a -> Set a

Qualifiable a => Qualifiable (TransInv a)

Methods

(.>>) :: IsName a => a -> TransInv a -> TransInv a

Qualifiable a => Qualifiable (b -> a)

Methods

(.>>) :: IsName a => a -> (b -> a) -> b -> a

(Qualifiable a, Qualifiable b) => Qualifiable (a, b)

Methods

(.>>) :: IsName a => a -> (a, b) -> (a, b)

Qualifiable a => Qualifiable (Map k a)

Methods

(.>>) :: IsName a => a -> Map k a -> Map k a

Qualifiable a => Qualifiable (Measured n a)

Methods

(.>>) :: IsName a => a -> Measured n a -> Measured n a

(Qualifiable a, Qualifiable b, Qualifiable c) => Qualifiable (a, b, c)

Methods

(.>>) :: IsName a => a -> (a, b, c) -> (a, b, c)

Qualifiable (SubMap b v n m)

SubMaps are qualifiable: if ns is a SubMap, then a |> ns is the same SubMap except with every name qualified by a.

Methods

(.>>) :: IsName a => a -> SubMap b v n m -> SubMap b v n m

(Metric v, OrderedField n, Semigroup m) => Qualifiable (QDiagram b v n m)

Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix.

Methods

(.>>) :: IsName a => a -> QDiagram b v n m -> QDiagram b v n m

(.>) :: (IsName a1, IsName a2) => a1 -> a2 -> Name infixr 5

Convenient operator for writing qualified names with atomic components of different types. Instead of writing toName a1 <> toName a2 <> toName a3 you can just write a1 .> a2 .> a3.

eachName :: (Typeable a, Ord a, Show a) => Traversal' Name a

Traversal over each name in a Name that matches the target type.

>>> toListOf eachName (a .> False .> b) :: String
"ab"
>>> a .> True .> b & eachName %~ not
a .> False .> b

Note that the type of the name is very important.

>>> sumOf eachName ((1::Int) .> (2 :: Integer) .> (3 :: Int)) :: Int
4
>>> sumOf eachName ((1::Int) .> (2 :: Integer) .> (3 :: Int)) :: Integer
2

Subdiagram maps

newtype SubMap b v n m

A SubMap is a map associating names to subdiagrams. There can be multiple associations for any given name.

Constructors

SubMap (Map Name [Subdiagram b v n m])

Instances

Action Name (SubMap b v n m)

A name acts on a name map by qualifying every name in it.

Methods

act :: Name -> SubMap b v n m -> SubMap b v n m

Functor (SubMap b v n)

Methods

fmap :: (a -> b) -> SubMap b v n a -> SubMap b v n b

(<$) :: a -> SubMap b v n b -> SubMap b v n a

Semigroup (SubMap b v n m)

Methods

(<>) :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m

sconcat :: NonEmpty (SubMap b v n m) -> SubMap b v n m

stimes :: Integral b => b -> SubMap b v n m -> SubMap b v n m

Monoid (SubMap b v n m)

SubMaps form a monoid with the empty map as the identity, and map union as the binary operation. No information is ever lost: if two maps have the same name in their domain, the resulting map will associate that name to the concatenation of the information associated with that name.

Methods

mempty :: SubMap b v n m

mappend :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m

mconcat :: [SubMap b v n m] -> SubMap b v n m

Wrapped (SubMap b v n m)

Associated Types

type Unwrapped (SubMap b v n m) :: *

Methods

_Wrapped' :: Iso' (SubMap b v n m) (Unwrapped (SubMap b v n m))

(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)

Methods

moveOriginTo :: Point (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

Transformable (SubMap b v n m)

Methods

transform :: Transformation (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

Qualifiable (SubMap b v n m)

SubMaps are qualifiable: if ns is a SubMap, then a |> ns is the same SubMap except with every name qualified by a.

Methods

(.>>) :: IsName a => a -> SubMap b v n m -> SubMap b v n m

Rewrapped (SubMap b v n m) (SubMap b' v' n' m')

type Unwrapped (SubMap b v n m)

type Unwrapped (SubMap b v n m) = Map Name [Subdiagram b v n m]

type N (SubMap b v n m)

type N (SubMap b v n m) = n

type V (SubMap b v n m)

type V (SubMap b v n m) = v

fromNames :: IsName a => [(a, Subdiagram b v n m)] -> SubMap b v n m

Construct a SubMap from a list of associations between names and subdiagrams.

rememberAs :: IsName a => a -> QDiagram b v n m -> SubMap b v n m -> SubMap b v n m

Add a name/diagram association to a submap.

lookupSub :: IsName nm => nm -> SubMap b v n m -> Maybe [Subdiagram b v n m]

Look for the given name in a name map, returning a list of subdiagrams associated with that name. If no names match the given name exactly, return all the subdiagrams associated with names of which the given name is a suffix.

Attributes and styles

class (Typeable a, Semigroup a) => AttributeClass a

Every attribute must be an instance of AttributeClass, which simply guarantees Typeable and Semigroup constraints. The Semigroup instance for an attribute determines how it will combine with other attributes of the same type.

data Attribute v n :: * where

An existential wrapper type to hold attributes. Some attributes are simply inert/static; some are affected by transformations; and some are affected by transformations and can be modified generically.

Constructors

Attribute :: AttributeClass a => a -> Attribute v n

MAttribute :: AttributeClass a => Measured n a -> Attribute v n

TAttribute :: (AttributeClass a, Transformable a, V a ~ v, N a ~ n) => a -> Attribute v n

Instances

Show (Attribute v n)

Shows the kind of attribute and the type contained in the attribute.

Methods

showsPrec :: Int -> Attribute v n -> ShowS

show :: Attribute v n -> String

showList :: [Attribute v n] -> ShowS

Typeable * n => Semigroup (Attribute v n)

Attributes form a semigroup, where the semigroup operation simply returns the right-hand attribute when the types do not match, and otherwise uses the semigroup operation specific to the (matching) types.

Methods

(<>) :: Attribute v n -> Attribute v n -> Attribute v n

sconcat :: NonEmpty (Attribute v n) -> Attribute v n

stimes :: Integral b => b -> Attribute v n -> Attribute v n

(Additive v, Traversable v, Floating n) => Transformable (Attribute v n)

TAttributes are transformed directly, MAttributes have their local scale multiplied by the average scale of the transform. Plain Attributes are unaffected.

Methods

transform :: Transformation (V (Attribute v n)) (N (Attribute v n)) -> Attribute v n -> Attribute v n

Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')

Methods

each :: Traversal (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')

type N (Attribute v n)

type N (Attribute v n) = n

type V (Attribute v n)

type V (Attribute v n) = v

data Style v n

A Style is a heterogeneous collection of attributes, containing at most one attribute of any given type.

Instances

Show (Style v n)

Show the attributes in the style.

Methods

showsPrec :: Int -> Style v n -> ShowS

show :: Style v n -> String

showList :: [Style v n] -> ShowS

Typeable * n => Semigroup (Style v n)

Combine a style by combining the attributes; if the two styles have attributes of the same type they are combined according to their semigroup structure.

Methods

(<>) :: Style v n -> Style v n -> Style v n

sconcat :: NonEmpty (Style v n) -> Style v n

stimes :: Integral b => b -> Style v n -> Style v n

Typeable * n => Monoid (Style v n)

The empty style contains no attributes.

Methods

mempty :: Style v n

mappend :: Style v n -> Style v n -> Style v n

mconcat :: [Style v n] -> Style v n

Ixed (Style v n)

Methods

ix :: Index (Style v n) -> Traversal' (Style v n) (IxValue (Style v n))

At (Style v n)

Methods

at :: Index (Style v n) -> Lens' (Style v n) (Maybe (IxValue (Style v n)))

Wrapped (Style v n)

Associated Types

type Unwrapped (Style v n) :: *

Methods

_Wrapped' :: Iso' (Style v n) (Unwrapped (Style v n))

(Additive v, Traversable v, Floating n) => Transformable (Style v n)

Methods

transform :: Transformation (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n

Typeable * n => HasStyle (Style v n)

Methods

applyStyle :: Style (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n

Action (Style v n) m

Styles have no action on other monoids.

Methods

act :: Style v n -> m -> m

Rewrapped (Style v n) (Style v' n')

Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')

Methods

each :: Traversal (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')

type Index (Style v n)

type Index (Style v n) = TypeRep

type IxValue (Style v n)

type IxValue (Style v n) = Attribute v n

type Unwrapped (Style v n)

type Unwrapped (Style v n) = HashMap TypeRep (Attribute v n)

type N (Style v n)

type N (Style v n) = n

type V (Style v n)

type V (Style v n) = v

class HasStyle a where

Type class for things which have a style.

Minimal complete definition

applyStyle

Methods

applyStyle :: Style (V a) (N a) -> a -> a

Apply a style by combining it (on the left) with the existing style.

Instances

HasStyle a => HasStyle [a]

Methods

applyStyle :: Style (V [a]) (N [a]) -> [a] -> [a]

(HasStyle a, Ord a) => HasStyle (Set a)

Methods

applyStyle :: Style (V (Set a)) (N (Set a)) -> Set a -> Set a

HasStyle b => HasStyle (a -> b)

Methods

applyStyle :: Style (V (a -> b)) (N (a -> b)) -> (a -> b) -> a -> b

(HasStyle a, HasStyle b, (~) (* -> *) (V a) (V b), (~) * (N a) (N b)) => HasStyle (a, b)

Methods

applyStyle :: Style (V (a, b)) (N (a, b)) -> (a, b) -> (a, b)

HasStyle a => HasStyle (Map k a)

Methods

applyStyle :: Style (V (Map k a)) (N (Map k a)) -> Map k a -> Map k a

HasStyle b => HasStyle (Measured n b)

Methods

applyStyle :: Style (V (Measured n b)) (N (Measured n b)) -> Measured n b -> Measured n b

Typeable * n => HasStyle (Style v n)

Methods

applyStyle :: Style (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n

(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)

Methods

applyStyle :: Style (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

getAttr :: forall a v n. AttributeClass a => Style v n -> Maybe a

Extract an attribute from a style of a particular type. If the style contains an attribute of the requested type, it will be returned wrapped in Just; otherwise, Nothing is returned.

Trying to extract a measured attibute will fail. It either has to be unmeasured with unmeasureAttrs or use the atMAttr lens.

atAttr :: AttributeClass a => Lens' (Style v n) (Maybe a)

Lens onto a plain attribute of a style.

atMAttr :: (AttributeClass a, Typeable n) => Lens' (Style v n) (Maybe (Measured n a))

Lens onto a measured attribute of a style.

atTAttr :: (V a ~ v, N a ~ n, AttributeClass a, Transformable a) => Lens' (Style v n) (Maybe a)

Lens onto a transformable attribute of a style.

applyAttr :: (AttributeClass a, HasStyle d) => a -> d -> d

Apply an attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d) => Measured n a -> d -> d

Apply a measured attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, N a ~ N d, HasStyle d) => a -> d -> d

Apply a transformable attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

Envelopes

newtype Envelope v n

Every diagram comes equipped with an envelope. What is an envelope?

Consider first the idea of a bounding box. A bounding box expresses the distance to a bounding plane in every direction parallel to an axis. That is, a bounding box can be thought of as the intersection of a collection of half-planes, two perpendicular to each axis.

More generally, the intersection of half-planes in every direction would give a tight "bounding region", or convex hull. However, representing such a thing intensionally would be impossible; hence bounding boxes are often used as an approximation.

An envelope is an extensional representation of such a "bounding region". Instead of storing some sort of direct representation, we store a function which takes a direction as input and gives a distance to a bounding half-plane as output. The important point is that envelopes can be composed, and transformed by any affine transformation.

Formally, given a vector v, the envelope computes a scalar s such that

• for every point u inside the diagram, if the projection of (u - origin) onto v is s' *^ v, then s' <= s.
• s is the smallest such scalar.

There is also a special "empty envelope".

The idea for envelopes came from Sebastian Setzer; see http://byorgey.wordpress.com/2009/10/28/collecting-attributes/#comment-2030. See also Brent Yorgey, Monoids: Theme and Variations, published in the 2012 Haskell Symposium: http://ozark.hendrix.edu/~yorgey/pub/monoid-pearl.pdf; video: http://www.youtube.com/watch?v=X-8NCkD2vOw.

Constructors

Envelope (Option (v n -> Max n))

Instances

Show (Envelope v n)

Methods

showsPrec :: Int -> Envelope v n -> ShowS

show :: Envelope v n -> String

showList :: [Envelope v n] -> ShowS

Ord n => Semigroup (Envelope v n)

Methods

(<>) :: Envelope v n -> Envelope v n -> Envelope v n

sconcat :: NonEmpty (Envelope v n) -> Envelope v n

stimes :: Integral b => b -> Envelope v n -> Envelope v n

Ord n => Monoid (Envelope v n)

Methods

mempty :: Envelope v n

mappend :: Envelope v n -> Envelope v n -> Envelope v n

mconcat :: [Envelope v n] -> Envelope v n

Wrapped (Envelope v n)

Associated Types

type Unwrapped (Envelope v n) :: *

Methods

_Wrapped' :: Iso' (Envelope v n) (Unwrapped (Envelope v n))

(Metric v, Fractional n) => HasOrigin (Envelope v n)

The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate.

Methods

moveOriginTo :: Point (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n

(Metric v, Floating n) => Transformable (Envelope v n)

Methods

transform :: Transformation (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n

(Metric v, OrderedField n) => Enveloped (Envelope v n)

Methods

getEnvelope :: Envelope v n -> Envelope (V (Envelope v n)) (N (Envelope v n))

(Metric v, OrderedField n) => Juxtaposable (Envelope v n)

Methods

juxtapose :: Vn (Envelope v n) -> Envelope v n -> Envelope v n -> Envelope v n

Rewrapped (Envelope v n) (Envelope v' n')

type Unwrapped (Envelope v n)

type Unwrapped (Envelope v n) = Option (v n -> Max n)

type N (Envelope v n)

type N (Envelope v n) = n

type V (Envelope v n)

type V (Envelope v n) = v

appEnvelope :: Envelope v n -> Maybe (v n -> n)

"Apply" an envelope by turning it into a function. Nothing is returned iff the envelope is empty.

onEnvelope :: ((v n -> n) -> v n -> n) -> Envelope v n -> Envelope v n

A convenient way to transform an envelope, by specifying a transformation on the underlying v n -> n function. The empty envelope is unaffected.

mkEnvelope :: (v n -> n) -> Envelope v n

Create an envelope from a v n -> n function.

class (Metric (V a), OrderedField (N a)) => Enveloped a where

Enveloped abstracts over things which have an envelope.

Minimal complete definition

getEnvelope

Methods

getEnvelope :: a -> Envelope (V a) (N a)

Compute the envelope of an object. For types with an intrinsic notion of "local origin", the envelope will be based there. Other types (e.g. Trail) may have some other default reference point at which the envelope will be based; their instances should document what it is.

Instances

Enveloped b => Enveloped [b]

Methods

getEnvelope :: [b] -> Envelope (V [b]) (N [b])

Enveloped b => Enveloped (Set b)

Methods

getEnvelope :: Set b -> Envelope (V (Set b)) (N (Set b))

Enveloped t => Enveloped (TransInv t)

Methods

getEnvelope :: TransInv t -> Envelope (V (TransInv t)) (N (TransInv t))

(Enveloped a, Enveloped b, (~) (* -> *) (V a) (V b), (~) * (N a) (N b)) => Enveloped (a, b)

Methods

getEnvelope :: (a, b) -> Envelope (V (a, b)) (N (a, b))

Enveloped b => Enveloped (Map k b)

Methods

getEnvelope :: Map k b -> Envelope (V (Map k b)) (N (Map k b))

(OrderedField n, Metric v) => Enveloped (Point v n)

Methods

getEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n))

(Metric v, OrderedField n) => Enveloped (Envelope v n)

Methods

getEnvelope :: Envelope v n -> Envelope (V (Envelope v n)) (N (Envelope v n))

(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)

Methods

getEnvelope :: Subdiagram b v n m -> Envelope (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)

Methods

getEnvelope :: QDiagram b v n m -> Envelope (V (QDiagram b v n m)) (N (QDiagram b v n m))

envelopeVMay :: Enveloped a => Vn a -> a -> Maybe (Vn a)

Compute the vector from the local origin to a separating hyperplane in the given direction, or Nothing for the empty envelope.

envelopeV :: Enveloped a => Vn a -> a -> Vn a

Compute the vector from the local origin to a separating hyperplane in the given direction. Returns the zero vector for the empty envelope.

envelopePMay :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Maybe (Point v n)

Compute the point on a separating hyperplane in the given direction, or Nothing for the empty envelope.

envelopeP :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n

Compute the point on a separating hyperplane in the given direction. Returns the origin for the empty envelope.

diameter :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n

Compute the diameter of a enveloped object along a particular vector. Returns zero for the empty envelope.

radius :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n

Compute the "radius" (1/2 the diameter) of an enveloped object along a particular vector.

size :: (V a ~ v, N a ~ n, Enveloped a, HasBasis v) => a -> v n

The smallest positive axis-parallel vector that bounds the envelope of an object.

Traces

newtype Trace v n

Every diagram comes equipped with a trace. Intuitively, the trace for a diagram is like a raytracer: given a line (represented as a base point and a direction vector), the trace computes a sorted list of signed distances from the base point to all intersections of the line with the boundary of the diagram.

Note that the outputs are not absolute distances, but multipliers relative to the input vector. That is, if the base point is p and direction vector is v, and one of the output scalars is s, then there is an intersection at the point p .+^ (s *^ v).

Constructors

Trace

Fields

• appTrace :: Point v n -> v n -> SortedList n

Instances

Show (Trace v n)

Methods

showsPrec :: Int -> Trace v n -> ShowS

show :: Trace v n -> String

showList :: [Trace v n] -> ShowS

Ord n => Semigroup (Trace v n)

Methods

(<>) :: Trace v n -> Trace v n -> Trace v n

sconcat :: NonEmpty (Trace v n) -> Trace v n

stimes :: Integral b => b -> Trace v n -> Trace v n

Ord n => Monoid (Trace v n)

Methods

mempty :: Trace v n

mappend :: Trace v n -> Trace v n -> Trace v n

mconcat :: [Trace v n] -> Trace v n

Wrapped (Trace v n)

Associated Types

type Unwrapped (Trace v n) :: *

Methods

_Wrapped' :: Iso' (Trace v n) (Unwrapped (Trace v n))

(Additive v, Num n) => HasOrigin (Trace v n)

Methods

moveOriginTo :: Point (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n

(Additive v, Num n) => Transformable (Trace v n)

Methods

transform :: Transformation (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n

(Additive v, Ord n) => Traced (Trace v n)

Methods

getTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n))

Rewrapped (Trace v n) (Trace v' n')

type Unwrapped (Trace v n)

type Unwrapped (Trace v n) = Point v n -> v n -> SortedList n

type N (Trace v n)

type N (Trace v n) = n

type V (Trace v n)

type V (Trace v n) = v

data SortedList a

A newtype wrapper around a list which maintains the invariant that the list is sorted. The constructor is not exported; use the smart constructor mkSortedList (which sorts the given list) instead.

Instances

Ord a => Semigroup (SortedList a)

SortedList forms a semigroup with merge as composition.

Methods

(<>) :: SortedList a -> SortedList a -> SortedList a

sconcat :: NonEmpty (SortedList a) -> SortedList a

stimes :: Integral b => b -> SortedList a -> SortedList a

Ord a => Monoid (SortedList a)

SortedList forms a monoid with merge and the empty list.

Methods

mempty :: SortedList a

mappend :: SortedList a -> SortedList a -> SortedList a

mconcat :: [SortedList a] -> SortedList a

mkSortedList :: Ord a => [a] -> SortedList a

A smart constructor for the SortedList type, which sorts the input to ensure the SortedList invariant.

getSortedList :: SortedList a -> [a]

Project the (guaranteed sorted) list out of a SortedList wrapper.

mkTrace :: (Point v n -> v n -> SortedList n) -> Trace v n

class (Additive (V a), Ord (N a)) => Traced a where

Traced abstracts over things which have a trace.

Minimal complete definition

getTrace

Methods

getTrace :: a -> Trace (V a) (N a)

Compute the trace of an object.

Instances

Traced b => Traced [b]

Methods

getTrace :: [b] -> Trace (V [b]) (N [b])

Traced b => Traced (Set b)

Methods

getTrace :: Set b -> Trace (V (Set b)) (N (Set b))

Traced t => Traced (TransInv t)

Methods

getTrace :: TransInv t -> Trace (V (TransInv t)) (N (TransInv t))

(Traced a, Traced b, SameSpace a b) => Traced (a, b)

Methods

getTrace :: (a, b) -> Trace (V (a, b)) (N (a, b))

Traced b => Traced (Map k b)

Methods

getTrace :: Map k b -> Trace (V (Map k b)) (N (Map k b))

(Additive v, Ord n) => Traced (Point v n)

The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).

Methods

getTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n))

(Additive v, Ord n) => Traced (Trace v n)

Methods

getTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n))

(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)

Methods

getTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)

Methods

getTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m))

traceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n)

Compute the vector from the given point p to the "smallest" boundary intersection along the given vector v. The "smallest" boundary intersection is defined as the one given by p .+^ (s *^ v) for the smallest (most negative) value of s. Return Nothing if there is no intersection. See also traceP.

See also rayTraceV which uses the smallest positive intersection, which is often more intuitive behavior.

traceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)

Compute the "smallest" boundary point along the line determined by the given point p and vector v. The "smallest" boundary point is defined as the one given by p .+^ (s *^ v) for the smallest (most negative) value of s. Return Nothing if there is no such boundary point. See also traceV.

See also rayTraceP which uses the smallest positive intersection, which is often more intuitive behavior.

maxTraceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n)

Like traceV, but computes a vector to the "largest" boundary point instead of the smallest. (Note, however, the "largest" boundary point may still be in the opposite direction from the given vector, if all the boundary points are, as in the third example shown below.)

maxTraceP :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)

Like traceP, but computes the "largest" boundary point instead of the smallest. (Note, however, the "largest" boundary point may still be in the opposite direction from the given vector, if all the boundary points are.)

rayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n)

Compute the vector from the given point to the closest boundary point of the given object in the given direction, or Nothing if there is no such boundary point (as in the third example below). Note that unlike traceV, only positive boundary points are considered, i.e. boundary points corresponding to a positive scalar multiple of the direction vector. This is intuitively the "usual" behavior of a raytracer, which only considers intersections "in front of" the camera. Compare the second example diagram below with the second example shown for traceV.

rayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)

Compute the boundary point on an object which is closest to the given base point in the given direction, or Nothing if there is no such boundary point. Note that unlike traceP, only positive boundary points are considered, i.e. boundary points corresponding to a positive scalar multiple of the direction vector. This is intuitively the "usual" behavior of a raytracer, which only considers intersection points "in front of" the camera.

maxRayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n)

Like rayTraceV, but computes a vector to the "largest" boundary point instead of the smallest. Considers only positive boundary points.

maxRayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)

Like rayTraceP, but computes the "largest" boundary point instead of the smallest. Considers only positive boundary points.

Things with local origins

class HasOrigin t where

Class of types which have an intrinsic notion of a "local origin", i.e. things which are not invariant under translation, and which allow the origin to be moved.

One might wonder why not just use Transformable instead of having a separate class for HasOrigin; indeed, for types which are instances of both we should have the identity

  moveOriginTo (origin .^+ v) === translate (negated v)
  

The reason is that some things (e.g. vectors, Trails) are transformable but are translationally invariant, i.e. have no origin.

Minimal complete definition

moveOriginTo

Methods

moveOriginTo :: Point (V t) (N t) -> t -> t

Move the local origin to another point.

Note that this function is in some sense dual to translate (for types which are also Transformable); moving the origin itself while leaving the object "fixed" is dual to fixing the origin and translating the diagram.

Instances

HasOrigin t => HasOrigin [t]

Methods

moveOriginTo :: Point (V [t]) (N [t]) -> [t] -> [t]

(HasOrigin t, Ord t) => HasOrigin (Set t)

Methods

moveOriginTo :: Point (V (Set t)) (N (Set t)) -> Set t -> Set t

HasOrigin (TransInv t)

Methods

moveOriginTo :: Point (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t

(HasOrigin t, HasOrigin s, SameSpace s t) => HasOrigin (s, t)

Methods

moveOriginTo :: Point (V (s, t)) (N (s, t)) -> (s, t) -> (s, t)

HasOrigin t => HasOrigin (Map k t)

Methods

moveOriginTo :: Point (V (Map k t)) (N (Map k t)) -> Map k t -> Map k t

(Additive v, Num n) => HasOrigin (Point v n)

Methods

moveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n

HasOrigin t => HasOrigin (Measured n t)

Methods

moveOriginTo :: Point (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t

(Additive v, Num n) => HasOrigin (Transformation v n)

Methods

moveOriginTo :: Point (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n

(Additive v, Num n) => HasOrigin (Trace v n)

Methods

moveOriginTo :: Point (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n

(Metric v, Fractional n) => HasOrigin (Envelope v n)

The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate.

Methods

moveOriginTo :: Point (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n

(Additive v, Num n) => HasOrigin (Query v n m)

Methods

moveOriginTo :: Point (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m

(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)

Methods

moveOriginTo :: Point (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)

Methods

moveOriginTo :: Point (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

(Metric v, OrderedField n, Semigroup m) => HasOrigin (QDiagram b v n m)

Every diagram has an intrinsic "local origin" which is the basis for all combining operations.

Methods

moveOriginTo :: Point (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

moveOriginBy :: (V t ~ v, N t ~ n, HasOrigin t) => v n -> t -> t

Move the local origin by a relative vector.

Juxtaposable things

class Juxtaposable a where

Class of things which can be placed "next to" other things, for some appropriate notion of "next to".

Minimal complete definition

juxtapose

Methods

juxtapose :: Vn a -> a -> a -> a

juxtapose v a1 a2 positions a2 next to a1 in the direction of v. In particular, place a2 so that v points from the local origin of a1 towards the old local origin of a2; a1's local origin becomes a2's new local origin. The result is just a translated version of a2. (In particular, this operation does not combine a1 and a2 in any way.)

Instances

(Enveloped b, HasOrigin b) => Juxtaposable [b]

Methods

juxtapose :: Vn [b] -> [b] -> [b] -> [b]

(Enveloped b, HasOrigin b, Ord b) => Juxtaposable (Set b)

Methods

juxtapose :: Vn (Set b) -> Set b -> Set b -> Set b

Juxtaposable a => Juxtaposable (b -> a)

Methods

juxtapose :: Vn (b -> a) -> (b -> a) -> (b -> a) -> b -> a

(Enveloped a, HasOrigin a, Enveloped b, HasOrigin b, (~) (* -> *) (V a) (V b), (~) * (N a) (N b)) => Juxtaposable (a, b)

Methods

juxtapose :: Vn (a, b) -> (a, b) -> (a, b) -> (a, b)

(Enveloped b, HasOrigin b) => Juxtaposable (Map k b)

Methods

juxtapose :: Vn (Map k b) -> Map k b -> Map k b -> Map k b

Juxtaposable a => Juxtaposable (Measured n a)

Methods

juxtapose :: Vn (Measured n a) -> Measured n a -> Measured n a -> Measured n a

(Metric v, OrderedField n) => Juxtaposable (Envelope v n)

Methods

juxtapose :: Vn (Envelope v n) -> Envelope v n -> Envelope v n -> Envelope v n

(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)

Methods

juxtapose :: Vn (QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

juxtaposeDefault :: (Enveloped a, HasOrigin a) => Vn a -> a -> a -> a

Default implementation of juxtapose for things which are instances of Enveloped and HasOrigin. If either envelope is empty, the second object is returned unchanged.

Queries

newtype Query v n m

A query is a function that maps points in a vector space to values in some monoid. Queries naturally form a monoid, with two queries being combined pointwise.

The idea for annotating diagrams with monoidal queries came from the graphics-drawingcombinators package, http://hackage.haskell.org/package/graphics-drawingcombinators.

Constructors

Query

Fields

• runQuery :: Point v n -> m

Instances

Functor v => Corepresentable (Query v)

Associated Types

type Corep (Query v :: * -> * -> *) :: * -> *

Methods

cotabulate :: (Corep (Query v) d -> c) -> Query v d c

Functor v => Profunctor (Query v)

Methods

dimap :: (a -> b) -> (c -> d) -> Query v b c -> Query v a d

lmap :: (a -> b) -> Query v b c -> Query v a c

rmap :: (b -> c) -> Query v a b -> Query v a c

(#.) :: Coercible * c b => (b -> c) -> Query v a b -> Query v a c

(.#) :: Coercible * b a => Query v b c -> (a -> b) -> Query v a c

Functor v => Closed (Query v)

Methods

closed :: Query v a b -> Query v (x -> a) (x -> b)

Functor v => Costrong (Query v)

Methods

unfirst :: Query v (a, d) (b, d) -> Query v a b

unsecond :: Query v (d, a) (d, b) -> Query v a b

Functor v => Cosieve (Query v) (Point v)

Methods

cosieve :: Query v a b -> Point v a -> b

Monad (Query v n)

Methods

(>>=) :: Query v n a -> (a -> Query v n b) -> Query v n b

(>>) :: Query v n a -> Query v n b -> Query v n b

return :: a -> Query v n a

fail :: String -> Query v n a

Functor (Query v n)

Methods

fmap :: (a -> b) -> Query v n a -> Query v n b

(<$) :: a -> Query v n b -> Query v n a

Applicative (Query v n)

Methods

pure :: a -> Query v n a

(<*>) :: Query v n (a -> b) -> Query v n a -> Query v n b

(*>) :: Query v n a -> Query v n b -> Query v n b

(<*) :: Query v n a -> Query v n b -> Query v n a

Distributive (Query v n)

Methods

distribute :: Functor f => f (Query v n a) -> Query v n (f a)

collect :: Functor f => (a -> Query v n b) -> f a -> Query v n (f b)

distributeM :: Monad m => m (Query v n a) -> Query v n (m a)

collectM :: Monad m => (a -> Query v n b) -> m a -> Query v n (m b)

Representable (Query v n)

Associated Types

type Rep (Query v n :: * -> *) :: *

Methods

tabulate :: (Rep (Query v n) -> a) -> Query v n a

index :: Query v n a -> Rep (Query v n) -> a

Semigroup m => Semigroup (Query v n m)

Methods

(<>) :: Query v n m -> Query v n m -> Query v n m

sconcat :: NonEmpty (Query v n m) -> Query v n m

stimes :: Integral b => b -> Query v n m -> Query v n m

Monoid m => Monoid (Query v n m)

Methods

mempty :: Query v n m

mappend :: Query v n m -> Query v n m -> Query v n m

mconcat :: [Query v n m] -> Query v n m

Wrapped (Query v n m)

Associated Types

type Unwrapped (Query v n m) :: *

Methods

_Wrapped' :: Iso' (Query v n m) (Unwrapped (Query v n m))

(Additive v, Num n) => HasOrigin (Query v n m)

Methods

moveOriginTo :: Point (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m

(Additive v, Num n) => Transformable (Query v n m)

Methods

transform :: Transformation (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m

Rewrapped (Query v a m) (Query v' a' m')

type Corep (Query v)

type Corep (Query v) = Point v

type Rep (Query v n)

type Rep (Query v n) = Point v n

type Unwrapped (Query v n m)

type Unwrapped (Query v n m) = Point v n -> m

type N (Query v n m)

type N (Query v n m) = n

type V (Query v n m)

type V (Query v n m) = v

Primitives

data Prim b v n where

A value of type Prim b v n is an opaque (existentially quantified) primitive which backend b knows how to render in vector space v.

Constructors

Prim :: (Transformable p, Typeable p, Renderable p b) => p -> Prim b (V p) (N p)

Instances

Transformable (Prim b v n)

The Transformable instance for Prim just pushes calls to transform down through the Prim constructor.

Methods

transform :: Transformation (V (Prim b v n)) (N (Prim b v n)) -> Prim b v n -> Prim b v n

Renderable (Prim b v n) b

The Renderable instance for Prim just pushes calls to render down through the Prim constructor.

Methods

render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n))

type N (Prim b v n)

type N (Prim b v n) = n

type V (Prim b v n)

type V (Prim b v n) = v

Diagrams

data QDiagram b v n m

The fundamental diagram type. The type variables are as follows:

• b represents the backend, such as SVG or Cairo. Note that each backend also exports a type synonym B for itself, so the type variable b may also typically be instantiated by B, meaning "use whatever backend is in scope".
• v represents the vector space of the diagram. Typical instantiations include V2 (for a two-dimensional diagram) or V3 (for a three-dimensional diagram).
• n represents the numerical field the diagram uses. Typically this will be a concrete numeric type like Double.
• m is the monoidal type of "query annotations": each point in the diagram has a value of type m associated to it, and these values are combined according to the Monoid instance for m. Most often, m is simply instantiated to Any, associating a simple Bool value to each point indicating whether the point is inside the diagram; Diagram is a synonym for QDiagram with m thus instantiated to Any.

Diagrams can be combined via their Monoid instance, transformed via their Transformable instance, and assigned attributes via their HasStyle instance.

Note that the Q in QDiagram stands for "Queriable", as distinguished from Diagram, where m is fixed to Any. This is not really a very good name, but it's probably not worth changing it at this point.

Instances

Functor (QDiagram b v n)

Methods

fmap :: (a -> b) -> QDiagram b v n a -> QDiagram b v n b

(<$) :: a -> QDiagram b v n b -> QDiagram b v n a

(Metric v, OrderedField n, Semigroup m) => Semigroup (QDiagram b v n m)

Methods

(<>) :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

sconcat :: NonEmpty (QDiagram b v n m) -> QDiagram b v n m

stimes :: Integral b => b -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Monoid (QDiagram b v n m)

Diagrams form a monoid since each of their components do: the empty diagram has no primitives, an empty envelope, an empty trace, no named subdiagrams, and a constantly empty query function.

Diagrams compose by aligning their respective local origins. The new diagram has all the primitives and all the names from the two diagrams combined, and query functions are combined pointwise. The first diagram goes on top of the second. "On top of" probably only makes sense in vector spaces of dimension lower than 3, but in theory it could make sense for, say, 3-dimensional diagrams when viewed by 4-dimensional beings.

Methods

mempty :: QDiagram b v n m

mappend :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

mconcat :: [QDiagram b v n m] -> QDiagram b v n m

Wrapped (QDiagram b v n m)

Associated Types

type Unwrapped (QDiagram b v n m) :: *

Methods

_Wrapped' :: Iso' (QDiagram b v n m) (Unwrapped (QDiagram b v n m))

(Metric v, OrderedField n, Semigroup m) => HasOrigin (QDiagram b v n m)

Every diagram has an intrinsic "local origin" which is the basis for all combining operations.

Methods

moveOriginTo :: Point (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)

Diagrams can be transformed by transforming each of their components appropriately.

Methods

transform :: Transformation (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Qualifiable (QDiagram b v n m)

Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix.

Methods

(.>>) :: IsName a => a -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)

Methods

applyStyle :: Style (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)

Methods

getTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m))

(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)

Methods

getEnvelope :: QDiagram b v n m -> Envelope (V (QDiagram b v n m)) (N (QDiagram b v n m))

(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)

Methods

juxtapose :: Vn (QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

Rewrapped (QDiagram b v n m) (QDiagram b' v' n' m')

type Unwrapped (QDiagram b v n m)

type Unwrapped (QDiagram b v n m) = DUALTree (DownAnnots v n) (UpAnnots b v n m) Annotation (QDiaLeaf b v n m)

type N (QDiagram b v n m)

type N (QDiagram b v n m) = n

type V (QDiagram b v n m)

type V (QDiagram b v n m) = v

type Diagram b = QDiagram b (V b) (N b) Any

Diagram b is a synonym for QDiagram b (V b) (N b) Any. That is, the default sort of diagram is one where querying at a point simply tells you whether the diagram contains that point or not. Transforming a default diagram into one with a more interesting query can be done via the Functor instance of QDiagram b v n or the value function.

mkQD :: Prim b v n -> Envelope v n -> Trace v n -> SubMap b v n m -> Query v n m -> QDiagram b v n m

Create a diagram from a single primitive, along with an envelope, trace, subdiagram map, and query function.

pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.

envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n)

Lens onto the Envelope of a QDiagram.

trace :: (Metric v, OrderedField n, Semigroup m) => Lens' (QDiagram b v n m) (Trace v n)

Lens onto the Trace of a QDiagram.

subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m)

Lens onto the SubMap of a QDiagram (i.e. an association from names to subdiagrams).

names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m -> [(Name, [Point v n])]

Get a list of names of subdiagrams and their locations.

query :: Monoid m => QDiagram b v n m -> Query v n m

Get the query function associated with a diagram.

nameSub :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Subdiagram b v n m) -> nm -> QDiagram b v n m -> QDiagram b v n m

Attach an atomic name to a certain subdiagram, computed from the given diagram /with the mapping from name to subdiagram included/. The upshot of this knot-tying is that if d' = d # named x, then lookupName x d' == Just d' (instead of Just d).

withName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> (Subdiagram b v n m -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a name and a diagram transformation indexed by a subdiagram, perform the transformation using the most recent subdiagram associated with (some qualification of) the name, or perform the identity transformation if the name does not exist.

withNameAll :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a name and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the collection of all such subdiagrams associated with (some qualification of) the given name.

withNames :: (IsName nm, Metric v, Semigroup m, OrderedField n) => [nm] -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a list of names and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the list of most recent subdiagrams associated with (some qualification of) each name. Do nothing (the identity transformation) if any of the names do not exist.

localize :: forall b v n m. (Metric v, OrderedField n, Semigroup m) => QDiagram b v n m -> QDiagram b v n m

"Localize" a diagram by hiding all the names, so they are no longer visible to the outside.

href :: (Metric v, OrderedField n, Semigroup m) => String -> QDiagram b v n m -> QDiagram b v n m

Make a diagram into a hyperlink. Note that only some backends will honor hyperlink annotations.

opacityGroup :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m

Change the transparency of a Diagram as a group.

groupOpacity :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m

Change the transparency of a Diagram as a group.

setEnvelope :: forall b v n m. (OrderedField n, Metric v, Monoid' m) => Envelope v n -> QDiagram b v n m -> QDiagram b v n m

Replace the envelope of a diagram.

setTrace :: forall b v n m. (OrderedField n, Metric v, Semigroup m) => Trace v n -> QDiagram b v n m -> QDiagram b v n m

Replace the trace of a diagram.

atop :: (OrderedField n, Metric v, Semigroup m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m infixl 6

A convenient synonym for mappend on diagrams, designed to be used infix (to help remember which diagram goes on top of which when combining them, namely, the first on top of the second).

Subdiagrams

data Subdiagram b v n m

A Subdiagram represents a diagram embedded within the context of a larger diagram. Essentially, it consists of a diagram paired with any accumulated information from the larger context (transformations, attributes, etc.).

Constructors

Subdiagram (QDiagram b v n m) (DownAnnots v n)

Instances

Functor (Subdiagram b v n)

Methods

fmap :: (a -> b) -> Subdiagram b v n a -> Subdiagram b v n b

(<$) :: a -> Subdiagram b v n b -> Subdiagram b v n a

(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)

Methods

moveOriginTo :: Point (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

Transformable (Subdiagram b v n m)

Methods

transform :: Transformation (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)

Methods

getTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)

Methods

getEnvelope :: Subdiagram b v n m -> Envelope (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

type N (Subdiagram b v n m)

type N (Subdiagram b v n m) = n

type V (Subdiagram b v n m)

type V (Subdiagram b v n m) = v

mkSubdiagram :: QDiagram b v n m -> Subdiagram b v n m

Turn a diagram into a subdiagram with no accumulated context.

getSub :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> QDiagram b v n m

Turn a subdiagram into a normal diagram, including the enclosing context. Concretely, a subdiagram is a pair of (1) a diagram and (2) a "context" consisting of an extra transformation and attributes. getSub simply applies the transformation and attributes to the diagram to get the corresponding "top-level" diagram.

rawSub :: Subdiagram b v n m -> QDiagram b v n m

Extract the "raw" content of a subdiagram, by throwing away the context.

location :: (Additive v, Num n) => Subdiagram b v n m -> Point v n

Get the location of a subdiagram; that is, the location of its local origin with respect to the vector space of its parent diagram. In other words, the point where its local origin "ended up".

subPoint :: (Metric v, OrderedField n) => Point v n -> Subdiagram b v n m

Create a "point subdiagram", that is, a pointDiagram (with no content and a point envelope) treated as a subdiagram with local origin at the given point. Note this is not the same as mkSubdiagram . pointDiagram, which would result in a subdiagram with local origin at the parent origin, rather than at the given point.

Measurements

data Measured n a

'Measured n a' is an object that depends on local, normalized and global scales. The normalized and global scales are calculated when rendering a diagram.

For attributes, the local scale gets multiplied by the average scale of the transform.

Instances

Profunctor Measured

Methods

dimap :: (a -> b) -> (c -> d) -> Measured b c -> Measured a d

lmap :: (a -> b) -> Measured b c -> Measured a c

rmap :: (b -> c) -> Measured a b -> Measured a c

(#.) :: Coercible * c b => (b -> c) -> Measured a b -> Measured a c

(.#) :: Coercible * b a => Measured b c -> (a -> b) -> Measured a c

Monad (Measured n)

Methods

(>>=) :: Measured n a -> (a -> Measured n b) -> Measured n b

(>>) :: Measured n a -> Measured n b -> Measured n b

return :: a -> Measured n a

fail :: String -> Measured n a

Functor (Measured n)

Methods

fmap :: (a -> b) -> Measured n a -> Measured n b

(<$) :: a -> Measured n b -> Measured n a

Applicative (Measured n)

Methods

pure :: a -> Measured n a

(<*>) :: Measured n (a -> b) -> Measured n a -> Measured n b

(*>) :: Measured n a -> Measured n b -> Measured n b

(<*) :: Measured n a -> Measured n b -> Measured n a

Distributive (Measured n)

Methods

distribute :: Functor f => f (Measured n a) -> Measured n (f a)

collect :: Functor f => (a -> Measured n b) -> f a -> Measured n (f b)

distributeM :: Monad m => m (Measured n a) -> Measured n (m a)

collectM :: Monad m => (a -> Measured n b) -> m a -> Measured n (m b)

Representable (Measured n)

Associated Types

type Rep (Measured n :: * -> *) :: *

Methods

tabulate :: (Rep (Measured n) -> a) -> Measured n a

index :: Measured n a -> Rep (Measured n) -> a

Additive (Measured n)

Methods

zero :: Num a => Measured n a

(^+^) :: Num a => Measured n a -> Measured n a -> Measured n a

(^-^) :: Num a => Measured n a -> Measured n a -> Measured n a

lerp :: Num a => a -> Measured n a -> Measured n a -> Measured n a

liftU2 :: (a -> a -> a) -> Measured n a -> Measured n a -> Measured n a

liftI2 :: (a -> b -> c) -> Measured n a -> Measured n b -> Measured n c

Floating a => Floating (Measured n a)

Methods

pi :: Measured n a

exp :: Measured n a -> Measured n a

log :: Measured n a -> Measured n a

sqrt :: Measured n a -> Measured n a

(**) :: Measured n a -> Measured n a -> Measured n a

logBase :: Measured n a -> Measured n a -> Measured n a

sin :: Measured n a -> Measured n a

cos :: Measured n a -> Measured n a

tan :: Measured n a -> Measured n a

asin :: Measured n a -> Measured n a

acos :: Measured n a -> Measured n a

atan :: Measured n a -> Measured n a

sinh :: Measured n a -> Measured n a

cosh :: Measured n a -> Measured n a

tanh :: Measured n a -> Measured n a

asinh :: Measured n a -> Measured n a

acosh :: Measured n a -> Measured n a

atanh :: Measured n a -> Measured n a

log1p :: Measured n a -> Measured n a

expm1 :: Measured n a -> Measured n a

log1pexp :: Measured n a -> Measured n a

log1mexp :: Measured n a -> Measured n a

Fractional a => Fractional (Measured n a)

Methods

(/) :: Measured n a -> Measured n a -> Measured n a

recip :: Measured n a -> Measured n a

fromRational :: Rational -> Measured n a

Num a => Num (Measured n a)

Methods

(+) :: Measured n a -> Measured n a -> Measured n a

(-) :: Measured n a -> Measured n a -> Measured n a

(*) :: Measured n a -> Measured n a -> Measured n a

negate :: Measured n a -> Measured n a

abs :: Measured n a -> Measured n a

signum :: Measured n a -> Measured n a

fromInteger :: Integer -> Measured n a

Semigroup a => Semigroup (Measured n a)

Methods

(<>) :: Measured n a -> Measured n a -> Measured n a

sconcat :: NonEmpty (Measured n a) -> Measured n a

stimes :: Integral b => b -> Measured n a -> Measured n a

Monoid a => Monoid (Measured n a)

Methods

mempty :: Measured n a

mappend :: Measured n a -> Measured n a -> Measured n a

mconcat :: [Measured n a] -> Measured n a

HasOrigin t => HasOrigin (Measured n t)

Methods

moveOriginTo :: Point (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t

(InSpace v n t, Transformable t, HasLinearMap v, Floating n) => Transformable (Measured n t)

Methods

transform :: Transformation (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t

Qualifiable a => Qualifiable (Measured n a)

Methods

(.>>) :: IsName a => a -> Measured n a -> Measured n a

HasStyle b => HasStyle (Measured n b)

Methods

applyStyle :: Style (V (Measured n b)) (N (Measured n b)) -> Measured n b -> Measured n b

Juxtaposable a => Juxtaposable (Measured n a)

Methods

juxtapose :: Vn (Measured n a) -> Measured n a -> Measured n a -> Measured n a

MonadReader (n, n, n) (Measured n)

Methods

ask :: Measured n (n, n, n)

local :: ((n, n, n) -> (n, n, n)) -> Measured n a -> Measured n a

reader :: ((n, n, n) -> a) -> Measured n a

type Rep (Measured n)

type Rep (Measured n) = (n, n, n)

type N (Measured n a)

type N (Measured n a) = N a

type V (Measured n a)

type V (Measured n a) = V a

type Measure n = Measured n n

A measure is a Measured number.

fromMeasured :: Num n => n -> n -> Measured n a -> a

fromMeasured globalScale normalizedScale measure -> a

output :: n -> Measure n

Output units don't change.

local :: Num n => n -> Measure n

Local units are scaled by the average scale of a transform.

global :: Num n => n -> Measure n

Global units are scaled so that they are interpreted relative to the size of the final rendered diagram.

normalized :: Num n => n -> Measure n

Normalized units get scaled so that one normalized unit is the size of the final diagram.

scaleLocal :: Num n => n -> Measured n a -> Measured n a

Scale the local units of a Measured thing.

atLeast :: Ord n => Measure n -> Measure n -> Measure n

Calculate the smaller of two measures.

atMost :: Ord n => Measure n -> Measure n -> Measure n

Calculate the larger of two measures.

Backends

class Backend b v n where

Abstract diagrams are rendered to particular formats by backends. Each backend/vector space combination must be an instance of the Backend class.

A minimal complete definition consists of Render, Result, Options, and renderRTree. However, most backends will want to implement adjustDia as well; the default definition does nothing. Some useful standard definitions are provided in the Diagrams.TwoD.Adjust module from the diagrams-lib package.

Minimal complete definition

renderRTree

Associated Types

data Render b v n :: *

An intermediate representation used for rendering primitives. (Typically, this will be some sort of monad, but it need not be.) The Renderable class guarantees that a backend will be able to convert primitives into this type; how these rendered primitives are combined into an ultimate Result is completely up to the backend.

type Result b v n :: *

The result of running/interpreting a rendering operation.

data Options b v n :: *

Backend-specific rendering options.

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => b -> Options b v n -> QDiagram b v n m -> (Options b v n, Transformation v n, QDiagram b v n m)

adjustDia allows the backend to make adjustments to the final diagram (e.g. to adjust the size based on the options) before rendering it. It returns a modified options record, the transformation applied to the diagram (which can be used to convert attributes whose value is Measure, or transform e.g. screen coordinates back into local diagram coordinates), and the adjusted diagram itself.

See the diagrams-lib package (particularly the Diagrams.TwoD.Adjust module) for some useful implementations.

renderRTree :: b -> Options b v n -> RTree b v n Annotation -> Result b v n

Given some options, take a representation of a diagram as a tree and render it. The RTree has already been simplified and has all measurements converted to Output units.

Instances

Backend NullBackend v n

Associated Types

data Render NullBackend (v :: * -> *) n :: *

type Result NullBackend (v :: * -> *) n :: *

data Options NullBackend (v :: * -> *) n :: *

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m)

renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n

class Transformable t => Renderable t b where

The Renderable type class connects backends to primitives which they know how to render.

Minimal complete definition

render

Methods

render :: b -> t -> Render b (V t) (N t)

Given a token representing the backend and a transformable object, render it in the appropriate rendering context.

Instances

Renderable (Prim b v n) b

The Renderable instance for Prim just pushes calls to render down through the Prim constructor.

Methods

render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n))

renderDia :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> Result b v n

Render a diagram.

renderDiaT :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> (Transformation v n, Result b v n)

Render a diagram, returning also the transformation which was used to convert the diagram from its ("global") coordinate system into the output coordinate system. The inverse of this transformation can be used, for example, to convert output/screen coordinates back into diagram coordinates. See also adjustDia.

The null backend

data NullBackend

A null backend which does no actual rendering. It is provided mainly for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't actually care which one. See D for more explanation and examples.

It is courteous, when defining a new primitive P, to make an instance

instance Renderable P NullBackend where
  render _ _ = mempty

This ensures that the trick with D annotations can be used for diagrams containing your primitive.

Instances

Backend NullBackend v n

Associated Types

data Render NullBackend (v :: * -> *) n :: *

type Result NullBackend (v :: * -> *) n :: *

data Options NullBackend (v :: * -> *) n :: *

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m)

renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n

Monoid (Render NullBackend v n)

Methods

mempty :: Render NullBackend v n

mappend :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n

mconcat :: [Render NullBackend v n] -> Render NullBackend v n

data Render NullBackend

data Render NullBackend = NullBackendRender

data Options NullBackend

data Options NullBackend

type Result NullBackend v n

type Result NullBackend v n = ()

type D v n = QDiagram NullBackend v n Any

The D type is provided for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't care which one. Such situations arise when you pass a diagram to a function which is polymorphic in its input but monomorphic in its output, such as width, height, phantom, or names. Such functions compute some property of the diagram, or use it to accomplish some other purpose, but do not result in the diagram being rendered. If the diagram does not have a monomorphic type, GHC complains that it cannot determine the diagram's type.

For example, here is the error we get if we try to compute the width of an image (this example requires diagrams-lib):

  ghci> width (image (uncheckedImageRef "foo.png" 200 200))
  <interactive>:11:8:
      No instance for (Renderable (DImage n0 External) b0)
        arising from a use of image
      The type variables n0, b0 are ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      Note: there is a potential instance available:
        instance Fractional n => Renderable (DImage n a) NullBackend
          -- Defined in Image
      Possible fix:
        add an instance declaration for
        (Renderable (DImage n0 External) b0)
      In the first argument of width, namely
        `(image (uncheckedImageRef "foo.png" 200 200))'
      In the expression:
        width (image (uncheckedImageRef "foo.png" 200 200))
      In an equation for it:
          it = width (image (uncheckedImageRef "foo.png" 200 200))
  

GHC complains that there is no instance for Renderable (DImage n0 External) b0; what is really going on is that it does not have enough information to decide what backend to use (hence the uninstantiated n0 and b0). This is annoying because we know that the choice of backend cannot possibly affect the width of the image (it's 200! it's right there in the code!); but there is no way for GHC to know that.

The solution is to annotate the call to image with the type D V2 Double, like so:

  ghci> width (image (uncheckedImageRef "foo.png" 200 200) :: D V2 Double)
  200.00000000000006
  

(It turns out the width wasn't 200 after all...)

As another example, here is the error we get if we try to compute the width of a radius-1 circle:

  ghci> width (circle 1)
  <interactive>:12:1:
      Couldn't match expected type V2 with actual type `V a0'
      The type variable a0 is ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      In the expression: width (circle 1)
      In an equation for it: it = width (circle 1)
  

There's even more ambiguity here. Whereas image always returns a Diagram, the circle function can produce any TrailLike type, and the width function can consume any Enveloped type, so GHC has no idea what type to pick to go in the middle. However, the solution is the same:

  ghci> width (circle 1 :: D V2 Double)
  1.9999999999999998
  

Convenience classes

class (HasBasis v, Traversable v) => HasLinearMap v

HasLinearMap is a poor man's class constraint synonym, just to help shorten some of the ridiculously long constraint sets.

Instances

(HasBasis v, Traversable v) => HasLinearMap v

class (Additive v, Representable v, Rep v ~ E v) => HasBasis v

An Additive vector space whose representation is made up of basis elements.

Instances

(Additive v, Representable v, (~) * (Rep v) (E v)) => HasBasis v

class (Floating s, Ord s) => OrderedField s

When dealing with envelopes we often want scalars to be an ordered field (i.e. support all four arithmetic operations and be totally ordered) so we introduce this class as a convenient shorthand.

Instances

(Floating s, Ord s) => OrderedField s

class (Typeable n, RealFloat n) => TypeableFloat n

Class of numbers that are RealFloat and Typeable. This class is used to shorten type constraints.

Instances

(Typeable * n, RealFloat n) => TypeableFloat n

class (Semigroup m, Monoid m) => Monoid' m

The Monoid' class is a synonym for things which are instances of both Semigroup and Monoid. Ideally, the Monoid class itself will eventually include a Semigroup superclass and we can get rid of this.

Instances

(Semigroup m, Monoid m) => Monoid' m