Copyright  (c) 20112015 diagramscore team (see LICENSE) 

License  BSDstyle (see LICENSE) 
Maintainer  diagramsdiscuss@googlegroups.com 
Safe Haskell  None 
Language  Haskell2010 
The core library of primitives forming the basis of an embedded
domainspecific 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 diagramslib package,
which reexports 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 reexports useful functionality from other modules in the core library. Library writers needing finergrained 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#typereference 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
 type family V a :: * > *
 type family N a :: *
 type Vn a = V a (N a)
 class (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
 data Point f a :: (* > *) > * > *
 origin :: (Additive f, Num a) => Point f a
 (*.) :: (Functor v, Num n) => n > Point v n > Point v n
 relative :: (Additive f, Num a) => Point f a > Iso' (Point f a) (f a)
 basis :: (Additive t, Traversable t, Num a) => [t a]
 dimension :: forall a v. (V a ~ v, Additive v, Traversable v) => a > Int
 determinant :: (Additive v, Traversable v, Num n) => Transformation v n > n
 isReflection :: (Additive v, Traversable v, Num n, Ord n) => Transformation v n > Bool
 data u :: v
 (<>) :: (u > v) > (v > u) > u :: v
 linv :: (u :: v) > v :: u
 lapp :: (u :: v) > u > v
 data Transformation v n
 inv :: (Functor v, Num n) => Transformation v n > Transformation v n
 transp :: Transformation v n > v n :: v n
 transl :: Transformation v n > v n
 dropTransl :: (Additive v, Num n) => Transformation v n > Transformation v n
 apply :: Transformation v n > v n > v n
 papply :: (Additive v, Num n) => Transformation v n > Point v n > Point v n
 fromLinear :: (Additive v, Num n) => (v n :: v n) > (v n :: v n) > Transformation v n
 translation :: v n > Transformation v n
 translate :: (Num (N t), Transformable t) => Vn t > t > t
 moveTo :: (InSpace v n t, HasOrigin t) => Point v n > t > t
 place :: (InSpace v n t, HasOrigin t) => t > Point v n > t
 scaling :: (Additive v, Fractional n) => n > Transformation v n
 scale :: (InSpace v n a, Eq n, Fractional n, Transformable a) => n > a > a
 avgScale :: (Additive v, Traversable v, Floating n) => Transformation v n > n
 class Transformable t where
 transform :: Transformation (V t) (N t) > t > t
 newtype TransInv t = TransInv t
 eye :: (HasBasis v, Num n) => v (v n)
 data AName
 data Name
 class (Typeable a, Ord a, Show a) => IsName a where
 class Qualifiable q where
 (.>) :: (IsName a1, IsName a2) => a1 > a2 > Name
 newtype SubMap b v n m = SubMap (Map Name [Subdiagram b v n m])
 fromNames :: IsName a => [(a, Subdiagram b v n m)] > SubMap b v n m
 rememberAs :: IsName a => a > QDiagram b v n m > SubMap b v n m > SubMap b v n m
 lookupSub :: IsName nm => nm > SubMap b v n m > Maybe [Subdiagram b v n m]
 class (Typeable a, Semigroup a) => AttributeClass a
 data Attribute v n :: * where
 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
 data Style v n
 class HasStyle a where
 applyStyle :: Style (V a) (N a) > a > a
 getAttr :: forall a v n. AttributeClass a => Style v n > Maybe a
 atAttr :: AttributeClass a => Lens' (Style v n) (Maybe a)
 atMAttr :: (AttributeClass a, Typeable n) => Lens' (Style v n) (Maybe (Measured n a))
 atTAttr :: (V a ~ v, N a ~ n, AttributeClass a, Transformable a) => Lens' (Style v n) (Maybe a)
 applyAttr :: (AttributeClass a, HasStyle d) => a > d > d
 applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d, Typeable n) => Measured n a > d > d
 applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, N a ~ N d, HasStyle d) => a > d > d
 newtype Envelope v n = Envelope (Option (v n > Max n))
 appEnvelope :: Envelope v n > Maybe (v n > n)
 onEnvelope :: ((v n > n) > v n > n) > Envelope v n > Envelope v n
 mkEnvelope :: (v n > n) > Envelope v n
 class (Metric (V a), OrderedField (N a)) => Enveloped a where
 getEnvelope :: a > Envelope (V a) (N a)
 envelopeVMay :: Enveloped a => Vn a > a > Maybe (Vn a)
 envelopeV :: Enveloped a => Vn a > a > Vn a
 envelopePMay :: (V a ~ v, N a ~ n, Enveloped a) => v n > a > Maybe (Point v n)
 envelopeP :: (V a ~ v, N a ~ n, Enveloped a) => v n > a > Point v n
 diameter :: (V a ~ v, N a ~ n, Enveloped a) => v n > a > n
 radius :: (V a ~ v, N a ~ n, Enveloped a) => v n > a > n
 size :: (V a ~ v, N a ~ n, Enveloped a, HasBasis v) => a > v n
 newtype Trace v n = Trace {
 appTrace :: Point v n > v n > SortedList n
 data SortedList a
 mkSortedList :: Ord a => [a] > SortedList a
 getSortedList :: SortedList a > [a]
 mkTrace :: (Point v n > v n > SortedList n) > Trace v n
 class (Additive (V a), Ord (N a)) => Traced a where
 traceV :: (n ~ N a, Num n, Traced a) => Point (V a) n > V a n > a > Maybe (V a n)
 traceP :: (n ~ N a, Traced a, Num n) => Point (V a) n > V a n > a > Maybe (Point (V a) n)
 maxTraceV :: (n ~ N a, Num n, Traced a) => Point (V a) n > V a n > a > Maybe (V a n)
 maxTraceP :: (n ~ N a, Num n, Traced a) => Point (V a) n > V a n > a > Maybe (Point (V a) n)
 rayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n > V a n > a > Maybe (V a n)
 rayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n > V a n > a > Maybe (Point (V a) n)
 maxRayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n > V a n > a > Maybe (V a n)
 maxRayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n > V a n > a > Maybe (Point (V a) n)
 class HasOrigin t where
 moveOriginTo :: Point (V t) (N t) > t > t
 moveOriginBy :: (V t ~ v, N t ~ n, Num n, HasOrigin t) => v n > t > t
 class Juxtaposable a where
 juxtaposeDefault :: (Enveloped a, HasOrigin a) => Vn a > a > a > a
 newtype Query v n m = Query {}
 data Prim b v n where
 Prim :: (Transformable p, Typeable p, Renderable p b) => p > Prim b (V p) (N p)
 data QDiagram b v n m
 type Diagram b = QDiagram b (V b) (N b) Any
 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
 pointDiagram :: (Metric v, Fractional n) => Point v n > QDiagram b v n m
 envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n)
 trace :: (Metric v, OrderedField n, Semigroup m) => Lens' (QDiagram b v n m) (Trace v n)
 subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m)
 names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m > [(Name, [Point v n])]
 query :: Monoid m => QDiagram b v n m > Query v n m
 sample :: Monoid m => QDiagram b v n m > Point v n > m
 value :: Monoid m => m > QDiagram b v n Any > QDiagram b v n m
 resetValue :: (Eq m, Monoid m) => QDiagram b v n m > QDiagram b v n Any
 clearValue :: QDiagram b v n m > QDiagram b v n Any
 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
 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
 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
 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
 localize :: forall b v n m. (Metric v, OrderedField n, Semigroup m) => QDiagram b v n m > QDiagram b v n m
 href :: (Metric v, OrderedField n, Semigroup m) => String > QDiagram b v n m > QDiagram b v n m
 opacityGroup :: (Metric v, OrderedField n, Semigroup m) => Double > QDiagram b v n m > QDiagram b v n m
 groupOpacity :: (Metric v, OrderedField n, Semigroup m) => Double > QDiagram b v n m > QDiagram b v n m
 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
 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
 atop :: (OrderedField n, Metric v, Semigroup m) => QDiagram b v n m > QDiagram b v n m > QDiagram b v n m
 data Subdiagram b v n m = Subdiagram (QDiagram b v n m) (DownAnnots v n)
 mkSubdiagram :: QDiagram b v n m > Subdiagram b v n m
 getSub :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m > QDiagram b v n m
 rawSub :: Subdiagram b v n m > QDiagram b v n m
 location :: (Additive v, Num n) => Subdiagram b v n m > Point v n
 subPoint :: (Metric v, OrderedField n, Semigroup m) => Point v n > Subdiagram b v n m
 data Measured n a
 type Measure n = Measured n n
 fromMeasured :: Num n => n > n > Measured n a > a
 output :: Num n => n > Measure n
 local :: Num n => n > Measure n
 global :: Num n => n > Measure n
 normalized :: Num n => n > Measure n
 scaleLocal :: Num n => n > Measured n a > Measured n a
 atLeast :: Ord n => Measure n > Measure n > Measure n
 atMost :: Ord n => Measure n > Measure n > Measure n
 class Backend b v n where
 class Transformable t => Renderable t b where
 renderDia :: (Backend b v n, HasLinearMap v, Metric v, Typeable v, Typeable n, OrderedField n, Monoid' m) => b > Options b v n > QDiagram b v n m > Result b v n
 renderDiaT :: (Backend b v n, HasLinearMap v, Metric v, Typeable v, Typeable n, OrderedField n, Monoid' m) => b > Options b v n > QDiagram b v n m > (Transformation v n, Result b v n)
 data NullBackend
 type D v n = QDiagram NullBackend v n Any
 class (HasBasis v, Traversable v) => HasLinearMap v
 class (Additive v, Representable v, Rep v ~ E v) => HasBasis v
 class (Floating s, Ord s) => OrderedField s
 class (Typeable n, RealFloat n) => TypeableFloat n
 class (Semigroup m, Monoid m) => Monoid' m
Associated vector spaces
type family V a :: * > * Source
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.
type V [a] = V a  
type V (Set a) = V a  
type V (Split m) = V m  
type V (Deletable m) = V m  
type V (Option a) = V a  
type V (TransInv t) = V t  
type V (a > b) = V b  
type V (a, b) = V a  
type V (Map k a) = V a  
type V (Point v n) = v  
type V ((:+:) m n) = V m  
type V (Measured n a) = V a  
type V (Transformation v n) = v  
type V (Style v n) = v  
type V (Attribute v n) = v  
type V (Trace v n) = v  
type V (Envelope v n) = v  
type V (a, b, c) = V a  
type V (Query v n m) = v  
type V (Prim b v n) = v  
type V (SubMap b v n m) = v  
type V (Subdiagram b v n m) = v  
type V (QDiagram b v n m) = v 
The numerical field for the object, the number type used for calculations.
type N [a] = N a  
type N (Set a) = N a  
type N (Split m) = N m  
type N (Deletable m) = N m  
type N (Option a) = N a  
type N (TransInv t) = N t  
type N (a > b) = N b  
type N (a, b) = N a  
type N (Map k a) = N a  
type N (Point v n) = n  
type N ((:+:) m n) = N m  
type N (Measured n a) = N a  
type N (Transformation v n) = n  
type N (Style v n) = n  
type N (Attribute v n) = n  
type N (Trace v n) = n  
type N (Envelope v n) = n  
type N (a, b, c) = N a  
type N (Query v n m) = n  
type N (Prim b v n) = n  
type N (SubMap b v n m) = n  
type N (Subdiagram b v n m) = n  
type N (QDiagram b v n m) = n 
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 b, N a ~ N b) => SameSpace a b Source
SameSpace a b
means the types a
and b
belong to the same
vector space v n
.
Points
data Point f a :: (* > *) > * > *
A handy wrapper to help distinguish points from vectors at the type level
Monad f => Monad (Point f)  
Functor f => Functor (Point f)  
Applicative f => Applicative (Point f)  
Foldable f => Foldable (Point f)  
Traversable f => Traversable (Point f)  
Generic1 (Point f)  
Distributive f => Distributive (Point f)  
Representable f => Representable (Point f)  
Serial1 f => Serial1 (Point f)  
Additive f => Affine (Point f)  
R4 f => R4 (Point f)  
R3 f => R3 (Point f)  
R2 f => R2 (Point f)  
R1 f => R1 (Point f)  
Metric f => Metric (Point f)  
Additive f => Additive (Point f)  
Apply f => Apply (Point f)  
Bind f => Bind (Point f)  
Eq1 f => Eq1 (Point f)  
Ord1 f => Ord1 (Point f)  
Read1 f => Read1 (Point f)  
Show1 f => Show1 (Point f)  
Eq (f a) => Eq (Point f a)  
Fractional (f a) => Fractional (Point f a)  
(Data (f a), Typeable (* > *) f, Typeable * a) => Data (Point f a)  
Num (f a) => Num (Point f a)  
Ord (f a) => Ord (Point f a)  
Read (f a) => Read (Point f a)  
Show (f a) => Show (Point f a)  
Ix (f a) => Ix (Point f a)  
Generic (Point f a)  
Storable (f a) => Storable (Point f a)  
Binary (f a) => Binary (Point f a)  
Serial (f a) => Serial (Point f a)  
Serialize (f a) => Serialize (Point f a)  
Hashable (f a) => Hashable (Point f a)  
Ixed (f a) => Ixed (Point f a)  
Wrapped (Point f a)  
Epsilon (f a) => Epsilon (Point f a)  
(Additive v, Num n) => HasOrigin (Point v n)  
(Additive v, Num n) => Transformable (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 floatingpoint inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope). 
(OrderedField n, Metric v) => Enveloped (Point v n)  
Typeable ((* > *) > * > *) Point  
(~) * t (Point g b) => Rewrapped (Point f a) t  
Traversable f => Each (Point f a) (Point f b) a b  
type Rep1 (Point f) = D1 D1Point (C1 C1_0Point (S1 NoSelector (Rec1 f)))  
type Rep (Point f) = Rep f  
type Diff (Point f) = f  
type Rep (Point f a) = D1 D1Point (C1 C1_0Point (S1 NoSelector (Rec0 (f a))))  
type Index (Point f a) = Index (f a)  
type IxValue (Point f a) = IxValue (f a)  
type Unwrapped (Point f a) = f a  
type N (Point v n) = n  
type V (Point v n) = v 
(*.) :: (Functor v, Num n) => n > Point v n > Point v n Source
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 v. (V a ~ v, Additive v, Traversable v) => a > Int Source
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 Source
The determinant of (the linear part of) a Transformation
.
isReflection :: (Additive v, Traversable v, Num n, Ord n) => Transformation v n > Bool Source
Determine whether a Transformation
includes a reflection
component, that is, whether it reverses orientation.
Invertible linear transformations
(v1 :: v2)
is a linear map paired with its inverse.
(<>) :: (u > v) > (v > u) > u :: v Source
Create an invertible linear map from two functions which are assumed to be linear inverses.
General transformations
data Transformation v n Source
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, noninvertible transformations, see
Diagrams.Deform
(in diagramslib
).
(Additive v, Num n) => Monoid (Transformation v n)  
(Additive v, Num n) => Semigroup (Transformation v n)  Transformations are closed under composition; 
(Additive v, Num n) => HasOrigin (Transformation v n)  
(Additive v, Num n) => Transformable (Transformation v n)  
(Transformable a, (~) (* > *) (V a) v, (~) * (N a) n) => Action (Transformation v n) a  Transformations can act on transformable things. 
type N (Transformation v n) = n  
type V (Transformation v n) = v 
inv :: (Functor v, Num n) => Transformation v n > Transformation v n Source
Invert a transformation.
transp :: Transformation v n > v n :: v n Source
Get the transpose of a transformation (ignoring the translation component).
transl :: Transformation v n > v n Source
Get the translational component of a transformation.
dropTransl :: (Additive v, Num n) => Transformation v n > Transformation v n Source
Drop the translational component of a transformation, leaving only the linear part.
apply :: Transformation v n > v n > v n Source
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 Source
Apply a transformation to a point.
fromLinear :: (Additive v, Num n) => (v n :: v n) > (v n :: v n) > Transformation v n Source
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 Source
Create a translation.
moveTo :: (InSpace v n t, HasOrigin t) => Point v n > t > t Source
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 Source
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 Source
Create a uniform scaling transformation.
scale :: (InSpace v n a, Eq n, Fractional n, Transformable a) => n > a > a Source
Scale uniformly in every dimension by the given scalar.
avgScale :: (Additive v, Traversable v, Floating n) => Transformation v n > n Source
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 Source
Type class for things t
which can be transformed.
transform :: Transformation (V t) (N t) > t > t Source
Apply a transformation to an object.
Transformable t => Transformable [t]  
(Transformable t, Ord t) => Transformable (Set t)  
Transformable m => Transformable (Deletable m)  
(Num (N t), Additive (V t), Transformable t) => Transformable (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)  
(Transformable t, Transformable s, (~) (* > *) (V t) (V s), (~) * (N t) (N s)) => Transformable (t, s)  
Transformable t => Transformable (Map k t)  
(Additive v, Num n) => Transformable (Point v n)  
(Additive v, Num n) => Transformable (Transformation v n)  
(Additive v, Traversable v, Floating n) => Transformable (Style v n)  
(Additive v, Traversable v, Floating n) => Transformable (Attribute v n) 

(Additive v, Num n) => Transformable (Trace v n)  
(Metric v, Floating n) => Transformable (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)  
(Additive v, Num n) => Transformable (Query v n m)  
Transformable (Prim b v n)  The 
(Metric v, Floating n) => Transformable (SubMap b v n m)  
(Metric v, Floating n) => Transformable (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. 
Translational invariance
TransInv
is a wrapper which makes a transformable type
translationally invariant; the translational component of
transformations will no longer affect things wrapped in
TransInv
.
TransInv t 
Eq t => Eq (TransInv t)  
Ord t => Ord (TransInv t)  
Show t => Show (TransInv t)  
Monoid t => Monoid (TransInv t)  
Semigroup t => Semigroup (TransInv t)  
Wrapped (TransInv t)  
HasOrigin (TransInv t)  
(Num (N t), Additive (V t), Transformable t) => Transformable (TransInv t)  
Qualifiable a => Qualifiable (TransInv a)  
Traced t => Traced (TransInv t)  
Enveloped t => Enveloped (TransInv t)  
Rewrapped (TransInv t) (TransInv t')  
type Unwrapped (TransInv t) = t  
type N (TransInv t) = N t  
type V (TransInv t) = V t 
Names
A (qualified) name is a (possibly empty) sequence of atomic names.
Eq Name  
Ord Name  
Show Name  
Monoid Name  
Semigroup Name  
Wrapped Name  
Qualifiable Name  Of course, names can be qualified using 
IsName Name  
Typeable * Name  
Rewrapped Name Name  
Action Name a => Action Name (Deletable a)  
Action Name (Trace v n)  
Action Name (Envelope v n)  
Action Name (Query v n m)  
Action Name (SubMap b v n m)  A name acts on a name map by qualifying every name in it. 
type Unwrapped Name = [AName] 
class (Typeable a, Ord a, Show a) => IsName a where Source
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
Nothing
class Qualifiable q where Source
Instances of Qualifiable
are things which can be qualified by
prefixing them with a name.
Qualifiable Name  Of course, names can be qualified using 
Qualifiable a => Qualifiable [a]  
(Ord a, Qualifiable a) => Qualifiable (Set a)  
Qualifiable a => Qualifiable (TransInv a)  
Qualifiable a => Qualifiable (b > a)  
(Qualifiable a, Qualifiable b) => Qualifiable (a, b)  
Qualifiable a => Qualifiable (Map k a)  
Qualifiable a => Qualifiable (Measured n a)  
(Qualifiable a, Qualifiable b, Qualifiable c) => Qualifiable (a, b, c)  
Qualifiable (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. 
(.>) :: (IsName a1, IsName a2) => a1 > a2 > Name infixr 5 Source
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
.
Subdiagram maps
A SubMap
is a map associating names to subdiagrams. There can
be multiple associations for any given name.
SubMap (Map Name [Subdiagram b v n m]) 
Action Name (SubMap b v n m)  A name acts on a name map by qualifying every name in it. 
Functor (SubMap b v n)  
Monoid (SubMap b v n m) 

Semigroup (SubMap b v n m)  
Wrapped (SubMap b v n m)  
(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)  
(Metric v, Floating n) => Transformable (SubMap b v n m)  
Qualifiable (SubMap b v n m) 

Rewrapped (SubMap b v n m) (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) = n  
type V (SubMap b v n m) = v 
fromNames :: IsName a => [(a, Subdiagram b v n m)] > SubMap b v n m Source
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 Source
Add a name/diagram association to a submap.
lookupSub :: IsName nm => nm > SubMap b v n m > Maybe [Subdiagram b v n m] Source
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 Source
data Attribute v n :: * where Source
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.
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 
Typeable * n => Show (Attribute v n)  Shows the kind of attribute and the type contained in the attribute. 
Typeable * n => Semigroup (Attribute v n)  Attributes form a semigroup, where the semigroup operation simply returns the righthand attribute when the types do not match, and otherwise uses the semigroup operation specific to the (matching) types. 
(Additive v, Traversable v, Floating n) => Transformable (Attribute v n) 

Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')  
type N (Attribute v n) = n  
type V (Attribute v n) = v 
A Style
is a heterogeneous collection of attributes, containing
at most one attribute of any given type.
Typeable * n => Show (Style v n)  Show the attributes in the style. 
Typeable * n => Monoid (Style v n)  The empty style contains no attributes. 
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. 
Ixed (Style v n)  
At (Style v n)  
Wrapped (Style v n)  
(Additive v, Traversable v, Floating n) => Transformable (Style v n)  
Typeable * n => HasStyle (Style v n)  
Action (Style v n) m  Styles have no action on other monoids. 
Rewrapped (Style v n) (Style v' n')  
Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')  
type Index (Style v n) = TypeRep  
type IxValue (Style v n) = Attribute v n  
type Unwrapped (Style v n) = HashMap TypeRep (Attribute v n)  
type N (Style v n) = n  
type V (Style v n) = v 
Type class for things which have a style.
applyStyle :: Style (V a) (N a) > a > a Source
Apply a style by combining it (on the left) with the existing style.
HasStyle a => HasStyle [a]  
(HasStyle a, Ord a) => HasStyle (Set a)  
HasStyle b => HasStyle (a > b)  
(HasStyle a, HasStyle b, (~) (* > *) (V a) (V b), (~) * (N a) (N b)) => HasStyle (a, b)  
HasStyle a => HasStyle (Map k a)  
HasStyle b => HasStyle (Measured n b)  
Typeable * n => HasStyle (Style v n)  
(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m) 
getAttr :: forall a v n. AttributeClass a => Style v n > Maybe a Source
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) Source
Lens onto a plain attribute of a style.
atMAttr :: (AttributeClass a, Typeable n) => Lens' (Style v n) (Maybe (Measured n a)) Source
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) Source
Lens onto a transformable attribute of a style.
applyAttr :: (AttributeClass a, HasStyle d) => a > d > d Source
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, Typeable n) => Measured n a > d > d Source
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 Source
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
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 halfplanes, two perpendicular to each axis.
More generally, the intersection of halfplanes 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 halfplane 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)
ontov
iss' *^ v
, thens' <= 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/collectingattributes/#comment2030. See also Brent Yorgey, Monoids: Theme and Variations, published in the 2012 Haskell Symposium: http://www.cis.upenn.edu/~byorgey/pub/monoidpearl.pdf; video: http://www.youtube.com/watch?v=X8NCkD2vOw.
Action Name (Envelope v n)  
Show (Envelope v n)  
Ord n => Monoid (Envelope v n)  
Ord n => Semigroup (Envelope v n)  
Wrapped (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. 
(Metric v, Floating n) => Transformable (Envelope v n)  
(Metric v, OrderedField n) => Enveloped (Envelope v n)  
(Metric v, OrderedField n) => Juxtaposable (Envelope v n)  
Rewrapped (Envelope v n) (Envelope v' n')  
type Unwrapped (Envelope v n) = Option (v n > Max n)  
type N (Envelope v n) = n  
type V (Envelope v n) = v 
appEnvelope :: Envelope v n > Maybe (v n > n) Source
onEnvelope :: ((v n > n) > v n > n) > Envelope v n > Envelope v n Source
mkEnvelope :: (v n > n) > Envelope v n Source
class (Metric (V a), OrderedField (N a)) => Enveloped a where Source
Enveloped
abstracts over things which have an envelope.
getEnvelope :: a > Envelope (V a) (N a) Source
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.
Enveloped b => Enveloped [b]  
Enveloped b => Enveloped (Set b)  
Enveloped t => Enveloped (TransInv t)  
(Enveloped a, Enveloped b, (~) (* > *) (V a) (V b), (~) * (N a) (N b)) => Enveloped (a, b)  
Enveloped b => Enveloped (Map k b)  
(OrderedField n, Metric v) => Enveloped (Point v n)  
(Metric v, OrderedField n) => Enveloped (Envelope v n)  
(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)  
(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m) 
envelopeVMay :: Enveloped a => Vn a > a > Maybe (Vn a) Source
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 Source
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) Source
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 Source
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 Source
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 Source
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 Source
The smallest positive vector that bounds the envelope of an object.
Traces
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)
.
Trace  

Action Name (Trace v n)  
Show (Trace v n)  
Ord n => Monoid (Trace v n)  
Ord n => Semigroup (Trace v n)  
Wrapped (Trace v n)  
(Additive v, Num n) => HasOrigin (Trace v n)  
(Additive v, Num n) => Transformable (Trace v n)  
(Additive v, Ord n) => Traced (Trace v n)  
Rewrapped (Trace v n) (Trace v' n')  
type Unwrapped (Trace v n) = Point v n > v n > SortedList n  
type N (Trace v n) = n  
type V (Trace v n) = v 
data SortedList a Source
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.
Ord a => Monoid (SortedList a) 

Ord a => Semigroup (SortedList a) 

mkSortedList :: Ord a => [a] > SortedList a Source
A smart constructor for the SortedList
type, which sorts the
input to ensure the SortedList
invariant.
getSortedList :: SortedList a > [a] Source
Project the (guaranteed sorted) list out of a SortedList
wrapper.
mkTrace :: (Point v n > v n > SortedList n) > Trace v n Source
class (Additive (V a), Ord (N a)) => Traced a where Source
Traced
abstracts over things which have a trace.
Traced b => Traced [b]  
Traced b => Traced (Set b)  
Traced t => Traced (TransInv t)  
(Traced a, Traced b, SameSpace a b) => Traced (a, b)  
Traced b => Traced (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 floatingpoint inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope). 
(Additive v, Ord n) => Traced (Trace v n)  
(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)  
(Metric v, OrderedField n, Semigroup m) => Traced (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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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) Source
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 Source
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, Trail
s) are
transformable but are translationally invariant, i.e. have no
origin.
moveOriginTo :: Point (V t) (N t) > t > t Source
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.
HasOrigin t => HasOrigin [t]  
(HasOrigin t, Ord t) => HasOrigin (Set t)  
HasOrigin (TransInv t)  
(HasOrigin t, HasOrigin s, SameSpace s t) => HasOrigin (s, t)  
HasOrigin t => HasOrigin (Map k t)  
(Additive v, Num n) => HasOrigin (Point v n)  
HasOrigin t => HasOrigin (Measured n t)  
(Additive v, Num n) => HasOrigin (Transformation v n)  
(Additive v, Num n) => HasOrigin (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. 
(Additive v, Num n) => HasOrigin (Query v n m)  
(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)  
(Metric v, OrderedField n) => HasOrigin (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. 
moveOriginBy :: (V t ~ v, N t ~ n, Num n, HasOrigin t) => v n > t > t Source
Move the local origin by a relative vector.
Juxtaposable things
class Juxtaposable a where Source
Class of things which can be placed "next to" other things, for some appropriate notion of "next to".
juxtapose :: Vn a > a > a > a Source
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.)
(Enveloped b, HasOrigin b) => Juxtaposable [b]  
(Enveloped b, HasOrigin b, Ord b) => Juxtaposable (Set b)  
Juxtaposable a => Juxtaposable (b > a)  
(Enveloped a, HasOrigin a, Enveloped b, HasOrigin b, (~) (* > *) (V a) (V b), (~) * (N a) (N b)) => Juxtaposable (a, b)  
(Enveloped b, HasOrigin b) => Juxtaposable (Map k b)  
Juxtaposable a => Juxtaposable (Measured n a)  
(Metric v, OrderedField n) => Juxtaposable (Envelope v n)  
(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m) 
juxtaposeDefault :: (Enveloped a, HasOrigin a) => Vn a > a > a > a Source
Queries
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 graphicsdrawingcombinators package, http://hackage.haskell.org/package/graphicsdrawingcombinators.
Action Name (Query v n m)  
Functor (Query v n)  
Applicative (Query v n)  
Monoid m => Monoid (Query v n m)  
Semigroup m => Semigroup (Query v n m)  
Wrapped (Query v n m)  
(Additive v, Num n) => HasOrigin (Query v n m)  
(Additive v, Num n) => Transformable (Query v n m)  
Rewrapped (Query v a m) (Query v' a' m')  
type Unwrapped (Query v n m) = Point v n > m  
type N (Query v n m) = n  
type V (Query v n m) = v 
Primtives
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
.
Prim :: (Transformable p, Typeable p, Renderable p b) => p > Prim b (V p) (N p) 
Transformable (Prim b v n)  The 
Renderable (Prim b v n) b  The 
type N (Prim b v n) = n  
type V (Prim b v n) = v 
Diagrams
The fundamental diagram type. The type variables are as follows:
b
represents the backend, such asSVG
orCairo
. Note that each backend also exports a type synonymB
for itself, so the type variableb
may also typically be instantiated byB
, meaning "use whatever backend is in scope".v
represents the vector space of the diagram. Typical instantiations includeV2
(for a twodimensional diagram) orV3
(for a threedimensional diagram).n
represents the numerical field the diagram uses. Typically this will be a concrete numeric type likeDouble
.m
is the monoidal type of "query annotations": each point in the diagram has a value of typem
associated to it, and these values are combined according to theMonoid
instance form
. Most often,m
is simply instantiated toAny
, associating a simpleBool
value to each point indicating whether the point is inside the diagram;Diagram
is a synonym forQDiagram
withm
thus instantiated toAny
.
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.
Typeable (* > (* > *) > * > * > *) QDiagram  
Functor (QDiagram b v n)  
(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, 3dimensional diagrams when viewed by 4dimensional beings. 
(Metric v, OrderedField n, Semigroup m) => Semigroup (QDiagram b v n m)  
Wrapped (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. 
(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)  Diagrams can be transformed by transforming each of their components appropriately. 
(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. 
(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)  
(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)  
(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)  
(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)  
Rewrapped (QDiagram b v n m) (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) = n  
type V (QDiagram b v n m) = v 
type Diagram b = QDiagram b (V b) (N b) Any Source
Diagram b
is a synonym for
. 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 QDiagram
b (V b) (N b) Any
Functor
instance of
or
the QDiagram
b v nvalue
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 Source
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 Source
Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.
subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m) Source
names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m > [(Name, [Point v n])] Source
Get a list of names of subdiagrams and their locations.
query :: Monoid m => QDiagram b v n m > Query v n m Source
Get the query function associated with a diagram.
sample :: Monoid m => QDiagram b v n m > Point v n > m Source
Sample a diagram's query function at a given point.
clearValue :: QDiagram b v n m > QDiagram b v n Any Source
Set all the query values of a diagram to False
.
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 Source
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 knottying 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 Source
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 Source
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 Source
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 Source
"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 Source
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 Source
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 Source
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 Source
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 Source
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 Source
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 Source
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.).
Subdiagram (QDiagram b v n m) (DownAnnots v n) 
Functor (Subdiagram b v n)  
(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)  
(Metric v, Floating n) => Transformable (Subdiagram b v n m)  
(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)  
(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)  
type N (Subdiagram b v n m) = n  
type V (Subdiagram b v n m) = v 
mkSubdiagram :: QDiagram b v n m > Subdiagram b v n m Source
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 Source
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 "toplevel"
diagram.
rawSub :: Subdiagram b v n m > QDiagram b v n m Source
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 Source
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, Semigroup m) => Point v n > Subdiagram b v n m Source
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
'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.
Profunctor Measured  
Monad (Measured n)  
Functor (Measured n)  
Applicative (Measured n)  
Distributive (Measured n)  
Representable (Measured n)  
Additive (Measured n)  
Floating a => Floating (Measured n a)  
Fractional a => Fractional (Measured n a)  
Num a => Num (Measured n a)  
Monoid a => Monoid (Measured n a)  
Semigroup a => Semigroup (Measured n a)  
HasOrigin t => HasOrigin (Measured n t)  
Qualifiable a => Qualifiable (Measured n a)  
HasStyle b => HasStyle (Measured n b)  
Juxtaposable a => Juxtaposable (Measured n a)  
Typeable (* > * > *) Measured  
MonadReader (n, n, n) (Measured n)  
type Rep (Measured n) = (n, n, n)  
type N (Measured n a) = N a  
type V (Measured n a) = V a 
fromMeasured :: Num n => n > n > Measured n a > a Source
fromMeasured globalScale normalizedScale measure > a
normalized :: Num n => n > Measure n Source
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 Source
Scale the local units of a Measured
thing.
atLeast :: Ord n => Measure n > Measure n > Measure n Source
Calculate the smaller of two measures.
Backends
class Backend b v n where Source
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 diagramslib
package.
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.
The result of running/interpreting a rendering operation.
data Options b v n :: * Source
Backendspecific rendering options.
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) Source
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 diagramslib 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 Source
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.
Backend NullBackend v n 
class Transformable t => Renderable t b where Source
The Renderable type class connects backends to primitives which they know how to render.
render :: b > t > Render b (V t) (N t) Source
Given a token representing the backend and a transformable object, render it in the appropriate rendering context.
Renderable (Prim b v n) b  The 
renderDia :: (Backend b v n, HasLinearMap v, Metric v, Typeable v, Typeable n, OrderedField n, Monoid' m) => b > Options b v n > QDiagram b v n m > Result b v n Source
Render a diagram.
renderDiaT :: (Backend b v n, HasLinearMap v, Metric v, Typeable v, Typeable n, OrderedField n, Monoid' m) => b > Options b v n > QDiagram b v n m > (Transformation v n, Result b v n) Source
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 Source
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.
Typeable * NullBackend  
Backend NullBackend v n  
Monoid (Render NullBackend v n)  
data Render NullBackend = NullBackendRender  
data Options NullBackend  
type Result NullBackend v n = () 
type D v n = QDiagram NullBackend v n Any Source
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 diagramslib
):
ghci> width (image (uncheckedImageRef "foo.png" 200 200)) <interactive>:11:8: No instance for (Renderable (DImage n0 External) b0) arising from a use ofimage
The type variablesn0
,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 inImage
Possible fix: add an instance declaration for (Renderable (DImage n0 External) b0) In the first argument ofwidth
, namely `(image (uncheckedImageRef "foo.png" 200 200))' In the expression: width (image (uncheckedImageRef "foo.png" 200 200)) In an equation forit
: 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
, like so:D
V2
Double
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 radius1 circle:
ghci> width (circle 1) <interactive>:12:1: Couldn't match expected typeV2
with actual type `V a0' The type variablea0
is ambiguous Possible fix: add a type signature that fixes these type variable(s) In the expression: width (circle 1) In an equation forit
: 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 Source
HasLinearMap
is a poor man's class constraint synonym, just to
help shorten some of the ridiculously long constraint sets.
(HasBasis v, Traversable v) => HasLinearMap v 
class (Additive v, Representable v, Rep v ~ E v) => HasBasis v Source
An Additive
vector space whose representation is made up of basis elements.
(Additive v, Representable v, (~) * (Rep v) (E v)) => HasBasis v 
class (Floating s, Ord s) => OrderedField s Source
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.
(Floating s, Ord s) => OrderedField s 
class (Typeable n, RealFloat n) => TypeableFloat n Source
(Typeable * n, RealFloat n) => TypeableFloat n 