Maintainer  diagramsdiscuss@googlegroups.com 

Safe Haskell  None 
Graphics.Rendering.Diagrams defines the core library of primitives forming the basis of an embedded domainspecific language for describing and rendering diagrams.
The Envelope
module defines a data type and type class for
"envelopes", aka functional bounding regions.
 newtype Envelope v = Envelope {
 unEnvelope :: Option (v > Max (Scalar v))
 inEnvelope :: (Option (v > Max (Scalar v)) > Option (v > Max (Scalar v))) > Envelope v > Envelope v
 appEnvelope :: Envelope v > Maybe (v > Scalar v)
 onEnvelope :: ((v > Scalar v) > v > Scalar v) > Envelope v > Envelope v
 mkEnvelope :: (v > Scalar v) > Envelope v
 class (InnerSpace (V b), OrderedField (Scalar (V b))) => Enveloped b where
 getEnvelope :: b > Envelope (V b)
 data LocatedEnvelope v = LocatedEnvelope (Point v) (TransInv (Envelope v))
 location :: LocatedEnvelope v > Point v
 locateEnvelope :: Point v > Envelope v > LocatedEnvelope v
 diameter :: Enveloped a => V a > a > Scalar (V a)
 radius :: Enveloped a => V a > a > Scalar (V a)
 envelopeV :: Enveloped a => V a > a > V a
 envelopeP :: Enveloped a => V a > a > Point (V a)
 boundaryFrom :: (OrderedField (Scalar v), InnerSpace v) => LocatedEnvelope v > v > Point v
 class (Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s
Envelopes
Every diagram comes equipped with an *envelope*.
Intuitively, the envelope for a diagram tells us the
minimum distance we have to go in a given direction to get to a
(hyper)plane entirely containing the diagram on one side of
it. Formally, given a vector v
, it returns 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.
This could probably be expressed in terms of a Galois connection; this is left as an exercise for the reader.
There is also a special "empty envelope".
Essentially, envelopes are a functional representation of (a conservative approximation to) convex bounding regions. The idea for this representation came from Sebastian Setzer; see http://byorgey.wordpress.com/2009/10/28/collectingattributes/#comment2030.
Envelope  

Show (Envelope v)  
Ord (Scalar v) => Monoid (Envelope v)  
Ord (Scalar v) => Semigroup (Envelope v)  
(InnerSpace v, AdditiveGroup (Scalar v), Fractional (Scalar v)) => HasOrigin (Envelope v)  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. 
(HasLinearMap v, InnerSpace v, Floating (Scalar v), AdditiveGroup (Scalar v)) => Transformable (Envelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Enveloped (Envelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Juxtaposable (Envelope v)  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
inEnvelope :: (Option (v > Max (Scalar v)) > Option (v > Max (Scalar v))) > Envelope v > Envelope vSource
appEnvelope :: Envelope v > Maybe (v > Scalar v)Source
mkEnvelope :: (v > Scalar v) > Envelope vSource
class (InnerSpace (V b), OrderedField (Scalar (V b))) => Enveloped b whereSource
Enveloped
abstracts over things which have an envelope.
getEnvelope :: b > Envelope (V b)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)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (Point v)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (LocatedEnvelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Enveloped (Envelope v)  
(Enveloped a, Enveloped b, ~ * (V a) (V b)) => Enveloped (a, b)  
Enveloped b => Enveloped (Map k b)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Enveloped (QDiagram b v m) 
data LocatedEnvelope v Source
A LocatedEnvelope
value represents an envelope with its
base point at a particular location.
LocatedEnvelope (Point v) (TransInv (Envelope v)) 
Show v => Show (LocatedEnvelope v)  
VectorSpace v => HasOrigin (LocatedEnvelope v)  
(HasLinearMap v, InnerSpace v, Floating (Scalar v), AdditiveGroup (Scalar v)) => Transformable (LocatedEnvelope v)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (LocatedEnvelope v)  
Newtype (NameMap v) (Map Name [LocatedEnvelope v]) 
location :: LocatedEnvelope v > Point vSource
Get the location of a located envelope.
locateEnvelope :: Point v > Envelope v > LocatedEnvelope vSource
Create a LocatedEnvelope
value by specifying a location and an
envelope.
Utility functions
diameter :: Enveloped a => V a > a > Scalar (V a)Source
Compute the diameter of a enveloped object along a particular vector. Returns zero for the empty envelope.
radius :: Enveloped a => V a > a > Scalar (V a)Source
Compute the "radius" (1/2 the diameter) of an enveloped object along a particular vector.
envelopeV :: Enveloped a => V a > a > V aSource
Compute the vector from the local origin to a separating hyperplane in the given direction. Returns the zero vector for the empty envelope.
envelopeP :: Enveloped a => V a > a > Point (V a)Source
Compute the point on a separating hyperplane in the given direction. Returns the origin for the empty envelope.
boundaryFrom :: (OrderedField (Scalar v), InnerSpace v) => LocatedEnvelope v > v > Point vSource
boundaryFrom v b
computes the point on the boundary of the
located envelope b
in the direction of v
from the
bounding region's base point. This is most often used to compute
a point on the boundary of a named subdiagram.
Miscellaneous
class (Fractional s, Floating s, Ord s, AdditiveGroup 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.
(Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s 