Copyright  (c) 2013 diagramslib team (see LICENSE) 

License  BSDstyle (see LICENSE) 
Maintainer  diagramsdiscuss@googlegroups.com 
Safe Haskell  None 
Language  Haskell2010 
"Envelopes", aka functional bounding regions. See Diagrams.Core.Envelope for internal implementation details.
Synopsis
 data Envelope (v :: Type > Type) n
 class (Metric (V a), OrderedField (N a)) => Enveloped a
 envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n)
 setEnvelope :: (OrderedField n, Metric v, Monoid' m) => Envelope v n > QDiagram b v n m > QDiagram b v n m
 withEnvelope :: (InSpace v n a, Monoid' m, Enveloped a) => a > QDiagram b v n m > QDiagram b v n m
 phantom :: (InSpace v n a, Monoid' m, Enveloped a, Traced a) => a > QDiagram b v n m
 pad :: (Metric v, OrderedField n, Monoid' m) => n > QDiagram b v n m > QDiagram b v n m
 extrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n > QDiagram b v n m > QDiagram b v n m
 intrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n > QDiagram b v n m > QDiagram b v n m
 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
Types
data Envelope (v :: Type > Type) 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 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://ozark.hendrix.edu/~yorgey/pub/monoidpearl.pdf; video: http://www.youtube.com/watch?v=X8NCkD2vOw.
Instances
Show (Envelope v n)  
Ord n => Semigroup (Envelope v n)  Envelopes form a semigroup with pointwise maximum as composition.
Hence, if 
Ord n => Monoid (Envelope v n)  The special empty envelope is the identity for the

(Metric v, OrderedField n) => Juxtaposable (Envelope v n)  
(Metric v, OrderedField n) => Enveloped (Envelope v n)  
Defined in Diagrams.Core.Envelope  
(Metric v, Floating n) => Transformable (Envelope v n)  
Defined in Diagrams.Core.Envelope  
(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. 
Defined in Diagrams.Core.Envelope  
Wrapped (Envelope v n)  
(Metric v, OrderedField n) => Alignable (Envelope v n) #  
Defined in Diagrams.Align alignBy' :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => (v0 n0 > Envelope v n > Point v0 n0) > v0 n0 > n0 > Envelope v n > Envelope v n # defaultBoundary :: (V (Envelope v n) ~ v0, N (Envelope v n) ~ n0) => v0 n0 > Envelope v n > Point v0 n0 # alignBy :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => v0 n0 > n0 > Envelope v n > Envelope v n #  
Rewrapped (Envelope v n) (Envelope v' n')  
Defined in Diagrams.Core.Envelope  
type V (Envelope v n)  
Defined in Diagrams.Core.Envelope  
type N (Envelope v n)  
Defined in Diagrams.Core.Envelope  
type Unwrapped (Envelope v n)  
Defined in Diagrams.Core.Envelope 
class (Metric (V a), OrderedField (N a)) => Enveloped a #
Enveloped
abstracts over things which have an envelope.
Instances
Diagram envelopes
setEnvelope :: (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.
withEnvelope :: (InSpace v n a, Monoid' m, Enveloped a) => a > QDiagram b v n m > QDiagram b v n m #
Use the envelope from some object as the envelope for a diagram, in place of the diagram's default envelope.
sqNewEnv = circle 1 # fc green  ( c # dashingG [0.1,0.1] 0 # lc white <> square 2 # withEnvelope (c :: D V2 Double) # fc blue ) c = circle 0.8 withEnvelopeEx = sqNewEnv # centerXY # pad 1.5
phantom :: (InSpace v n a, Monoid' m, Enveloped a, Traced a) => a > QDiagram b v n m #
phantom x
produces a "phantom" diagram, which has the same
envelope and trace as x
but produces no output.
pad :: (Metric v, OrderedField n, Monoid' m) => n > QDiagram b v n m > QDiagram b v n m #
pad s
"pads" a diagram, expanding its envelope by a factor of
s
(factors between 0 and 1 can be used to shrink the envelope).
Note that the envelope will expand with respect to the local
origin, so if the origin is not centered the padding may appear
"uneven". If this is not desired, the origin can be centered
(using, e.g., centerXY
for 2D diagrams) before applying pad
.
extrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n > QDiagram b v n m > QDiagram b v n m #
extrudeEnvelope v d
asymmetrically "extrudes" the envelope of
a diagram in the given direction. All parts of the envelope
within 90 degrees of this direction are modified, offset outwards
by the magnitude of the vector.
This works by offsetting the envelope distance proportionally to the cosine of the difference in angle, and leaving it unchanged when this factor is negative.
intrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n > QDiagram b v n m > QDiagram b v n m #
intrudeEnvelope v d
asymmetrically "intrudes" the envelope of
a diagram away from the given direction. All parts of the envelope
within 90 degrees of this direction are modified, offset inwards
by the magnitude of the vector.
Note that this could create strange inverted envelopes, where
diameter v d < 0
.
Querying envelopes
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.