{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
-----------------------------------------------------------------------------
-- |
-- Module : Diagrams.Combinators
-- Copyright : (c) 2011 diagrams-lib team (see LICENSE)
-- License : BSD-style (see LICENSE)
-- Maintainer : diagrams-discuss@googlegroups.com
--
-- Higher-level tools for combining diagrams.
--
-----------------------------------------------------------------------------
module Diagrams.Combinators
( -- * Unary operations
withEnvelope, withTrace
, phantom, strut
, pad, frame
, extrudeEnvelope, intrudeEnvelope
-- * Binary operations
, atop
, beneath
, beside
-- * n-ary operations
, appends
, position, decorateTrail, decorateLocatedTrail, decoratePath
, cat, cat'
, CatOpts(_catMethod, _sep), catMethod, sep
, CatMethod(..)
) where
import Data.Typeable
import Control.Lens (Lens', generateSignatures, lensField,
lensRules, makeLensesWith, (%~), (&), (.~),
(^.), _Wrapping)
import Data.AdditiveGroup
import Data.AffineSpace ((.+^))
import Data.Default.Class
import Data.Proxy
import Data.Semigroup
import Data.VectorSpace
import Diagrams.Core
import Diagrams.Located
import Diagrams.Path
import Diagrams.Segment (straight)
import Diagrams.Trail (Trail, trailVertices)
import Diagrams.Util
------------------------------------------------------------
-- Working with envelopes
------------------------------------------------------------
-- | 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 # dashing [0.1,0.1] 0 # lc white
-- > <> square 2 # withEnvelope (c :: D R2) # fc blue
-- > )
-- > c = circle 0.8
-- > withEnvelopeEx = sqNewEnv # centerXY # pad 1.5
withEnvelope :: (HasLinearMap (V a), Enveloped a, Monoid' m)
=> a -> QDiagram b (V a) m -> QDiagram b (V a) m
withEnvelope = setEnvelope . getEnvelope
-- | Use the trace from some object as the trace for a diagram, in
-- place of the diagram's default trace.
withTrace :: (HasLinearMap (V a), Traced a, OrderedField (Scalar (V a)), InnerSpace (V a), Monoid' m)
=> a -> QDiagram b (V a) m -> QDiagram b (V a) m
withTrace = setTrace . getTrace
-- | @phantom x@ produces a \"phantom\" diagram, which has the same
-- envelope and trace as @x@ but produces no output.
phantom :: (Backend b (V a), Typeable (V a), Enveloped a, Traced a, Monoid' m) => a -> QDiagram b (V a) m
phantom a = mkQD nullPrim (getEnvelope a) (getTrace a) mempty mempty
-- | @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@.
pad :: ( Backend b v
, InnerSpace v, OrderedField (Scalar v)
, Monoid' m )
=> Scalar v -> QDiagram b v m -> QDiagram b v m
pad s d = withEnvelope (d # scale s) d
-- | @frame s@ increases the envelope of a diagram by and absolute amount @s@,
-- s is in the local units of the diagram. This function is similar to @pad@,
-- only it takes an absolute quantity and pre-centering should not be
-- necessary.
frame :: ( Backend b v, InnerSpace v, OrderedField (Scalar v), Monoid' m)
=> Scalar v -> QDiagram b v m -> QDiagram b v m
frame s d = setEnvelope (onEnvelope t (d^.envelope)) d
where
t f = \x -> f x + s
-- | @strut v@ is a diagram which produces no output, but with respect
-- to alignment and envelope acts like a 1-dimensional segment
-- oriented along the vector @v@, with local origin at its
-- center. (Note, however, that it has an empty trace; for 2D struts
-- with a nonempty trace see 'strutR2', 'strutX', and 'strutY' from
-- "Diagrams.TwoD.Combinators".) Useful for manually creating
-- separation between two diagrams.
--
-- <>
--
-- > strutEx = (circle 1 ||| strut unitX ||| circle 1) # centerXY # pad 1.1
strut :: ( Backend b v, Typeable v
, InnerSpace v
, OrderedField (Scalar v)
, Monoid' m
)
=> v -> QDiagram b v m
strut v = mkQD nullPrim env mempty mempty mempty
where env = translate ((-0.5) *^ v) . getEnvelope $ straight v
-- note we can't use 'phantom' here because it tries to construct a
-- trace as well, and segments do not have a trace in general (only
-- in 2D; see Diagrams.TwoD.Segment). This is a good reason to have
-- a special 'strut' combinator (before the introduction of traces
-- it was mostly just for convenience).
--
-- also note that we can't remove the call to getEnvelope, since
-- translating a segment has no effect.
-- | @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.
extrudeEnvelope
:: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
, Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
=> v -> QDiagram b v m -> QDiagram b v m
extrudeEnvelope = deformEnvelope 0.5
-- | @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 @.
intrudeEnvelope
:: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
, Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
=> v -> QDiagram b v m -> QDiagram b v m
intrudeEnvelope = deformEnvelope (-0.5)
-- Utility for extrudeEnvelope / intrudeEnvelope
deformEnvelope
:: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
, Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
=> (Scalar v) -> v -> QDiagram b v m -> QDiagram b v m
deformEnvelope s v d = setEnvelope (getEnvelope d & _Wrapping Envelope %~ deformE) d
where
deformE = Option . fmap deformE' . getOption
deformE' env v'
| dot > 0 = Max $ getMax (env v') + (dot * s) / magnitude v'
| otherwise = env v'
where
dot = v' <.> v
------------------------------------------------------------
-- Combining two objects
------------------------------------------------------------
-- | @beneath@ is just a convenient synonym for @'flip' 'atop'@; that is,
-- @d1 \`beneath\` d2@ is the diagram with @d2@ superimposed on top of
-- @d1@.
beneath :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Monoid' m)
=> QDiagram b v m -> QDiagram b v m -> QDiagram b v m
beneath = flip atop
infixl 6 `beneath`
-- | Place two monoidal objects (/i.e./ diagrams, paths,
-- animations...) next to each other along the given vector. In
-- particular, place the second object so that the vector points
-- from the local origin of the first object to the local origin of
-- the second object, at a distance so that their envelopes are just
-- tangent. The local origin of the new, combined object is the
-- local origin of the first object (unless the first object is the
-- identity element, in which case the second object is returned
-- unchanged).
--
-- <>
--
-- > besideEx = beside (r2 (20,30))
-- > (circle 1 # fc orange)
-- > (circle 1.5 # fc purple)
-- > # showOrigin
-- > # centerXY # pad 1.1
--
-- Note that @beside v@ is associative, so objects under @beside v@
-- form a semigroup for any given vector @v@. In fact, they also
-- form a monoid: 'mempty' is clearly a right identity (@beside v d1
-- mempty === d1@), and there should also be a special case to make
-- it a left identity, as described above.
--
-- In older versions of diagrams, @beside@ put the local origin of
-- the result at the point of tangency between the two inputs. That
-- semantics can easily be recovered by performing an alignment on
-- the first input before combining. That is, if @beside'@ denotes
-- the old semantics,
--
-- > beside' v x1 x2 = beside v (x1 # align v) x2
--
-- To get something like @beside v x1 x2@ whose local origin is
-- identified with that of @x2@ instead of @x1@, use @beside
-- (negateV v) x2 x1@.
beside :: (Juxtaposable a, Semigroup a) => V a -> a -> a -> a
beside v d1 d2 = d1 <> juxtapose v d1 d2
------------------------------------------------------------
-- Combining multiple objects
------------------------------------------------------------
-- | @appends x ys@ appends each of the objects in @ys@ to the object
-- @x@ in the corresponding direction. Note that each object in
-- @ys@ is positioned beside @x@ /without/ reference to the other
-- objects in @ys@, so this is not the same as iterating 'beside'.
--
-- <>
--
-- > appendsEx = appends c (zip (iterateN 6 (rotateBy (1/6)) unitX) (repeat c))
-- > # centerXY # pad 1.1
-- > where c = circle 1
appends :: (Juxtaposable a, Monoid' a) => a -> [(V a,a)] -> a
appends d1 apps = d1 <> mconcat (map (\(v,d) -> juxtapose v d1 d) apps)
-- | Position things absolutely: combine a list of objects
-- (e.g. diagrams or paths) by assigning them absolute positions in
-- the vector space of the combined object.
--
-- <>
--
-- > positionEx = position (zip (map mkPoint [-3, -2.8 .. 3]) (repeat dot))
-- > where dot = circle 0.2 # fc black
-- > mkPoint x = p2 (x,x^2)
position :: (HasOrigin a, Monoid' a) => [(Point (V a), a)] -> a
position = mconcat . map (uncurry moveTo)
-- | Combine a list of diagrams (or paths) by using them to
-- \"decorate\" a trail, placing the local origin of one object at
-- each successive vertex of the trail. The first vertex of the
-- trail is placed at the origin. If the trail and list of objects
-- have different lengths, the extra tail of the longer one is
-- ignored.
decorateTrail :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
=> Trail (V a) -> [a] -> a
decorateTrail = decorateLocatedTrail . (`at` origin)
-- | Combine a list of diagrams (or paths) by using them to
-- \"decorate\" a concretely located trail, placing the local origin
-- of one object at each successive vertex of the trail. If the
-- trail and list of objects have different lengths, the extra tail
-- of the longer one is ignored.
decorateLocatedTrail :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
=> Located (Trail (V a)) -> [a] -> a
decorateLocatedTrail t = position . zip (trailVertices t)
-- | Combine a list of diagrams (or paths) by using them to
-- \"decorate\" a path, placing the local origin of one object at
-- each successive vertex of the path. If the path and list of objects
-- have different lengths, the extra tail of the longer one is
-- ignored.
decoratePath :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
=> Path (V a) -> [a] -> a
decoratePath p = position . zip (concat $ pathVertices p)
-- | Methods for concatenating diagrams.
data CatMethod = Cat -- ^ Normal catenation: simply put diagrams
-- next to one another (possibly with a
-- certain distance in between each). The
-- distance between successive diagram
-- /envelopes/ will be consistent; the
-- distance between /origins/ may vary if
-- the diagrams are of different sizes.
| Distrib -- ^ Distribution: place the local origins of
-- diagrams at regular intervals. With
-- this method, the distance between
-- successive /origins/ will be consistent
-- but the distance between envelopes may
-- not be. Indeed, depending on the amount
-- of separation, diagrams may overlap.
-- | Options for 'cat''.
data CatOpts v = CatOpts { _catMethod :: CatMethod
, _sep :: Scalar v
, _catOptsvProxy__ :: Proxy v
}
-- The reason the proxy field is necessary is that without it,
-- altering the sep field could theoretically change the type of a
-- CatOpts record. This causes problems when using record update, as
-- in @with { _sep = 10 }@, because knowing the type of the whole
-- expression does not tell us anything about the type of @with@, and
-- therefore the @Num (Scalar v)@ constraint cannot be satisfied.
-- Adding the Proxy field constrains the type of @with@ in @with {_sep
-- = 10}@ to be the same as the type of the whole expression. Note
-- this is not a problem when using the 'sep' lens, as its type is
-- more restricted.
makeLensesWith
( lensRules
-- don't make a lens for the proxy field
& lensField .~ (\label ->
case label of
"_catOptsvProxy__" -> Nothing
_ -> Just (drop 1 label)
)
& generateSignatures .~ False
)
''CatOpts
-- | Which 'CatMethod' should be used:
-- normal catenation (default), or distribution?
catMethod :: forall v. Lens' (CatOpts v) CatMethod
-- | How much separation should be used between successive diagrams
-- (default: 0)? When @catMethod = Cat@, this is the distance between
-- /envelopes/; when @catMethod = Distrib@, this is the distance
-- between /origins/.
sep :: forall v. Lens' (CatOpts v) (Scalar v)
instance Num (Scalar v) => Default (CatOpts v) where
def = CatOpts { _catMethod = Cat
, _sep = 0
, _catOptsvProxy__ = Proxy
}
-- | @cat v@ positions a list of objects so that their local origins
-- lie along a line in the direction of @v@. Successive objects
-- will have their envelopes just touching. The local origin
-- of the result will be the same as the local origin of the first
-- object.
--
-- See also 'cat'', which takes an extra options record allowing
-- certain aspects of the operation to be tweaked.
cat :: ( Juxtaposable a, Monoid' a, HasOrigin a
, InnerSpace (V a), OrderedField (Scalar (V a))
)
=> V a -> [a] -> a
cat v = cat' v def
-- | Like 'cat', but taking an extra 'CatOpts' arguments allowing the
-- user to specify
--
-- * The spacing method: catenation (uniform spacing between
-- envelopes) or distribution (uniform spacing between local
-- origins). The default is catenation.
--
-- * The amount of separation between successive diagram
-- envelopes/origins (depending on the spacing method). The
-- default is 0.
--
-- 'CatOpts' is an instance of 'Default', so 'with' may be used for
-- the second argument, as in @cat' (1,2) (with & sep .~ 2)@.
--
-- Note that @cat' v (with & catMethod .~ Distrib) === mconcat@
-- (distributing with a separation of 0 is the same as
-- superimposing).
cat' :: ( Juxtaposable a, Monoid' a, HasOrigin a
, InnerSpace (V a), OrderedField (Scalar (V a))
)
=> V a -> CatOpts (V a) -> [a] -> a
cat' v (CatOpts { _catMethod = Cat, _sep = s }) = foldB comb mempty
where comb d1 d2 = d1 <> (juxtapose v d1 d2 # moveOriginBy vs)
vs = s *^ normalized (negateV v)
cat' v (CatOpts { _catMethod = Distrib, _sep = s }) =
position . zip (iterate (.+^ (s *^ normalized v)) origin)