Diagrams.Combinators

Higher-level tools for combining diagrams.

Unary operations

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

withTrace :: (InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a) => a -> QDiagram b v n m -> QDiagram b v n m

Use the trace from some object as the trace for a diagram, in place of the diagram's default trace.

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.

strut :: (Metric v, OrderedField n) => v n -> QDiagram b v n m

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 from Diagrams.TwoD.Combinators.) Useful for manually creating separation between two diagrams.

strutEx = (circle 1 ||| strut unitX ||| circle 1) # centerXY # pad 1.1

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.

frame :: (Metric v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m

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.

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 .

Binary operations

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

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

beneath :: (Metric v, OrderedField n, Monoid' m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m infixl 6

beneath is just a convenient synonym for flip atop; that is, d1 `beneath` d2 is the diagram with d2 superimposed on top of d1.

beside :: (Juxtaposable a, Semigroup a) => Vn a -> a -> a -> a

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.

atDirection :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Semigroup a) => Direction v n -> a -> a -> a

Place two diagrams (or other juxtaposable objects) adjacent to one another, with the second diagram placed in the direction d from the first. The local origin of the resulting combined diagram is the same as the local origin of the first. See the documentation of beside for more information.

n-ary operations

appends :: (Juxtaposable a, Monoid' a) => a -> [(Vn a, a)] -> a

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

position :: (InSpace v n a, HasOrigin a, Monoid' a) => [(Point v n, a)] -> a

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 spot))
  where spot      = circle 0.2 # fc black
        mkPoint :: Double -> P2 Double
        mkPoint x = p2 (x,x*x)

atPoints :: (InSpace v n a, HasOrigin a, Monoid' a) => [Point v n] -> [a] -> a

Curried version of position, takes a list of points and a list of objects.

cat :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> [a] -> a

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' :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> CatOpts n -> [a] -> a

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).

data CatOpts n

Options for cat'.

Instances

Num n => Default (CatOpts n)

Methods

def :: CatOpts n

catMethod :: Lens' (CatOpts n) CatMethod

Which CatMethod should be used: normal catenation (default), or distribution?

sep :: Lens' (CatOpts n) n

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.

data CatMethod

Methods for concatenating diagrams.

Constructors

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.

composeAligned

Arguments

:: (Monoid' m, Floating n, Ord n, Metric v)

=> (QDiagram b v n m -> QDiagram b v n m)

Alignment function

-> ([QDiagram b v n m] -> QDiagram b v n m)

Composition function

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

Compose a list of diagrams using the given composition function, first aligning them all according to the given alignment, but retain the local origin of the first diagram, as it would be if the composition function were applied directly. That is, composeAligned algn comp is equivalent to translate v . comp . map algn for some appropriate translation vector v.

Unfortunately, this only works for diagrams (and not, say, paths) because there is no most general type for alignment functions, and no generic way to find out what an alignment function does to the origin of things. (However, it should be possible to make a version of this function that works specifically on paths, if such a thing were deemed useful.)

alignedEx1 = (hsep 2 # composeAligned alignT) (map circle [1,3,5,2])
           # showOrigin
           # frame 0.5

alignedEx2 = (mconcat # composeAligned alignTL) [circle 1, square 1, triangle 1, pentagon 1]
           # showOrigin
           # frame 0.1