Diagrams.Path

This module defines paths, which are collections of concretely located Trails. Many drawing systems (cairo, svg, ...) have a similar notion of "path". Note that paths with multiple trails are necessary for being able to draw e.g. filled objects with holes in them.

Paths

newtype Path v n

A path is a (possibly empty) list of Located Trails. Hence, unlike trails, paths are not translationally invariant, and they form a monoid under superposition (placing one path on top of another) rather than concatenation.

Constructors

Path [Located (Trail v n)]

Instances

Eq (v n) => Eq (Path v n)

Methods

(==) :: Path v n -> Path v n -> Bool

(/=) :: Path v n -> Path v n -> Bool

Ord (v n) => Ord (Path v n)

Methods

compare :: Path v n -> Path v n -> Ordering

(<) :: Path v n -> Path v n -> Bool

(<=) :: Path v n -> Path v n -> Bool

(>) :: Path v n -> Path v n -> Bool

(>=) :: Path v n -> Path v n -> Bool

max :: Path v n -> Path v n -> Path v n

min :: Path v n -> Path v n -> Path v n

Show (v n) => Show (Path v n)

Methods

showsPrec :: Int -> Path v n -> ShowS

show :: Path v n -> String

showList :: [Path v n] -> ShowS

Semigroup (Path v n)

Methods

(<>) :: Path v n -> Path v n -> Path v n

sconcat :: NonEmpty (Path v n) -> Path v n

stimes :: Integral b => b -> Path v n -> Path v n

Monoid (Path v n)

Methods

mempty :: Path v n

mappend :: Path v n -> Path v n -> Path v n

mconcat :: [Path v n] -> Path v n

(Metric v, OrderedField n) => Juxtaposable (Path v n)

Methods

juxtapose :: Vn (Path v n) -> Path v n -> Path v n -> Path v n

(Metric v, OrderedField n) => Enveloped (Path v n)

Methods

getEnvelope :: Path v n -> Envelope (V (Path v n)) (N (Path v n))

(HasLinearMap v, Metric v, OrderedField n) => Transformable (Path v n)

Methods

transform :: Transformation (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n

(Additive v, Num n) => HasOrigin (Path v n)

Methods

moveOriginTo :: Point (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n

AsEmpty (Path v n)

Methods

_Empty :: Prism' (Path v n) ()

Wrapped (Path v n)

Associated Types

type Unwrapped (Path v n) :: *

Methods

_Wrapped' :: Iso' (Path v n) (Unwrapped (Path v n))

(Metric v, OrderedField n) => Reversing (Path v n)

Same as reversePath.

Methods

reversing :: Path v n -> Path v n

(Metric v, OrderedField n) => TrailLike (Path v n)

Paths are trail-like; a trail can be used to construct a singleton path.

Methods

trailLike :: Located (Trail (V (Path v n)) (N (Path v n))) -> Path v n

(Metric v, OrderedField n) => Alignable (Path v n)

Methods

alignBy' :: (InSpace v n (Path v n), Fractional n, HasOrigin (Path v n)) => (v n -> Path v n -> Point v n) -> v n -> n -> Path v n -> Path v n

defaultBoundary :: (((* -> *) ~ V (Path v n)) v, (* ~ N (Path v n)) n) => v n -> Path v n -> Point v n

alignBy :: (InSpace v n (Path v n), Fractional n, HasOrigin (Path v n)) => v n -> n -> Path v n -> Path v n

ToPath (Path v n)

Methods

toPath :: Path v n -> Path (V (Path v n)) (N (Path v n))

(HasLinearMap v, Metric v, OrderedField n) => Renderable (Path v n) NullBackend

Methods

render :: NullBackend -> Path v n -> Render NullBackend (V (Path v n)) (N (Path v n))

(Metric v, Metric u, OrderedField n, (~) * r (Path u n)) => Deformable (Path v n) r

Methods

deform' :: N (Path v n) -> Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r

deform :: Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r

(Metric v, Metric u, OrderedField n, (~) * r (Path u n)) => AffineMappable (Path v n) r

Methods

amap :: AffineMap (V (Path v n)) (V r) (N r) -> Path v n -> r

(Metric v, Metric u, OrderedField n, OrderedField m, (~) * r (Path u m)) => LinearMappable (Path v n) r

Methods

vmap :: (Vn (Path v n) -> Vn r) -> Path v n -> r

Rewrapped (Path v n) (Path v' n')

Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Methods

_Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n')

Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Methods

_Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n'))

Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

Methods

each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))

type V (Path v n)

type V (Path v n) = v

type N (Path v n)

type N (Path v n) = n

type Unwrapped (Path v n)

type Unwrapped (Path v n) = [Located (Trail v n)]

pathTrails :: Path v n -> [Located (Trail v n)]

Extract the located trails making up a Path.

Constructing paths

Since paths are TrailLike, any function producing a TrailLike can be used to construct a (singleton) path. The functions in this section are provided for convenience.

class ToPath t where

Type class for things that can be converted to a Path.

Note that this class is very different from TrailLike. TrailLike is usually the result of a library function to give you a convenient, polymorphic result (Path, Diagram etc.).

Minimal complete definition

toPath

Methods

toPath :: (Metric (V t), OrderedField (N t)) => t -> Path (V t) (N t)

toPath takes something that can be converted to Path and returns the Path.

Instances

ToPath a => ToPath [a]

Methods

toPath :: [a] -> Path (V [a]) (N [a])

ToPath (Located [Segment Closed v n])

Methods

toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n]))

ToPath (Located (Segment Closed v n))

Methods

toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n)))

ToPath (Located (Trail v n))

Methods

toPath :: Located (Trail v n) -> Path (V (Located (Trail v n))) (N (Located (Trail v n)))

ToPath (Located (Trail' l v n))

Methods

toPath :: Located (Trail' l v n) -> Path (V (Located (Trail' l v n))) (N (Located (Trail' l v n)))

ToPath (FixedSegment v n)

Methods

toPath :: FixedSegment v n -> Path (V (FixedSegment v n)) (N (FixedSegment v n))

ToPath (Trail v n)

Methods

toPath :: Trail v n -> Path (V (Trail v n)) (N (Trail v n))

ToPath (Path v n)

Methods

toPath :: Path v n -> Path (V (Path v n)) (N (Path v n))

pathFromTrail :: (Metric v, OrderedField n) => Trail v n -> Path v n

Convert a trail to a path beginning at the origin.

pathFromTrailAt :: (Metric v, OrderedField n) => Trail v n -> Point v n -> Path v n

Convert a trail to a path with a particular starting point.

pathFromLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Path v n

Convert a located trail to a singleton path. This is equivalent to trailLike, but provided with a more specific name and type for convenience.

Eliminating paths

pathPoints :: (Metric v, OrderedField n) => Path v n -> [[Point v n]]

Extract the points of a path, resulting in a separate list of points for each component trail. Here a point is any place where two segments join; see also pathVertices and trailPoints.

This function allows you "observe" the fact that trails are implemented as lists of segments, which may be problematic if we want to think of trails as parametric vector functions. This also means that the behavior of this function may not be stable under future changes to the implementation of trails and paths. For an unproblematic version which only yields vertices at which there is a sharp corner, excluding points differentiable points, see pathVertices.

This function is not re-exported from Diagrams.Prelude; to use it, import Diagrams.Path.

pathVertices' :: (Metric v, OrderedField n) => n -> Path v n -> [[Point v n]]

Extract the vertices of a path, resulting in a separate list of vertices for each component trail. Here a vertex is defined as a non-differentiable point on the trail, i.e. a sharp corner. (Vertices are thus a subset of the places where segments join; if you want all joins between segments, see pathPoints.) The tolerance determines how close the tangents of two segments must be at their endpoints to consider the transition point to be differentiable. See trailVertices for more information.

pathVertices :: (Metric v, OrderedField n) => Path v n -> [[Point v n]]

Like pathVertices', with a default tolerance.

pathOffsets :: (Metric v, OrderedField n) => Path v n -> [v n]

Compute the total offset of each trail comprising a path (see trailOffset).

pathCentroid :: (Metric v, OrderedField n) => Path v n -> Point v n

Compute the centroid of a path (i.e. the average location of its vertices; see pathVertices).

pathLocSegments :: (Metric v, OrderedField n) => Path v n -> [[Located (Segment Closed v n)]]

Convert a path into a list of lists of located segments.

fixPath :: (Metric v, OrderedField n) => Path v n -> [[FixedSegment v n]]

Convert a path into a list of lists of FixedSegments.

Modifying paths

scalePath :: (HasLinearMap v, Metric v, OrderedField n) => n -> Path v n -> Path v n

Scale a path using its centroid (see pathCentroid) as the base point for the scale.

reversePath :: (Metric v, OrderedField n) => Path v n -> Path v n

Reverse all the component trails of a path.

Miscellaneous

explodePath :: (V t ~ v, N t ~ n, TrailLike t) => Path v n -> [[t]]

"Explode" a path by exploding every component trail (see explodeTrail).

partitionPath :: (Located (Trail v n) -> Bool) -> Path v n -> (Path v n, Path v n)

Partition a path into two paths based on a predicate on trails: the first containing all the trails for which the predicate returns True, and the second containing the remaining trails.