Maintainer | diagrams-discuss@googlegroups.com |
---|---|

Safe Haskell | None |

This module defines *paths*, which are collections of concretely
located `Trail`

s. 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.

- newtype Path v = Path [Located (Trail v)]
- pathTrails :: Path v -> [Located (Trail v)]
- pathFromTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Path v
- pathFromTrailAt :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Point v -> Path v
- pathFromLocTrail :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> Path v
- pathVertices :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[Point v]]
- pathOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [v]
- pathCentroid :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Point v
- fixPath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[FixedSegment v]]
- scalePath :: (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Scalar v -> Path v -> Path v
- reversePath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Path v
- explodePath :: (VectorSpace (V t), TrailLike t) => Path (V t) -> [[t]]
- partitionPath :: (Located (Trail v) -> Bool) -> Path v -> (Path v, Path v)

# Paths

A *path* is a (possibly empty) list of `Located`

`Trail`

s.
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.

# 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.

pathFromTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Path vSource

Convert a trail to a path beginning at the origin.

pathFromTrailAt :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Point v -> Path vSource

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

pathFromLocTrail :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> Path vSource

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

pathVertices :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[Point v]]Source

Extract the vertices of a path, resulting in a separate list of
vertices for each component trail (see `trailVertices`

).

pathOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [v]Source

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

).

pathCentroid :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Point vSource

Compute the *centroid* of a path (*i.e.* the average location of
its vertices).

fixPath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[FixedSegment v]]Source

Convert a path into a list of lists of `FixedSegment`

s.

# Modifying paths

scalePath :: (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Scalar v -> Path v -> Path vSource

Scale a path using its centroid (see `pathCentroid`

) as the base
point for the scale.

reversePath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Path vSource

Reverse all the component trails of a path.

# Miscellaneous

explodePath :: (VectorSpace (V t), TrailLike t) => Path (V t) -> [[t]]Source

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

).