Maintainer  diagramsdiscuss@googlegroups.com 

Safe Haskell  None 
This module defines trails (translationally invariant sequences of linear or cubic Bézier segments) and paths (collections of concretely located trails). Trails and paths can be used for drawing shapes, laying out other diagrams, clipping, and other things.
 class (Monoid' p, VectorSpace (V p)) => PathLike p where
 fromSegments :: PathLike p => [Segment (V p)] > p
 fromOffsets :: PathLike p => [V p] > p
 fromVertices :: PathLike p => [Point (V p)] > p
 segmentsFromVertices :: AdditiveGroup v => [Point v] > [Segment v]
 pathLikeFromTrail :: PathLike p => Trail (V p) > p
 class PathLike p => Closeable p where
 data Trail v = Trail {
 trailSegments :: [Segment v]
 isClosed :: Bool
 trailSegments' :: AdditiveGroup v => Trail v > [Segment v]
 trailOffsets :: Trail v > [v]
 trailOffset :: AdditiveGroup v => Trail v > v
 trailVertices :: AdditiveGroup v => Point v > Trail v > [Point v]
 reverseTrail :: AdditiveGroup v => Trail v > Trail v
 addClosingSegment :: AdditiveGroup v => Trail v > Trail v
 fixTrail :: AdditiveGroup v => Point v > Trail v > [FixedSegment v]
 newtype Path v = Path {
 pathTrails :: [(Point v, Trail v)]
 pathFromTrail :: AdditiveGroup v => Trail v > Path v
 pathFromTrailAt :: Trail v > Point v > Path v
 pathVertices :: AdditiveGroup v => Path v > [[Point v]]
 pathOffsets :: AdditiveGroup v => Path v > [v]
 pathCentroid :: (VectorSpace v, Fractional (Scalar v)) => Path v > Point v
 scalePath :: (HasLinearMap v, VectorSpace v, Fractional (Scalar v), Eq (Scalar v)) => Scalar v > Path v > Path v
 reversePath :: AdditiveGroup v => Path v > Path v
 fixPath :: AdditiveGroup v => Path v > [[FixedSegment v]]
 explodeTrail :: (VectorSpace (V p), PathLike p) => Point (V p) > Trail (V p) > [p]
 explodePath :: (VectorSpace (V p), PathLike p) => Path (V p) > [[p]]
 (~~) :: PathLike p => Point (V p) > Point (V p) > p
Constructing pathlike things
class (Monoid' p, VectorSpace (V p)) => PathLike p whereSource
Type class for pathlike things, which must be monoids.
Instances include Trail
s, Path
s, and twodimensional Diagram
s.
(Monoid' [Point v], VectorSpace (V [Point v]), VectorSpace v) => PathLike [Point v]  A list of points is pathlike; this instance simply computes the vertices of a pathlike thing. 
(Monoid' (Active p), VectorSpace (V (Active p)), PathLike p) => PathLike (Active p)  
(Monoid' (Path v), VectorSpace (V (Path v)), VectorSpace v) => PathLike (Path v)  Paths are (of course) pathlike. 
(Monoid' (Trail v), VectorSpace (V (Trail v)), VectorSpace v) => PathLike (Trail v)  Trails are 
(Monoid' (QDiagram b R2 Any), VectorSpace (V (QDiagram b R2 Any)), Renderable (Path R2) b) => PathLike (QDiagram b R2 Any) 
fromSegments :: PathLike p => [Segment (V p)] > pSource
Construct an open pathlike thing with the origin as a starting point.
fromOffsets :: PathLike p => [V p] > pSource
Construct an open pathlike thing of linear segments from a list of offsets. The starting point is the origin.
fromVertices :: PathLike p => [Point (V p)] > pSource
Construct a pathlike thing of linear segments from a list of vertices, with the first vertex as the starting point.
segmentsFromVertices :: AdditiveGroup v => [Point v] > [Segment v]Source
Construct a list of linear segments from a list of vertices. The input list must contain at least two points to generate a nonempty list of segments.
pathLikeFromTrail :: PathLike p => Trail (V p) > pSource
Convert a trail to any pathlike thing. pathLikeFromTrail
is the
identity on trails.
Closeable things
class PathLike p => Closeable p whereSource
Pathlike things that can be "open" or "closed".
"Open" a pathlike thing.
"Close" a pathlike thing, by implicitly connecting the endpoint(s) back to the starting point(s).
(PathLike (Path v), VectorSpace v) => Closeable (Path v)  
(PathLike (Trail v), VectorSpace v) => Closeable (Trail v) 
Trails
A trail is a sequence of segments placed endtoend. Trails are thus translationally invariant, and form a monoid under concatenation. Trails can also be open (the default) or closed (the final point in a closed trail is implicitly connected back to the starting point).
Trail  

Functor Trail  
Eq v => Eq (Trail v)  
(Eq (Trail v), Ord v) => Ord (Trail v)  
Show v => Show (Trail v)  
Semigroup (Trail v)  
Monoid (Trail v)  The empty trail has no segments. Trails are composed via
concatenation. 
(InnerSpace (V (Trail v)), OrderedField (Scalar (V (Trail v))), InnerSpace v, OrderedField (Scalar v)) => Enveloped (Trail v)  The envelope for a trail is based at the trail's start. 
Traced (Trail R2)  
(HasLinearMap (V (Trail v)), HasLinearMap v) => Transformable (Trail v)  
(PathLike (Trail v), VectorSpace v) => Closeable (Trail v)  
(Monoid' (Trail v), VectorSpace (V (Trail v)), VectorSpace v) => PathLike (Trail v)  Trails are 
(Transformable (Trail v), HasLinearMap v) => Renderable (Trail v) NullBackend  
(Transformable (Trail v), Show v, HasLinearMap v) => Renderable (Trail v) ShowBackend  
Newtype (Path v) [(Point v, Trail v)] 
Computing with trails
trailSegments' :: AdditiveGroup v => Trail v > [Segment v]Source
trailSegments'
is like trailSegments
, but explicitly includes
the implicit closing segment at the end of the list for closed trails.
trailOffsets :: Trail v > [v]Source
Extract the offsets of the segments of a trail.
trailOffset :: AdditiveGroup v => Trail v > vSource
Compute the offset from the start of a trail to the end.
trailVertices :: AdditiveGroup v => Point v > Trail v > [Point v]Source
Extract the vertices of a trail, given a concrete location at which to place the first vertex.
reverseTrail :: AdditiveGroup v => Trail v > Trail vSource
Reverse a trail's direction of travel.
addClosingSegment :: AdditiveGroup v => Trail v > Trail vSource
If the trail is closed, this adds in the closing segment. Otherwise, the trail is returned unmodified.
fixTrail :: AdditiveGroup v => Point v > Trail v > [FixedSegment v]Source
Convert a starting point and a trail into a list of fixed segments.
Paths
A path is a (possibly empty) list of trails, with each trail paired with an absolute starting point. Hence, paths are not translationally invariant, and form a monoid under superposition.
Path  

Eq v => Eq (Path v)  
(Eq (Path v), Ord v) => Ord (Path v)  
Show v => Show (Path v)  
Semigroup (Path v)  
Monoid (Path v)  
(InnerSpace v, OrderedField (Scalar v)) => Juxtaposable (Path v)  
(InnerSpace (V (Path v)), OrderedField (Scalar (V (Path v))), InnerSpace v, OrderedField (Scalar v)) => Enveloped (Path v)  
Traced (Path R2)  
(HasLinearMap (V (Path v)), HasLinearMap v) => Transformable (Path v)  
(VectorSpace (V (Path v)), VectorSpace v) => HasOrigin (Path v)  
(InnerSpace v, OrderedField (Scalar v)) => Alignable (Path v)  
(PathLike (Path v), VectorSpace v) => Closeable (Path v)  
(Monoid' (Path v), VectorSpace (V (Path v)), VectorSpace v) => PathLike (Path v)  Paths are (of course) pathlike. 
(Transformable (Path v), HasLinearMap v) => Renderable (Path v) NullBackend  
(Transformable (Path v), Ord v, Show v, HasLinearMap v) => Renderable (Path v) ShowBackend  
Newtype (Path v) [(Point v, Trail v)] 
Constructing paths from trails
pathFromTrail :: AdditiveGroup v => Trail v > Path vSource
Convert a trail to a path beginning at the origin.
pathFromTrailAt :: Trail v > Point v > Path vSource
Convert a trail to a path with a particular starting point.
Computing with paths
pathVertices :: AdditiveGroup v => Path v > [[Point v]]Source
Extract the vertices of a path.
pathOffsets :: AdditiveGroup v => Path v > [v]Source
Compute the total offset of each trail comprising a path.
pathCentroid :: (VectorSpace v, Fractional (Scalar v)) => Path v > Point vSource
Compute the centroid of a path (i.e. the average of its vertices).
scalePath :: (HasLinearMap v, VectorSpace v, Fractional (Scalar v), Eq (Scalar v)) => Scalar v > Path v > Path vSource
Scale a path using its centroid (see pathCentroid
) as the base
point for the scale.
reversePath :: AdditiveGroup v => Path v > Path vSource
Reverse the direction of all the component trails of a path.
fixPath :: AdditiveGroup v => Path v > [[FixedSegment v]]Source
Convert a path into a list of lists of FixedSegment
s.
Miscellaneous
explodeTrail :: (VectorSpace (V p), PathLike p) => Point (V p) > Trail (V p) > [p]Source
Given a starting point, "explode" a trail by turning each segment (including the implicit closing segment, if the trail is closed) into its own separate path. Useful for (say) applying a different style to each segment.
explodePath :: (VectorSpace (V p), PathLike p) => Path (V p) > [[p]]Source
"Explode" a path by exploding every component trail (see explodeTrail
).