diagrams-lib-1.1.0.7: Embedded domain-specific language for declarative graphics

Diagrams.Trail

Description

This module defines trails, translationally invariant paths through space. Trails form a central part of the diagrams-lib API, so the documentation for this module merits careful study.

Related modules include:

• The `TrailLike` class (Diagrams.TrailLike) exposes a generic API for building a wide range of things out of trails.
• `Path`s (Diagrams.Path) are collections of `Located` (Diagrams.Located) trails.
• Trails are composed of `Segment`s (see Diagrams.Segment), though most users should not need to work with segments directly.

Synopsis

# Type definitions

## Lines and loops

data Trail' l v where Source

Intuitively, a trail is a single, continuous path through space. However, a trail has no fixed starting point; it merely specifies how to move through space, not where. For example, "take three steps forward, then turn right twenty degrees and take two more steps" is an intuitive analog of a trail; these instructions specify a path through space from any given starting location. To be precise, trails are translation-invariant; applying a translation to a trail has no effect.

A `Located Trail`, on the other hand, is a trail paired with some concrete starting location ("start at the big tree on the corner, then take three steps forward, ..."). See the Diagrams.Located module for help working with `Located` values.

Formally, the semantics of a trail is a continuous (though not necessarily differentiable) function from the real interval [0,1] to vectors in some vector space. (In contrast, a `Located` trail is a continuous function from [0,1] to points in some affine space.)

There are two types of trails:

• A "line" (think of the "train", "subway", or "bus" variety, rather than the "straight" variety...) is a trail with two distinct endpoints. Actually, a line can have the same start and end points, but it is still drawn as if it had distinct endpoints: the two endpoints will have the appropriate end caps, and the trail will not be filled. Lines have a `Monoid` instance where `mappend` corresponds to concatenation, i.e. chaining one line after the other.
• A "loop" is required to end in the same place it starts (that is, t(0) = t(1)). Loops are filled and are drawn as one continuous loop, with the appropriate join at the start/endpoint rather than end caps. Loops do not have a `Monoid` instance.

To convert between lines and loops, see `glueLine`, `closeLine`, and `cutLoop`.

To construct trails, see `emptyTrail`, `trailFromSegments`, `trailFromVertices`, `trailFromOffsets`, and friends. You can also get any type of trail from any function which returns a `TrailLike` (e.g. functions in Diagrams.TwoD.Shapes, and many others; see Diagrams.TrailLike).

To extract information from trails, see `withLine`, `isLoop`, `trailSegments`, `trailOffsets`, `trailVertices`, and friends.

Constructors

 Line :: SegTree v -> Trail' Line v Loop :: SegTree v -> Segment Open v -> Trail' Loop v

Instances

 (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (GetSegment (Trail' Loop v)) (InnerSpace v, OrderedField (Scalar v)) => EndValues (GetSegment (Trail' Line v)) (Parametric (GetSegment (Trail' c v)), EndValues (GetSegment (Trail' c v)), VectorSpace v, Num (Scalar v)) => EndValues (Tangent (Trail' c v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (GetSegment (Trail' Loop v)) The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1". (InnerSpace v, OrderedField (Scalar v)) => Parametric (GetSegment (Trail' Line v)) Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values). (Parametric (GetSegment (Trail' c v)), VectorSpace v, Num (Scalar v)) => Parametric (Tangent (Trail' c v)) Eq v => Eq (Trail' l v) Ord v => Ord (Trail' l v) Show v => Show (Trail' l v) (OrderedField (Scalar v), InnerSpace v) => Semigroup (Trail' Line v) (OrderedField (Scalar v), InnerSpace v) => Monoid (Trail' Line v) The empty trail is constantly the zero vector. Trails are composed via concatenation. Note that only lines have a monoid instance (and not loops). (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Trail' l v) The envelope for a trail is based at the trail's start. (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Transformable (Trail' l v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => HasArcLength (Trail' l v) (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v)) => Sectionable (Trail' Line v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (Trail' l v) Num (Scalar v) => DomainBounds (Trail' l v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (Trail' l v) (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Loop v) Loops are trail-like. If given a `Trail` containing a line, the line will be turned into a loop using `glueLine`. The location is ignored. (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Line v) Lines are trail-like. If given a `Trail` which contains a loop, the loop will be cut with `cutLoop`. The location is ignored. (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Renderable (Trail' o v) NullBackend type Codomain (Tangent (Trail' c v)) = Codomain (Trail' c v) type V (Trail' l v) = v type Codomain (Trail' l v) = v

glueLine :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> Trail' Loop v Source

Make a line into a loop by "gluing" the endpoint to the starting point. In particular, the offset of the final segment is modified so that it ends at the starting point of the entire trail. Typically, you would first construct a line which you know happens to end where it starts, and then call `glueLine` to turn it into a loop.

```glueLineEx = pad 1.1 . hcat' (with & sep .~ 1)
\$ [almostClosed # strokeLine, almostClosed # glueLine # strokeLoop]

almostClosed :: Trail' Line R2
almostClosed = fromOffsets \$ map r2 [(2, -1), (-3, -0.5), (-2, 1), (1, 0.5)]```

`glueLine` is left inverse to `cutLoop`, that is,

```  glueLine . cutLoop === id
```

Make a line into a loop by adding a new linear segment from the line's end to its start.

`closeLine` does not have any particularly nice theoretical properties, but can be useful e.g. when you want to make a closed polygon out of a list of points where the initial point is not repeated at the end. To use `glueLine`, one would first have to duplicate the initial vertex, like

````glueLine` . `lineFromVertices` \$ ps ++ [head ps]
```

Using `closeLine`, however, one can simply

```closeLine . lineFromVertices \$ ps
```

```closeLineEx = pad 1.1 . centerXY . hcat' (with & sep .~ 1)
\$ [almostClosed # strokeLine, almostClosed # closeLine # strokeLoop]```

cutLoop :: forall v. (InnerSpace v, OrderedField (Scalar v)) => Trail' Loop v -> Trail' Line v Source

Turn a loop into a line by "cutting" it at the common start/end point, resulting in a line which just happens to start and end at the same place.

`cutLoop` is right inverse to `glueLine`, that is,

```  glueLine . cutLoop === id
```

## Generic trails

data Trail v where Source

`Trail` is a wrapper around `Trail'`, hiding whether the underlying `Trail'` is a line or loop (though which it is can be recovered; see e.g. `withTrail`).

Constructors

 Trail :: Trail' l v -> Trail v

Instances

 Eq v => Eq (Trail v) Ord v => Ord (Trail v) Show v => Show (Trail v) (OrderedField (Scalar v), InnerSpace v) => Semigroup (Trail v) Two `Trail`s are combined by first ensuring they are both lines (using `cutTrail` on loops) and then concatenating them. The result, in general, is a line. However, there is a special case for the empty line, which acts as the identity (so combining the empty line with a loop results in a loop). (OrderedField (Scalar v), InnerSpace v) => Monoid (Trail v) `Trail`s are combined as described in the `Semigroup` instance; the empty line is the identity element, with special cases so that combining the empty line with a loop results in the unchanged loop (in all other cases loops will be cut). Note that this does, in fact, satisfy the monoid laws, though it is a bit strange. Mostly it is provided for convenience, so one can work directly with `Trail`s instead of working with `Trail' Line`s and then wrapping. (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Trail v) Traced (Trail R2) (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Transformable (Trail v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => HasArcLength (Trail v) (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v)) => Sectionable (Trail v) Note that there is no `Sectionable` instance for `Trail' Loop`, because it does not make sense (splitting a loop at a parameter results in a single line, not two loops). However, it's convenient to have a `Sectionable` instance for `Trail`; if the `Trail` contains a loop the loop will first be cut and then `splitAtParam` called on the resulting line. This is semantically a bit silly, so please don't rely on it. (*E.g.* if this is really the behavior you want, consider first calling `cutLoop` yourself.) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (Trail v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (GetSegment (Trail v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (Tangent (Trail v)) Num (Scalar v) => DomainBounds (Trail v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (Trail v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (GetSegment (Trail v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (Tangent (Trail v)) (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail v) `Trail`s are trail-like; the location is simply ignored. (VectorSpace v, InnerSpace v, (~) * s (Scalar v), Ord s, Fractional s, Floating s, Show s, Show v) => Deformable (Located (Trail v)) (Show v, OrderedField (Scalar v), InnerSpace v, HasLinearMap v) => Renderable (Trail v) ShowBackend type V (Trail v) = v type Codomain (Trail v) = v type Codomain (Tangent (Trail v)) = Codomain (Trail v)

wrapTrail :: Trail' l v -> Trail v Source

Convert a `Trail'` into a `Trail`, hiding the type-level distinction between lines and loops.

Convert a line into a `Trail`. This is the same as `wrapTrail`, but with a more specific type, which can occasionally be convenient for fixing the type of a polymorphic expression.

Convert a loop into a `Trail`. This is the same as `wrapTrail`, but with a more specific type, which can occasionally be convenient for fixing the type of a polymorphic expression.

onTrail :: (Trail' Line v -> Trail' l1 v) -> (Trail' Loop v -> Trail' l2 v) -> Trail v -> Trail v Source

Modify a `Trail`, specifying two separate transformations for the cases of a line or a loop.

onLine :: (InnerSpace v, OrderedField (Scalar v)) => (Trail' Line v -> Trail' Line v) -> Trail v -> Trail v Source

Modify a `Trail` by specifying a transformation on lines. If the trail is a line, the transformation will be applied directly. If it is a loop, it will first be cut using `cutLoop`, the transformation applied, and then glued back into a loop with `glueLine`. That is,

```  onLine f === onTrail f (glueLine . f . cutLoop)
```

Note that there is no corresponding `onLoop` function, because there is no nice way in general to convert a line into a loop, operate on it, and then convert back.

glueTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Trail v Source

`glueTrail` is a variant of `glueLine` which works on `Trail`s. It performs `glueLine` on lines and is the identity on loops.

closeTrail :: Trail v -> Trail v Source

`closeTrail` is a variant of `closeLine` for `Trail`, which performs `closeLine` on lines and is the identity on loops.

cutTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Trail v Source

`cutTrail` is a variant of `cutLoop` for `Trail`; it is the is the identity on lines and performs `cutLoop` on loops.

# Constructing trails

emptyLine :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v Source

The empty line, which is the identity for concatenation of lines.

emptyTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v Source

A wrapped variant of `emptyLine`.

lineFromVertices :: (InnerSpace v, OrderedField (Scalar v)) => [Point v] -> Trail' Line v Source

Construct a line containing only linear segments from a list of vertices. Note that only the relative offsets between the vertices matters; the information about their absolute position will be discarded. That is, for all vectors `v`,

```lineFromVertices === lineFromVertices . `translate` v
```

If you want to retain the position information, you should instead use the more general `fromVertices` function to construct, say, a `Located (Trail' Line v)` or a ```Located (Trail v)```.

```import Diagrams.Coordinates
lineFromVerticesEx = pad 1.1 . centerXY . strokeLine
\$ lineFromVertices [origin, 0 ^& 1, 1 ^& 2, 5 ^& 1]```

trailFromVertices :: (InnerSpace v, OrderedField (Scalar v)) => [Point v] -> Trail v Source

`trailFromVertices === wrapTrail . lineFromVertices`, for conveniently constructing a `Trail` instead of a `Trail' Line`.

lineFromOffsets :: (InnerSpace v, OrderedField (Scalar v)) => [v] -> Trail' Line v Source

Construct a line containing only linear segments from a list of vectors, where each vector represents the offset from one vertex to the next. See also `fromOffsets`.

```import Diagrams.Coordinates
lineFromOffsetsEx = strokeLine \$ lineFromOffsets [ 2 ^& 1, 2 ^& (-1), 2 ^& 0.5 ]```

trailFromOffsets :: (InnerSpace v, OrderedField (Scalar v)) => [v] -> Trail v Source

`trailFromOffsets === wrapTrail . lineFromOffsets`, for conveniently constructing a `Trail` instead of a `Trail' Line`.

lineFromSegments :: (InnerSpace v, OrderedField (Scalar v)) => [Segment Closed v] -> Trail' Line v Source

Construct a line from a list of closed segments.

trailFromSegments :: (InnerSpace v, OrderedField (Scalar v)) => [Segment Closed v] -> Trail v Source

`trailFromSegments === wrapTrail . lineFromSegments`, for conveniently constructing a `Trail` instead of a `Trail'`.

# Eliminating trails

withTrail' :: (Trail' Line v -> r) -> (Trail' Loop v -> r) -> Trail' l v -> r Source

A generic eliminator for `Trail'`, taking functions specifying what to do in the case of a line or a loop.

withTrail :: (Trail' Line v -> r) -> (Trail' Loop v -> r) -> Trail v -> r Source

A generic eliminator for `Trail`, taking functions specifying what to do in the case of a line or a loop.

withLine :: (InnerSpace v, OrderedField (Scalar v)) => (Trail' Line v -> r) -> Trail v -> r Source

An eliminator for `Trail` based on eliminating lines: if the trail is a line, the given function is applied; if it is a loop, it is first converted to a line with `cutLoop`. That is,

```withLine f === `withTrail` f (f . `cutLoop`)
```

isLineEmpty :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> Bool Source

Test whether a line is empty.

isTrailEmpty :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Bool Source

Test whether a trail is empty. Note that loops are never empty.

isLine :: Trail v -> Bool Source

Determine whether a trail is a line.

isLoop :: Trail v -> Bool Source

Determine whether a trail is a loop.

trailSegments :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> [Segment Closed v] Source

Extract the segments of a trail. If the trail is a loop it will first have `cutLoop` applied.

Extract the segments comprising a line.

loopSegments :: Trail' Loop v -> ([Segment Closed v], Segment Open v) Source

Extract the segments comprising a loop: a list of closed segments, and one final open segment.

onLineSegments :: (InnerSpace v, OrderedField (Scalar v)) => ([Segment Closed v] -> [Segment Closed v]) -> Trail' Line v -> Trail' Line v Source

Modify a line by applying a function to its list of segments.

trailOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> [v] Source

Extract the offsets of the segments of a trail.

trailOffset :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> v Source

Compute the offset from the start of a trail to the end. Satisfies

```  trailOffset === sumV . trailOffsets
```

but is more efficient.

```trailOffsetEx = (strokeLine almostClosed <> showOffset) # centerXY # pad 1.1
where showOffset = fromOffsets [trailOffset (wrapLine almostClosed)]
# stroke # lc red # lw 0.05```

lineOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> [v] Source

Extract the offsets of the segments of a line.

lineOffset :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> v Source

Compute the offset from the start of a line to the end. (Note, there is no corresponding `loopOffset` function because by definition it would be constantly zero.)

loopOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Loop v -> [v] Source

Extract the offsets of the segments of a loop.

trailVertices :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> [Point v] Source

Extract the vertices of a concretely located trail. Note that for loops, the starting vertex will not be repeated at the end. If you want this behavior, you can use `cutTrail` to make the loop into a line first, which happens to repeat the same vertex at the start and end, e.g. with ```trailVertices . mapLoc cutTrail```.

Note that it does not make sense to ask for the vertices of a `Trail` by itself; if you want the vertices of a trail with the first vertex at, say, the origin, you can use `trailVertices . (`at` origin)`.

lineVertices :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail' Line v) -> [Point v] Source

Extract the vertices of a concretely located line. See `trailVertices` for more information.

loopVertices :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail' Loop v) -> [Point v] Source

Extract the vertices of a concretely located loop. Note that the initial vertex is not repeated at the end. See `trailVertices` for more information.

fixTrail :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> [FixedSegment v] Source

Convert a concretely located trail into a list of fixed segments.

# Modifying trails

reverseTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Trail v Source

Reverse a trail. Semantically, if a trail given by a function t from [0,1] to vectors, then the reverse of t is given by t'(s) = t(1-s). `reverseTrail` is an involution, that is,

```  reverseTrail . reverseTrail === id
```

reverseLocTrail :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> Located (Trail v) Source

Reverse a concretely located trail. The endpoint of the original trail becomes the starting point of the reversed trail, so the original and reversed trails comprise exactly the same set of points. `reverseLocTrail` is an involution, i.e.

```  reverseLocTrail . reverseLocTrail === id
```

reverseLine :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> Trail' Line v Source

Reverse a line. See `reverseTrail`.

reverseLocLine :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail' Line v) -> Located (Trail' Line v) Source

Reverse a concretely located line. See `reverseLocTrail`.

reverseLoop :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Loop v -> Trail' Loop v Source

Reverse a loop. See `reverseTrail`.

reverseLocLoop :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail' Loop v) -> Located (Trail' Loop v) Source

Reverse a concretely located loop. See `reverseLocTrail`. Note that this is guaranteed to preserve the location.

# Internals

Most users of diagrams should not need to use anything in this section directly, but they are exported on the principle that we can't forsee what uses people might have for them.

## Type tags

data Line Source

Type tag for trails with distinct endpoints.

Instances

 (InnerSpace v, OrderedField (Scalar v)) => EndValues (GetSegment (Trail' Line v)) (InnerSpace v, OrderedField (Scalar v)) => Parametric (GetSegment (Trail' Line v)) Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values). (OrderedField (Scalar v), InnerSpace v) => Semigroup (Trail' Line v) (OrderedField (Scalar v), InnerSpace v) => Monoid (Trail' Line v) The empty trail is constantly the zero vector. Trails are composed via concatenation. Note that only lines have a monoid instance (and not loops). (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v)) => Sectionable (Trail' Line v) (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Line v) Lines are trail-like. If given a `Trail` which contains a loop, the loop will be cut with `cutLoop`. The location is ignored.

data Loop Source

Instances

 (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (GetSegment (Trail' Loop v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (GetSegment (Trail' Loop v)) The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1". (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Loop v) Loops are trail-like. If given a `Trail` containing a line, the line will be turned into a loop using `glueLine`. The location is ignored.

## Segment trees

newtype SegTree v Source

A `SegTree` represents a sequence of closed segments, stored in a fingertree so we can easily recover various monoidal measures of the segments (number of segments, arc length, envelope...) and also easily slice and dice them according to the measures (e.g., split off the smallest number of segments from the beginning which have a combined arc length of at least 5).

Constructors

 SegTree (FingerTree (SegMeasure v) (Segment Closed v))

Instances

 Eq v => Eq (SegTree v) Ord v => Ord (SegTree v) Show v => Show (SegTree v) (OrderedField (Scalar v), InnerSpace v) => Monoid (SegTree v) (HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Transformable (SegTree v) Wrapped (SegTree v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => HasArcLength (SegTree v) (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v)) => Sectionable (SegTree v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v), Num (Scalar v)) => EndValues (SegTree v) Num (Scalar v) => DomainBounds (SegTree v) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (SegTree v) (OrderedField (Scalar v), InnerSpace v) => Measured (SegMeasure v) (SegTree v) Rewrapped (SegTree v) (SegTree v') type V (SegTree v) = v type Unwrapped (SegTree v) = FingerTree (SegMeasure v) (Segment Closed v) type Codomain (SegTree v) = v

trailMeasure :: (InnerSpace v, OrderedField (Scalar v), SegMeasure v :>: m, Measured (SegMeasure v) t) => a -> (m -> a) -> t -> a Source

Given a default result (to be used in the case of an empty trail), and a function to map a single measure to a result, extract the given measure for a trail and use it to compute a result. Put another way, lift a function on a single measure (along with a default value) to a function on an entire trail.

numSegs :: (Floating (Scalar v), Num c, Ord (Scalar v), InnerSpace v, Measured (SegMeasure v) a) => a -> c Source

Compute the number of segments of anything measured by `SegMeasure` (e.g. `SegMeasure` itself, `Segment`, `SegTree`, `Trail`s...)

offset :: (Floating (Scalar v), Ord (Scalar v), InnerSpace v, Measured (SegMeasure v) t) => t -> v Source

Compute the total offset of anything measured by `SegMeasure`.

## Extracting segments

newtype GetSegment t Source

A newtype wrapper around trails which exists solely for its `Parametric`, `DomainBounds` and `EndValues` instances. The idea is that if `tr` is a trail, you can write, e.g.

```  getSegment tr `atParam` 0.6
```

or

```  atStart (getSegment tr)
```

to get the segment at parameter 0.6 or the first segment in the trail, respectively.

The codomain for `GetSegment`, i.e. the result you get from calling `atParam`, `atStart`, or `atEnd`, is ```Maybe (v, Segment Closed v, AnIso' (Scalar v) (Scalar v))```. `Nothing` results if the trail is empty; otherwise, you get:

• the offset from the start of the trail to the beginning of the segment,
• the segment itself, and
• a reparameterization isomorphism: in the forward direction, it translates from parameters on the whole trail to a parameters on the segment. Note that for technical reasons you have to call `cloneIso` on the `AnIso'` value to get a real isomorphism you can use.

Constructors

 GetSegment t

Instances

 (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (GetSegment (Trail v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => EndValues (GetSegment (Trail' Loop v)) (InnerSpace v, OrderedField (Scalar v)) => EndValues (GetSegment (Trail' Line v)) DomainBounds t => DomainBounds (GetSegment t) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (GetSegment (Trail v)) (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v)) => Parametric (GetSegment (Trail' Loop v)) The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1". (InnerSpace v, OrderedField (Scalar v)) => Parametric (GetSegment (Trail' Line v)) Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values). type V (GetSegment t) = V t type Codomain (GetSegment t) = Maybe (V t, Segment Closed (V t), AnIso' (Scalar (V t)) (Scalar (V t)))

getSegment :: t -> GetSegment t Source

Create a `GetSegment` wrapper around a trail, after which you can call `atParam`, `atStart`, or `atEnd` to extract a segment.