diagrams-lib-0.4: Embedded domain-specific language for declarative graphics

Diagrams.Segment

Description

Generic functionality for constructing and manipulating linear or cubic Bezier segments.

Synopsis

# Constructing segments

data Segment v Source

The atomic constituents of paths are segments, which are single straight lines or cubic Bezier curves. Segments are translationally invariant, that is, they have no particular "location" and are unaffected by translations. They are, however, affected by other transformations such as rotations and scales.

Constructors

 Linear v A linear segment with given offset. Cubic v v v A cubic bezier segment specified by three offsets from the starting point to the first control point, second control point, and ending point, respectively.

Instances

 Functor Segment Eq v => Eq (Segment v) Ord v => Ord (Segment v) Show v => Show (Segment v) (InnerSpace v, OrderedField (Scalar v)) => Boundable (Segment v) The bounding function for a segment is based at the segment's start. HasLinearMap v => Transformable (Segment v) (Show v, HasLinearMap v) => Renderable (Segment v) ShowBackend

straight :: v -> Segment vSource

`straight v` constructs a translationally invariant linear segment with direction and length given by the vector `v`.

bezier3 :: v -> v -> v -> Segment vSource

`bezier3 v1 v2 v3` constructs a translationally invariant cubic Bezier curve where the offsets from the first endpoint to the first and second control point and endpoint are respectively given by `v1`, `v2`, and `v3`.

# Computing with segments

atParam :: (VectorSpace v, Num (Scalar v)) => Segment v -> Scalar v -> vSource

`atParam` yields a parametrized view of segments as continuous functions `[0,1] -> v`, which give the offset from the start of the segment for each value of the parameter between `0` and `1`. It is designed to be used infix, like `seg `atParam` 0.5`.

segOffset :: Segment v -> vSource

Compute the offset from the start of a segment to the end. Note that in the case of a Bezier segment this is not the same as the length of the curve itself; for that, see `arcLength`.

Reverse the direction of a segment.

splitAtParam :: VectorSpace v => Segment v -> Scalar v -> (Segment v, Segment v)Source

`splitAtParam` splits a segment `s` into two new segments `(l,r)` at the parameter `t` where `l` corresponds to the portion of `s` for parameter values from `0` to `t` and `r` for `s` from `t` to `1`. The following should hold for splitting:

``` paramSplit s t u
| u < t     = atParam s u == atParam l (u / t)
| otherwise = atParam s u == atParam s t ^+^ atParam l ((u - t) / (1.0 - t))
where (l,r) = splitAtParam s t
```

That is to say, the parameterization scales linearly with splitting.

`splitAtParam` can also be used with parameters outside the range (0,1). For example, using the parameter `2` gives two result segments where the first is the original segment extended to the parameter 2, and the second result segment travels backwards from the end of the first to the end of the original segment.

arcLength :: (InnerSpace v, Floating (Scalar v), Ord (Scalar v)) => Segment v -> Scalar v -> Scalar vSource

`arcLength` `s m` approximates the arc length of the segment curve `s` with accuracy of at least plus or minus `m`. For a `Cubic` segment this is computed by subdividing until the arc length of the path through the control points is within `m` of distance from start to end.

arcLengthToParam :: (InnerSpace v, Floating (Scalar v), Ord (Scalar v), AdditiveGroup v) => Segment v -> Scalar v -> Scalar v -> Scalar vSource

`arcLengthToParam s l m` converts the absolute arc length `l`, measured from the segment starting point, to a parameter on the segment `s`, with accuracy of at least plus or minus `m`. Works for any arc length, and may return any parameter value (not just parameters between 0 and 1).

adjustSegment :: (InnerSpace v, OrderedField (Scalar v)) => Segment v -> AdjustOpts v -> Segment vSource

Adjust the length of a segment. The second parameter is an option record which controls how the adjustment should be performed; see `AdjustOpts`.

data AdjustOpts v Source

How should a segment, trail, or path be adjusted?

Constructors

Instances

 Fractional (Scalar v) => Default (AdjustOpts v)

data AdjustMethod v Source

What method should be used for adjusting a segment, trail, or path?

Constructors

 ByParam (Scalar v) Extend by the given parameter value (use a negative parameter to shrink) ByAbsolute (Scalar v) Extend by the given arc length (use a negative length to shrink) ToAbsolute (Scalar v) Extend or shrink to the given arc length

Instances

 Fractional (Scalar v) => Default (AdjustMethod v)

Which side of a segment, trail, or path should be adjusted?

Constructors

 Start Adjust only the beginning End Adjust only the end Both Adjust both sides equally

adjustSegmentToParams :: (Fractional (Scalar v), VectorSpace v) => Segment v -> Scalar v -> Scalar v -> Segment vSource

Given a segment and parameters `t1`, `t2`, produce the segment which lies on the (infinitely extended) original segment beginning at `t1` and ending at `t2`.

# Fixed (absolutely located) segments

data FixedSegment v Source

`FixedSegment`s are like `Segment`s except that they have absolute locations.

Constructors

 FLinear (Point v) (Point v) FCubic (Point v) (Point v) (Point v) (Point v)

Instances

 Show v => Show (FixedSegment v) HasLinearMap v => Transformable (FixedSegment v) VectorSpace v => HasOrigin (FixedSegment v)

mkFixedSeg :: AdditiveGroup v => Point v -> Segment v -> FixedSegment vSource

Create a `FixedSegment` from a starting point and a `Segment`.

fAtParam :: VectorSpace v => FixedSegment v -> Scalar v -> Point vSource

Compute the point on a fixed segment at a given parameter. A parameter of 0 corresponds to the starting point and 1 corresponds to the ending point.