Copyright	(c) 2013 diagrams-lib team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	None
Language	Haskell2010

Diagrams.Tangent

Contents

Tangents
Normals
Tangent newtype

Description

Computing tangent and normal vectors for segments and trails.

Synopsis

Tangents

tangentAtParam :: Parametric (Tangent t) => t -> N t -> Vn t #

Compute the tangent vector to a segment or trail at a particular parameter.

Examples of more specific types this function can have include

Segment Closed V2 -> Double -> V2 Double

```
Trail' Line V2 -> Double -> V2 Double
```

Located (Trail V2) -> Double -> V2 Double

See the instances listed for the Tangent newtype for more.

tangentAtStart :: EndValues (Tangent t) => t -> Vn t #

Compute the tangent vector at the start of a segment or trail.

tangentAtEnd :: EndValues (Tangent t) => t -> Vn t #

Compute the tangent vector at the end of a segment or trail.

Normals

normalAtParam :: (InSpace V2 n t, Parametric (Tangent t), Floating n) => t -> n -> V2 n #

Compute the (unit) normal vector to a segment or trail at a particular parameter.

Examples of more specific types this function can have include

Segment Closed V2 Double -> Double -> V2 Double

Trail' Line V2 Double -> Double -> V2 Double

Located (Trail V2 Double) -> Double -> V2 Double

See the instances listed for the Tangent newtype for more.

normalAtStart :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n #

Compute the normal vector at the start of a segment or trail.

normalAtEnd :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n #

Compute the normal vector at the end of a segment or trail.

Tangent newtype

newtype Tangent t #

A newtype wrapper used to give different instances of Parametric and EndValues that compute tangent vectors.

Constructors

Tangent t

Instances

(DomainBounds t, EndValues (Tangent t)) => EndValues (Tangent (Located t)) #
Methods atStart :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) # atEnd :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(Additive v, Num n) => EndValues (Tangent (FixedSegment v n)) #
Methods atStart :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) # atEnd :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
(Additive v, Num n) => EndValues (Tangent (Segment Closed v n)) #
Methods atStart :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) # atEnd :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Metric v, OrderedField n, Real n) => EndValues (Tangent (Trail v n)) #
Methods atStart :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) # atEnd :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Parametric (GetSegment (Trail' c v n)), EndValues (GetSegment (Trail' c v n)), Additive v, Num n) => EndValues (Tangent (Trail' c v n)) #
Methods atStart :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) # atEnd :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
DomainBounds t => DomainBounds (Tangent t) #
Methods domainLower :: Tangent t -> N (Tangent t) # domainUpper :: Tangent t -> N (Tangent t) #
Parametric (Tangent t) => Parametric (Tangent (Located t)) #
Methods atParam :: Tangent (Located t) -> N (Tangent (Located t)) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(Additive v, Num n) => Parametric (Tangent (FixedSegment v n)) #
Methods atParam :: Tangent (FixedSegment v n) -> N (Tangent (FixedSegment v n)) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
(Additive v, Num n) => Parametric (Tangent (Segment Closed v n)) #
Methods atParam :: Tangent (Segment Closed v n) -> N (Tangent (Segment Closed v n)) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Metric v, OrderedField n, Real n) => Parametric (Tangent (Trail v n)) #
Methods atParam :: Tangent (Trail v n) -> N (Tangent (Trail v n)) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Parametric (GetSegment (Trail' c v n)), Additive v, Num n) => Parametric (Tangent (Trail' c v n)) #
Methods atParam :: Tangent (Trail' c v n) -> N (Tangent (Trail' c v n)) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
type V (Tangent t) #
type V (Tangent t) = V t
type N (Tangent t) #
type N (Tangent t) = N t
type Codomain (Tangent t) #
type Codomain (Tangent t) = V t