Diagrams.Tangent

Computing tangent and normal vectors for segments and trails.

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