Diagrams.TwoD.Segment.Bernstein

Bernstein polynomials, used internally by code to find intersections of paths. This module is probably not of any relevance to most users of diagrams.

Documentation

data BernsteinPoly n

Constructors

BernsteinPoly

Fields

• bernsteinDegree :: Int
• bernsteinCoeffs :: [n]

Instances

Functor BernsteinPoly

Methods

fmap :: (a -> b) -> BernsteinPoly a -> BernsteinPoly b

(<$) :: a -> BernsteinPoly b -> BernsteinPoly a

Fractional n => Num (BernsteinPoly n)

Methods

(+) :: BernsteinPoly n -> BernsteinPoly n -> BernsteinPoly n

(-) :: BernsteinPoly n -> BernsteinPoly n -> BernsteinPoly n

(*) :: BernsteinPoly n -> BernsteinPoly n -> BernsteinPoly n

negate :: BernsteinPoly n -> BernsteinPoly n

abs :: BernsteinPoly n -> BernsteinPoly n

signum :: BernsteinPoly n -> BernsteinPoly n

fromInteger :: Integer -> BernsteinPoly n

Show n => Show (BernsteinPoly n)

Methods

showsPrec :: Int -> BernsteinPoly n -> ShowS

show :: BernsteinPoly n -> String

showList :: [BernsteinPoly n] -> ShowS

Fractional n => Sectionable (BernsteinPoly n)

Methods

splitAtParam :: BernsteinPoly n -> N (BernsteinPoly n) -> (BernsteinPoly n, BernsteinPoly n)

section :: BernsteinPoly n -> N (BernsteinPoly n) -> N (BernsteinPoly n) -> BernsteinPoly n

reverseDomain :: BernsteinPoly n -> BernsteinPoly n

Fractional n => EndValues (BernsteinPoly n)

Methods

atStart :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n))

atEnd :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n))

Num n => DomainBounds (BernsteinPoly n)

Methods

domainLower :: BernsteinPoly n -> N (BernsteinPoly n)

domainUpper :: BernsteinPoly n -> N (BernsteinPoly n)

Fractional n => Parametric (BernsteinPoly n)

Methods

atParam :: BernsteinPoly n -> N (BernsteinPoly n) -> Codomain (BernsteinPoly n) (N (BernsteinPoly n))

type V (BernsteinPoly n)

type V (BernsteinPoly n) = V1

type N (BernsteinPoly n)

type N (BernsteinPoly n) = n

type Codomain (BernsteinPoly n)

type Codomain (BernsteinPoly n) = V1

listToBernstein :: Fractional n => [n] -> BernsteinPoly n

Create a bernstein polynomial from a list of coëfficients.

evaluateBernstein :: Fractional n => BernsteinPoly n -> n -> n

Evaluate the bernstein polynomial.

degreeElevate :: Fractional n => BernsteinPoly n -> Int -> BernsteinPoly n

Degree elevate a bernstein polynomial a number of times.

bernsteinDeriv :: Fractional n => BernsteinPoly n -> BernsteinPoly n

Find the derivative of a bernstein polynomial.

evaluateBernsteinDerivs :: Fractional n => BernsteinPoly n -> n -> [n]

Evaluate the bernstein polynomial and its derivatives.