Copyright	(c) 2014-2015 diagrams-lib team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe
Language	Haskell2010

Diagrams.TwoD.Segment.Bernstein

Description

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

Synopsis

data BernsteinPoly n = BernsteinPoly {
- bernsteinDegree :: Int
- bernsteinCoeffs :: [n]
}
listToBernstein :: Fractional n => [n] -> BernsteinPoly n
evaluateBernstein :: Fractional n => BernsteinPoly n -> n -> n
degreeElevate :: Fractional n => BernsteinPoly n -> Int -> BernsteinPoly n
bernsteinDeriv :: Fractional n => BernsteinPoly n -> BernsteinPoly n
evaluateBernsteinDerivs :: Fractional n => BernsteinPoly n -> n -> [n]

Documentation

data BernsteinPoly n #

Constructors

BernsteinPoly
Fields bernsteinDegree :: Int bernsteinCoeffs :: [n]

Instances

Functor BernsteinPoly #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods fmap :: (a -> b) -> BernsteinPoly a -> BernsteinPoly b # (<$) :: a -> BernsteinPoly b -> BernsteinPoly a #
Fractional n => Num (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein 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) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods showsPrec :: Int -> BernsteinPoly n -> ShowS # show :: BernsteinPoly n -> String # showList :: [BernsteinPoly n] -> ShowS #
Fractional n => Sectionable (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein 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) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods atStart :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) # atEnd :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) #
Num n => DomainBounds (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods domainLower :: BernsteinPoly n -> N (BernsteinPoly n) # domainUpper :: BernsteinPoly n -> N (BernsteinPoly n) #
Fractional n => Parametric (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods atParam :: BernsteinPoly n -> N (BernsteinPoly n) -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) #
type V (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein type V (BernsteinPoly n) = V1
type N (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein type N (BernsteinPoly n) = n
type Codomain (BernsteinPoly n) #
Instance details Defined in Diagrams.TwoD.Segment.Bernstein 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.