Math.BernsteinPoly

Algebra on polynomials in the Bernstein form. It is based on the paper /Algebraic manipulation in the Bernstein form made simple via convolutions/ by J. Sanchez-Reyes. It's an efficient implementation using the scaled basis, and using ghc rewrite rules to eliminate intermediate polynomials.

Documentation

data BernsteinPoly a

Constructors

BernsteinPoly

Fields

• bernsteinCoeffs :: Vector a

Instances

(Unbox a, Show a) => Show (BernsteinPoly a)

Methods

showsPrec :: Int -> BernsteinPoly a -> ShowS

show :: BernsteinPoly a -> String

showList :: [BernsteinPoly a] -> ShowS

bernsteinSubsegment :: (Unbox a, Ord a, Fractional a) => BernsteinPoly a -> a -> a -> BernsteinPoly a

Return the subsegment between the two parameters.

listToBernstein :: (Unbox a, Num a) => [a] -> BernsteinPoly a

Create a bernstein polynomail from a list of coëfficients.

zeroPoly :: (Num a, Unbox a) => BernsteinPoly a

The constant zero.

(~*) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a infixl 7

Multiply two bernstein polynomials using convolution. The final degree will be the sum of either degrees. This operation takes O((n+m)^2) with n and m the degree of the beziers. Note that convolution can be done in O(n log n) using the FFT, which may be faster for large polynomials.

(*~) :: (Unbox a, Num a) => a -> BernsteinPoly a -> BernsteinPoly a infixl 7

Scale a bernstein polynomial by a constant.

(~+) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a infixl 6

Sum two bernstein polynomials. The final degree will be the maximum of either degrees.

(~-) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a infixl 6

Subtract two bernstein polynomials. The final degree will be the maximum of either degrees.

degreeElevate :: (Unbox a, Fractional a) => BernsteinPoly a -> Int -> BernsteinPoly a

bernsteinSplit :: (Unbox a, Num a) => BernsteinPoly a -> a -> (BernsteinPoly a, BernsteinPoly a)

Split a bernstein polynomial

bernsteinEval :: (Unbox a, Fractional a) => BernsteinPoly a -> a -> a

Evaluate the bernstein polynomial using the horner rule adapted for bernstein polynomials.

bernsteinEvalDeriv :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> (t, t)

Evaluate the bernstein polynomial and first derivative

binCoeff :: (Num a, Unbox a) => Int -> Vector a

Give the binomial coefficients of degree n.

convolve :: (Unbox a, Num a) => Vector a -> Vector a -> Vector a

Calculate the convolution of two vectors.

bernsteinEvalDerivs :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> [t]

Evaluate the bernstein polynomial and its derivatives.

bernsteinDeriv :: (Unbox a, Num a) => BernsteinPoly a -> BernsteinPoly a

Find the derivative of a bernstein polynomial.