| Safe Haskell | None |
|---|---|
| Language | Haskell98 |
Math.BernsteinPoly
Description
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.
- data BernsteinPoly a = BernsteinPoly {
- bernsteinCoeffs :: Vector a
- bernsteinSubsegment :: (Unbox a, Ord a, Fractional a) => BernsteinPoly a -> a -> a -> BernsteinPoly a
- listToBernstein :: (Unbox a, Num a) => [a] -> BernsteinPoly a
- zeroPoly :: (Num a, Unbox a) => BernsteinPoly a
- (~*) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a
- (*~) :: (Unbox a, Num a) => a -> BernsteinPoly a -> BernsteinPoly a
- (~+) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a
- (~-) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a
- degreeElevate :: (Unbox a, Fractional a) => BernsteinPoly a -> Int -> BernsteinPoly a
- bernsteinSplit :: (Unbox a, Num a) => BernsteinPoly a -> a -> (BernsteinPoly a, BernsteinPoly a)
- bernsteinEval :: (Unbox a, Fractional a) => BernsteinPoly a -> a -> a
- bernsteinEvalDeriv :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> (t, t)
- binCoeff :: (Num a, Unbox a) => Int -> Vector a
- convolve :: (Unbox a, Num a) => Vector a -> Vector a -> Vector a
- bernsteinEvalDerivs :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> [t]
- bernsteinDeriv :: (Unbox a, Num a) => BernsteinPoly a -> BernsteinPoly a
Documentation
data BernsteinPoly a Source
Constructors
| BernsteinPoly | |
Fields
| |
Instances
| (Show a, Unbox a) => Show (BernsteinPoly a) |
bernsteinSubsegment :: (Unbox a, Ord a, Fractional a) => BernsteinPoly a -> a -> a -> BernsteinPoly a Source
Return the subsegment between the two parameters.
listToBernstein :: (Unbox a, Num a) => [a] -> BernsteinPoly a Source
Create a bernstein polynomail from a list of coëfficients.
zeroPoly :: (Num a, Unbox a) => BernsteinPoly a Source
The constant zero.
(~*) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a infixl 7 Source
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 Source
Scale a bernstein polynomial by a constant.
(~+) :: (Unbox a, Fractional a) => BernsteinPoly a -> BernsteinPoly a -> BernsteinPoly a infixl 6 Source
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 Source
Subtract two bernstein polynomials. The final degree will be the maximum of either degrees.
degreeElevate :: (Unbox a, Fractional a) => BernsteinPoly a -> Int -> BernsteinPoly a Source
bernsteinSplit :: (Unbox a, Num a) => BernsteinPoly a -> a -> (BernsteinPoly a, BernsteinPoly a) Source
Split a bernstein polynomial
bernsteinEval :: (Unbox a, Fractional a) => BernsteinPoly a -> a -> a Source
Evaluate the bernstein polynomial using the horner rule adapted for bernstein polynomials.
bernsteinEvalDeriv :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> (t, t) Source
Evaluate the bernstein polynomial and first derivative
convolve :: (Unbox a, Num a) => Vector a -> Vector a -> Vector a Source
Calculate the convolution of two vectors.
bernsteinEvalDerivs :: (Unbox t, Fractional t) => BernsteinPoly t -> t -> [t] Source
Evaluate the bernstein polynomial and its derivatives.
bernsteinDeriv :: (Unbox a, Num a) => BernsteinPoly a -> BernsteinPoly a Source
Find the derivative of a bernstein polynomial.