Algebra.Polynomials.Bernstein

Various functions for manipulating polynomials, essentially when represented in the Bernstein basis, in one or two variables.

Documentation

data Bernsteinp a b

The type for Bernstein polynomials with an arbitrary number of variables

Constructors

Bernsteinp

Fields

bounds :: a

coefs :: Vector b

Instances

Num (Bernsteinp a Interval) => Intervalize (Bernsteinp a)

(Eq a, Eq b, Unbox b) => Eq (Bernsteinp a b)

(Num a, Fractional a, Unbox a) => Num (Bernsteinp Int a)

(Fractional a, Num a, Unbox a) => Num (Bernsteinp (Int, Int) a)

(Fractional a, Num a, Unbox a) => Num (Bernsteinp (Int, Int, Int) a)

(Fractional a, Num a, Unbox a) => Num (Bernsteinp (Int, Int, Int, Int) a)

(Show a, Show b, Unbox b) => Show (Bernsteinp a b)

solve :: (Show a, Show i, Eq a, Box a i) => Double -> Vector (Bernsteinp i Interval) -> a -> [a]

Computes the intersection of a given Bezier hypersurface, given by its graph, with plane z=0.

class Bernstein a where

Minimal complete definition

(?), constant, promote, elevate, eval, restriction

Methods

(?) :: Unbox b => Bernsteinp a b -> a -> b

constant :: (Unbox b, Num b, Fractional b) => b -> Bernsteinp a b

scale :: (Num b, Fractional b, Unbox b) => b -> Bernsteinp a b -> Bernsteinp a b

promote :: (Unbox b, Num b, Fractional b) => Int -> Bernsteinp Int b -> Bernsteinp a b

elevate :: (Unbox b, Num b, Fractional b) => a -> Bernsteinp a b -> Bernsteinp a b

eval :: (Unbox b, Num b, Fractional b) => Bernsteinp a b -> Param a b -> b

restriction :: (Unbox b, Fractional b, Num b) => Bernsteinp a b -> Param a b -> Param a b -> Bernsteinp a b

Instances

Bernstein Int

Bernstein (Int, Int)

Bernstein (Int, Int, Int)

Bernstein (Int, Int, Int, Int)

derivate :: (Unbox a, Num a) => Bernsteinp Int a -> Bernsteinp Int a

Computes the derivative of a univariate Bernstein polynomial.

reorient :: Unbox a => Bernsteinp Int a -> Bernsteinp Int a

Computes f(1-x) (useful when used with Bezier curves).