Data.Spline.Polynomial

Polynomial

data Polynomial s a

A Polynomial is used to interpolate in between a spline’s control points.

Polynomials for interpolation

hold :: Ord s => Polynomial s a

Constant polynomial – a.k.a. no interpolation.

Given two control points and a sample value in between, the hold polynomial won’t perform any interpolation but it just holds the value carried by the lower control point along the whole curve between the two control points.

linear :: (Additive a, Fractional s, Ord s) => Polynomial s (a s)

1-degree polynomial – a.k.a. straight line interpolation, or /linear interpolation/.

This polynomial connects control points with straight lines.

Note: implemented with linearBy id.

linearBy :: (Additive a, Fractional s, Ord s) => (s -> s) -> Polynomial s (a s)

Parametric linear polynomial.

This form applies a pre-filter on the input before performing a linear interpolation. Instead of:

 lerp x a b

We have:

 lerp (pref x) a b

This can be used to implement 1-degree splines if pref = id, basic cubic non-hermitian splines if pref = (^3), cosine splines if pref = x -> (1 - cos (x*pi)) * 0.5, and so on and so forth.

cosine :: (Additive a, Floating s, Ord s) => Polynomial s (a s)

Cosine polynomial.

Helpers

bsearchLower :: (a -> Ordering) -> Vector a -> Maybe Int

Helper binary search that search the ceiling index for the value to be searched according to the predicate.