smoothie-0.4.2: Smooth curves via several interpolation modes

Copyright(C) 2015 Dimitri Sabadie
MaintainerDimitri Sabadie <>
Safe HaskellNone






Key type

data Key a Source

A Key is a point on the spline with extra information added. It can be, for instance, left and right handles for a Bezier curve, or whatever the interpolation might need.

Hold v is used to express no interpolation and holds its latest value until the next key.

Linear v represents a linear interpolation until the next key.

Cosine v represents a cosine interpolation until the next key.

CubicHermite v represents a cubic hermitian interpolation until the next key.

Bezier l v r represents a cubic Bezier interpolation, where l refers to the input – left – tangent of the key and r is the output – right – tangent of the key.


Hold a 
Linear a 
Cosine a 
CubicHermite a 
Bezier a a a 


keyValue :: Key a -> a Source

Extract the value out of a Key.


interpolateKeys :: (Additive a, Floating s) => s -> Key (a s) -> Key (a s) -> a s Source

interpolateKeys t start end interpolates between start and end using s as a normalized sampling value.

Satisfies the following laws:

  interpolateKeys 0 start _ = start
  interpolateKeys 1 _ end   = end

normalizeSampling :: Fractional s => (a s -> s) -> s -> Key (a s) -> Key (a s) -> s Source

Normalize a sampling value by clamping and scaling it between two Keys.

The following laws should be satisfied in order to get a coherent output:

  sampler :: a s -> s

  sampler (keyValue k1) s= sampler (keyValue k0)
  0 <= normalizeSampling sampler s k0 k1 <= 1