Sound.SC3.Common.Math.Interpolate

Interpolation functions, ie. for envelope segments.

Documentation

type Interpolation_F t = t -> t -> t -> t

An interpolation function takes three arguments. x0 is the left or begin value, x1 is the right or end value, and t is a (0,1) index.

interpolate :: (Num t, Ord t) => Interpolation_F t -> (t, t) -> t -> t

Clip x to (0,1) and run f.

interpolate linear (-1,1) 0.5 == 0

step :: Interpolation_F t

Step function, ignores t and returns x1.

linear :: Num t => Interpolation_F t

Linear interpolation funtion, x0 is at t of zero, and x1 at t of one.

map (linear 1 10) [0,0.25 .. 1] == [1,3.25,5.5,7.75,10]

import Sound.SC3.Plot {- hsc3-plot -}
plotTable1 (map (linear (-1) 1) [0,0.01 .. 1])

exponential :: Floating t => Interpolation_F t

Exponential interpolation, x0 must not be 0, (x0,x1) must not span 0.

plotTable1 (map (exponential 0.001 1) [0,0.01 .. 1])

exponential' :: (Eq t, Floating t) => Interpolation_F t

Variant that allows x0 to be 0, though (x0,x1) must not span 0.

plotTable1 (map (exponential' 0 1) [0,0.01 .. 1])
plotTable1 (map (exponential' 0 (-1)) [0,0.01 .. 1])

exponential'' :: (Eq t, Floating t) => Interpolation_F t

linear of exponential', ie. allows (x0,x1) to span 0.

plotTable1 (map (exponential'' (-1) 1) [0,0.01 .. 1])

sine :: Floating t => Interpolation_F t

linear with t transformed by sine function over (-pi2,pi2).

plotTable1 (map (sine (-1) 1) [0,0.01 .. 1])

welch :: (Ord t, Floating t) => Interpolation_F t

If x0 < x1 rising sine segment (0,pi/2), else falling segment (pi/2,pi).

plotTable1 (map (welch (-1) 1) [0,0.01 .. 1])
plotTable1 (map (welch 1 (-1)) [0,0.01 .. 1])

curve :: (Ord t, Floating t) => t -> Interpolation_F t

Curvature controlled by single parameter c. 0 is linear, increasing c approaches exponential.

plotTable (map (\c-> map (curve c (-1) 1) [0,0.01 .. 1]) [-6,-4 .. 6])

squared :: Floating t => Interpolation_F t

Square of linear of sqrt of x0 and x1, therefore neither may be negative.

plotTable1 (map (squared 0 1) [0,0.01 .. 1])

cubed :: Floating t => Interpolation_F t

Cubic variant of squared.

plotTable1 (map (cubed 0 1) [0,0.01 .. 1])

hold :: (Num t, Ord t) => Interpolation_F t

x0 until end, then immediately x1.

plotTable1 (map (hold 0 1) [0,0.01 .. 1])