Implement Interpolation

[jsbean]

Extract from Rhythm, and implement generically. See: dn-m/Rhythm/issues:40.

[jsbean]

Just spit-ballin' here:

In order to make this process generic, for more types than just Tempo over MetricalDuration, we could do the following?:

• [ ] Extract out Easing:

  enum Easing {
  case linear
  case exponentialIn(exponent: Double)
  case exponentialInOut(exponent: Double)
  case sineInOut
  func evaluate(at: Double) -> Double { ... }
  func integrate(at: Double) -> Double { ... }
  }

• [ ] Refactor Interpolation as InterpolationProtocol

  protocol InterpolationProtocol {
  associatedtype XType // naming, constraints?
  associatedtype YType // naming, constraints?
  let start: YType
  let end: YType
  let length: XType // naming?
  let easing: Easing
  
  // Transform associated types to `Easing`-acceptable values
  func position(x: XType) -> Double // naming?
  func x(position: Double) -> XType // naming?
  func position(y: YType) -> Double // naming?
  func y(position: Double) -> YType // naming?
  }

• [ ] Refactor Tempo.Interpolation as an implementation of InterpolationProtocol

  extension Tempo {
  struct Interpolation: InterpolationProtocol {
      var duration: Seconds { return position(x: length) }
      let start: Tempo
      let end: Tempo
      let length: MetricalDuration
  
      func concreteOffset(for metricalOffset: MetricalDuration) -> Seconds {
          return easing.integrate(at: position(x: metricalOffset))
      }
  
      // MARK: - InterpolationProtocol
      func position(x: MetricalDuration) -> Double { ... }
      func position(y: Tempo) -> Double { ... }
      func x(position: Double) -> MetricalDuration { ... }
      func y(position: Double) -> Tempo { ... }
  }
  }

  Could be on a completely different planet, but would like to hear your thoughts, @brianlheim.

[jsbean]

Or, perhaps the InterpolationProtocol could be much lighter:

protocol InterpolationProtocol {
    let start: YType
    let end: YType
    let length: XType
    func y(for x: XType) -> YType
}