Swift: Interpolation

// Interpol.playground

import CoreGraphics

typealias Time   = CFTimeInterval
typealias Value  = CGFloat
typealias Point  = CGPoint
typealias Vector = CGVector
typealias Size   = CGSize
typealias Rect   = CGRect

struct Interpolator<T> {
    typealias Interpolation = Time -> T

    let interpolation: Interpolation
    
    init(_ interpolation: Interpolation) {
        self.interpolation = interpolation
    }
    
    func interpolate(t: Time) -> T {
        return interpolation(t)
    }
}

extension Interpolator {
    subscript(t: Time) -> T {
        return interpolate(t)
    }
}

func interpolation(from: Value, to: Value) -> Interpolator<Value> {
    return Interpolator { t in
        Value(1 - t) * from + Value(t) * to
    }
}

func interpolation(from: Point, to: Point) -> Interpolator<Point> {
    let interpolator = (
        x: interpolation(from.x, to.x),
        y: interpolation(from.y, to.y)
    )
    
    return Interpolator { t in
        Point(x: interpolator.x[t], y: interpolator.y[t])
    }
}

func interpolation(from: Vector, to: Vector) -> Interpolator<Vector> {
    let interpolator = (
        dx: interpolation(from.dx, to.dx),
        dy: interpolation(from.dy, to.dy)
    )
    
    return Interpolator { t in
        Vector(dx: interpolator.dx[t], dy: interpolator.dy[t])
    }
}

func interpolation(from: Size, to: Size) -> Interpolator<Size> {
    let interpolator = (
        width:  interpolation(from.width,  to.width),
        height: interpolation(from.height, to.height)
    )
    
    return Interpolator { t in
        Size(width: interpolator.width[t], height: interpolator.height[t])
    }
}

func interpolation(from: Rect, to: Rect) -> Interpolator<Rect> {
    let interpolator = (
        origin: interpolation(from.origin, to.origin),
        size:   interpolation(from.size,   to.size)
    )
    
    return Interpolator { t in
        Rect(origin: interpolator.origin[t], size: interpolator.size[t])
    }
}


// Examples

let valueInterpolation = interpolation(0, 100)
valueInterpolation.interpolate(0.0) // =>   0.0
valueInterpolation.interpolate(0.5) // =>  50.0
valueInterpolation.interpolate(1.0) // => 100.0

let pointInterpolation = interpolation(CGPointZero, CGPoint(x: 100, y: 200))
pointInterpolation.interpolate(0.0) // => (  0.0,   0.0)
pointInterpolation.interpolate(0.5) // => ( 50.0, 100.0)
pointInterpolation.interpolate(1.0) // => (100.0, 200.0)

let vectorInterpolation = interpolation(CGVector(dx: 0, dy: 0), CGVector(dx: 100, dy: 200))
vectorInterpolation.interpolate(0.0) // => (  0.0,   0.0)
vectorInterpolation.interpolate(0.5) // => ( 50.0, 100.0)
vectorInterpolation.interpolate(1.0) // => (100.0, 200.0)

let sizeInterpolation = interpolation(CGSizeZero, CGSize(width: 100, height: 200))
sizeInterpolation.interpolate(0.0) // => (  0.0,   0.0)
sizeInterpolation.interpolate(0.5) // => ( 50.0, 100.0)
sizeInterpolation.interpolate(1.0) // => (100.0, 200.0)

let rectInterpolation = interpolation(CGRectZero, CGRect(x: 500, y: 500, width: 100, height: 200))
rectInterpolation.interpolate(0.0) // => (  0.0,   0.0,   0.0,   0.0)
rectInterpolation.interpolate(0.5) // => (250.0, 250.0,  50.0, 100.0)
rectInterpolation.interpolate(1.0) // => (500.0, 500.0, 100.0, 200.0)