typealias ValueBuilderType = (CGFloat) -> CGFloat

func BuildPath(f : ValueBuilderType)(p0: CGPoint, p1: CGPoint)(x: CGFloat) -> CGPoint {
    let dx = p1.x - p0.x
    let dy = p1.y - p0.y
    let magnitude = sqrt(dy * dy + dx * dx)
    let theta = atan2(dy, dx)

    var outPoint = CGPointMake(x * magnitude, f(x) * magnitude)
    outPoint = CGPointApplyAffineTransform(outPoint, CGAffineTransformMakeRotation(theta))
    outPoint = CGPointApplyAffineTransform(outPoint, CGAffineTransformMakeTranslation(p0.x, p0.y))
    return CGPointMake(outPoint.x, outPoint.y)
}

// A few functions to kick around
let fnsin : ValueBuilderType = {CGFloat(0.5 * sin($0 * CGFloat(M_PI)))}
let fnsoftsin : ValueBuilderType = {CGFloat(0.5 * sin($0 * CGFloat(2.0 * M_PI)))}
let fnsawtooth : ValueBuilderType = {($0 * 5) % 1}

let randomPosition = {CGFloat(arc4random_uniform(200))}
var p0 = CGPointMake(randomPosition(), randomPosition())
var p1 = CGPointMake(randomPosition(), randomPosition())
let tuple = (p0: p0, p1: p1)
let base = BuildPath([fnsin, fnsoftsin, fnsawtooth][Int(arc4random_uniform(3))])
let f = base(tuple)

let path = UIBezierPath(); path.moveToPoint(p1); path.addLineToPoint(p0)
for value in stride(from: 0.0, to: 1.01, by: 0.01) {
    path.addLineToPoint(f(x: CGFloat(value)))
}
path.closePath()