/*

    Copyright (C) 2016 Apple Inc. All Rights Reserved.

    See LICENSE.txt for this sample’s licensing information

    Abstract:

    Convenience math operators

*/

import QuartzCore

func clip<T : Comparable>(_ x0: T, _ x1: T, _ v: T) -> T {

    return max(x0, min(x1, v))

}

func lerp<T : FloatingPoint>(_ v0: T, _ v1: T, _ t: T) -> T {

    return v0 + (v1 - v0) * t

}

func -(lhs: CGPoint, rhs: CGPoint) -> CGVector {

    return CGVector(dx: lhs.x - rhs.x, dy: lhs.y - rhs.y)

}

func -(lhs: CGPoint, rhs: CGVector) -> CGPoint {

    return CGPoint(x: lhs.x - rhs.dx, y: lhs.y - rhs.dy)

}

func -(lhs: CGVector, rhs: CGVector) -> CGVector {

    return CGVector(dx: lhs.dx - rhs.dx, dy: lhs.dy - rhs.dy)

}

func +(lhs: CGPoint, rhs: CGPoint) -> CGVector {

    return CGVector(dx: lhs.x + rhs.x, dy: lhs.y + rhs.y)

}

func +(lhs: CGPoint, rhs: CGVector) -> CGPoint {

    return CGPoint(x: lhs.x + rhs.dx, y: lhs.y + rhs.dy)

}

func +(lhs: CGVector, rhs: CGVector) -> CGVector {

    return CGVector(dx: lhs.dx + rhs.dx, dy: lhs.dy + rhs.dy)

}

func *(left: CGVector, right:CGFloat) -> CGVector {

    return CGVector(dx: left.dx * right, dy: left.dy * right)

}

extension CGPoint {

    var vector: CGVector {

        return CGVector(dx: x, dy: y)

    }

}

extension CGVector {

    var magnitude: CGFloat {

        return sqrt(dx*dx + dy*dy)

    }

    var point: CGPoint {

        return CGPoint(x: dx, y: dy)

    }

    func apply(transform t: CGAffineTransform) -> CGVector {

        return point.applying(t).vector

    }

}