Drawing dots and lines on to a UIView

To draw UIBezierPath on UIView do this:

let xCoord = 10
let yCoord = 20
let radius = 8

let dotPath = UIBezierPath(ovalInRect: CGRectMake(xCoord, yCoord, radius, radius))

let layer = CAShapeLayer()
layer.path = dotPath.CGPath
layer.strokeColor = UIColor.blueColor().CGColor

drawingView.layer.addSublayer(layer)

This code will draw a dot with radius 8 with coordinates 10,20 on your view.

Update: Swift 4+

let xCoord = 10
let yCoord = 20
let radius = 8

let dotPath = UIBezierPath(ovalIn: CGRect(x: xCoord, y: yCoord, width: radius, height: radius))

let layer = CAShapeLayer()
layer.path = dotPath.cgPath
layer.strokeColor = UIColor.blue.cgColor

drawingView.layer.addSublayer(layer)

Here is an attempt at the lines part of the equation:

    var offset:CGFloat    = 0;    var squareWidth:Int = 20
    var squareRows:Int    = Int(view.frame.size.width/CGFloat(squareWidth))
    var squareColumns:Int = Int(view.frame.size.height/CGFloat(squareWidth))

    for (index,element) in (0...squareRows).enumerate(){
        for (column,element) in (0...squareColumns).enumerate(){
            // Build The Square
            let rectanglePath = UIBezierPath(roundedRect: CGRectMake(
                view.frame.minX + CGFloat(squareWidth * index) - offset,
                view.frame.minY + CGFloat(column * squareWidth), 20, 20
                ),
                cornerRadius: 0.00)

            // Style Square
            let a = CAShapeLayer()
                a.path = rectanglePath.CGPath
                a.strokeColor = UIColor.whiteColor().CGColor
                a.fillColor = nil
                a.opacity = 0.3
                a.lineWidth = 1.5
            view.layer.insertSublayer(a, atIndex: 1)
        }
    }