function to create a UIBezierPath for a (rounded corner) polygon in Swift

rounded_polygon_path

// this is a port from the following Objective C code
// http://stackoverflow.com/a/24770675/1269132

func roundedPolygonPath(
    #square:CGRect,
    #lineWidth:Double,
    #sides:NSInteger,
    #cornerRadius:Double) -> UIBezierPath {
        
        let path = UIBezierPath()
        
        // how much to turn at every corner
        let theta = 2.0 * M_PI / Double(sides)
        // offset from which to start rounding corners
        let offset = cornerRadius * tan(theta / 2.0)
        let squareWidth = min(Double(square.size.width), Double(square.size.height))
        // calculate the length of the sides of the polygon
        var length = squareWidth - lineWidth
        
        // if not dealing with polygon which will be square with all sides...
        if sides % 4 != 0 {
            // ... offset it inside a circle inside the square
            length = length * cos(theta / 2.0) + offset/2.0
        }
        let sideLength = length * tan(theta / 2.0)
        
        // start drawing at `point` in lower right corner
        
        var point = CGPointMake(CGFloat(squareWidth / 2.0 + sideLength / 2.0 - offset),
                                CGFloat(squareWidth - (squareWidth - length) / 2.0))
        var angle = M_PI
        path.moveToPoint(point)
        
        // draw the sides and rounded corners of the polygon
        
        for var side = 0; side < sides; side++ {
            point = CGPointMake(CGFloat(Double(point.x) + (sideLength - offset * 2.0) * cos(angle)),
                                CGFloat(Double(point.y) + (sideLength - offset * 2.0) * sin(angle)))
            path.addLineToPoint(point)
            let center = CGPointMake(CGFloat(Double(point.x) + cornerRadius * cos(angle + M_PI_2)),
                CGFloat(Double(point.y) + cornerRadius * sin(angle + M_PI_2)))
            
            path.addArcWithCenter(center, radius: CGFloat(cornerRadius), startAngle: CGFloat(angle - M_PI_2), endAngle: CGFloat(angle + theta - M_PI_2), clockwise: true)
            
            point = path.currentPoint // we don't have to calculate where the arc ended ... UIBezierPath did that for us

            angle += theta
        }
        path.closePath()
        
        return path
}