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(squareLength: CGFloat, lineWidth: CGFloat, sides: Int, cornerRadius: CGFloat) -> UIBezierPath {
    let path = UIBezierPath()
    // how much to turn at every corner
    let theta = 2.0 * CGFloat.pi / CGFloat(sides)
    // offset from which to start rounding corners
    let offset = cornerRadius * tan(theta / 2.0)
    let sideLength: CGFloat = {
        // calculate the length of the sides of the polygon
        var length = squareLength - 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
        }
        return length * tan(theta / 2.0)
    }()

    // start drawing at `point` in lower right corner
    var point = CGPoint(x: squareLength / 2.0 + sideLength / 2.0 - offset, y: squareLength - (squareLength - length) / 2.0)
    var angle = CGFloat.pi
    path.move(to: point)

    // draw the sides and rounded corners of the polygon
    for _ in 0..<sides {
        point = CGPoint(x: point.x + (sideLength - offset * 2.0) * cos(angle), y: point.y + (sideLength - offset * 2.0) * sin(angle))
        path.addLine(to: point)
        let center = CGPoint(x: point.x + cornerRadius * cos(angle + .pi/2), y: point.y + cornerRadius * sin(angle + .pi/2))

        path.addArc(withCenter: center, radius: cornerRadius, startAngle: angle - .pi/2, endAngle: angle + theta - .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.close()
    return path
}