The interaction of the Lifesum app was nice, so I tried to recreate it.

	import UIKit

	@UIApplicationMain
	class AppDelegate: UIResponder, UIApplicationDelegate {

	var window: UIWindow?
	var navigationController: UINavigationController?

	func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplication.LaunchOptionsKey: Any]?) -> Bool {

	self.window = UIWindow(frame: UIScreen.main.bounds)
	self.window!.makeKeyAndVisible()
	let firstViewController: FirstViewController? = FirstViewController()
	navigationController = UINavigationController(rootViewController: firstViewController!)
	navigationController?.setNavigationBarHidden(true, animated: false)
	window!.rootViewController = navigationController

	return true
	}

	func applicationWillResignActive(_ application: UIApplication) {
	}

	func applicationDidEnterBackground(_ application: UIApplication) {
	}

	func applicationWillEnterForeground(_ application: UIApplication) {
	}

	func applicationDidBecomeActive(_ application: UIApplication) {
	}

	func applicationWillTerminate(_ application: UIApplication) {
	}
	}

view raw AppDelegate.swift hosted with ❤ by GitHub

	import UIKit

	class CustomButton: UIButton {
	required init(coder aDecoder: NSCoder) {
	super.init(coder: aDecoder)!
	}

	override init(frame: CGRect) {
	super.init(frame: frame)
	backgroundColor = UIColor(named: "emerald")
	setTitleColor(UIColor.white, for: UIControl.State.normal)
	titleLabel?.font = UIFont.systemFont(ofSize: 24)
	layer.masksToBounds = false
	layer.cornerRadius = 20.0
	layer.shadowColor = UIColor.lightGray.cgColor
	layer.shadowOffset = CGSize(width: 2.0, height: 2.0)
	layer.shadowOpacity = 0.8
	}
	}

view raw CustomButton.swift hosted with ❤ by GitHub

	import UIKit

	class FirstViewController: UIViewController {

	override func viewDidLoad() {
	super.viewDidLoad()

	view.backgroundColor = .white
	let buttonHeight: CGFloat = 60

	let button = CustomButton()
	button.frame.size = CGSize(width: view.frame.width * 0.6, height: buttonHeight)
	button.addTarget(self, action: #selector(buttonTaped(sender:)), for: .touchUpInside)
	button.setTitle("Push Me", for: UIControl.State.normal)
	button.center = view.center
	view.addSubview(button)
	}

	@objc func buttonTaped(sender: UIButton) {
	navigationController?.pushViewController(SecondViewController(), animated: true)
	}
	}

view raw FirstViewController.swift hosted with ❤ by GitHub

	import UIKit

	class SecondViewController: UIViewController {

	var width: CGFloat!
	var height: CGFloat!
	let buttonHeight: CGFloat = 60
	let radius: CGFloat = 100

	var button: CustomButton!

	override func viewDidLoad() {
	super.viewDidLoad()

	view.backgroundColor = .white
	width = view.frame.width
	height = view.frame.height

	//ボタンの生成
	button = CustomButton()
	button.frame.size = CGSize(width: width * 0.6, height: buttonHeight)
	button.center.x = view.frame.width / 2
	button.center.y = view.frame.height / 2 + 40
	button.addTarget(self, action: #selector(cornerCircleButtonClicked(sender:)), for: .touchUpInside)
	button.setTitle("Show Snorlax", for: UIControl.State.normal)
	button.alpha = 0.3
	button.isEnabled = false
	view.addSubview(button)

	// 起動直後のアニメーション
	UIView.animate(withDuration: 0.3, delay: 0.1, options: [.curveLinear], animations: {
	self.button.isEnabled = true
	self.button.alpha = 1.0
	self.button.center = self.view.center
	self.button.frame.size = CGSize(width: self.width * 0.6, height: self.buttonHeight)
	}, completion: nil)
	}

	//角丸ボタンが押されたら呼ばれます
	@objc func cornerCircleButtonClicked(sender: UIButton) {
	button.setTitle("", for: .normal)
	// 丸くするアニメーション
	UIView.animate(withDuration: 0.2, delay: 0.0, options: [.curveLinear], animations: {
	self.button.layer.cornerRadius = self.radius / 2
	self.button.frame.size = CGSize(width: self.radius, height: self.radius)
	self.button.center = self.view.center
	}, completion: { _ in
	// 広がっていくアニメーション
	UIView.animate(withDuration: 0.2, delay: 0.1, options: [.curveLinear], animations: {
	self.button.layer.cornerRadius = self.width
	self.button.frame.size = CGSize(width: self.height * 1.5, height: self.height * 1.5)
	self.button.center = self.view.center
	}, completion: { _ in
	self.pushViewController()
	})
	})
	}

	func pushViewController() {
	// 画面遷移のアニメーション
	let transition = CATransition()
	transition.duration = 0.5
	transition.timingFunction = CAMediaTimingFunction(name: CAMediaTimingFunctionName.easeIn)
	transition.type = CATransitionType.fade
	self.navigationController?.view.layer.add(transition, forKey: nil)
	let viewController = ThirdViewController()
	self.navigationController?.pushViewController(viewController, animated: false)
	}
	}

view raw SecondViewController.swift hosted with ❤ by GitHub

	import UIKit

	class ThirdViewController: UIViewController {

	override func viewDidLoad() {
	super.viewDidLoad()

	view.backgroundColor = .white
	let imageView = UIImageView()
	imageView.frame = view.frame
	imageView.image = UIImage(named: "icon")
	view.addSubview(imageView)
	}
	}

view raw ThirdViewController.swift hosted with ❤ by GitHub