If you want you can do this in Unity3d in 1 day. For iOS ,Android, also Windows Phone 8. The mobile version is Free.
Thanks, but I needed to integrate it into an existing Objective-C and Java application, so Unity wasn't an option.
In the end I've decided to use different libraries for each platform. For Android I'm not sure what I'm gonna use, but for iOS8+ I've decided to use Apple's SceneKit.