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Basically, I am from a Swift SpriteKit background where UIScreen.mainScreen().bounds is a CGRect which represents the screen and can be manipulated in various ways like getting the middle of the screen by using

var screenCenter = CGPointMake(UIScreen.mainScreen().bounds.width/2, UIScreen.mainScreen().bounds.height/2)

What is an equivalent of UIScreen.mainScreen().bounds in Unity (C# Scripting) that can manipulated to get various positions in a similar manner?

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Sounds like you want the Screen class:

var screenCenter = new Vector2(
                         Screen.width,
                         Screen.height,
                       ) * 0.5f;

Note that this will give you the pixel coordinates of the center of the screen, in screenspace. To translate this into a position within the world coordinate system, you'll want to use something like Camera.ScreenToWorldPoint.

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