Shorthand comparison ends up being too long to understand - ios

Question

There's a "Clamp" function from a library of Ray Wenderlich class's - SKTUtils to be exact. This clamp function is written in shorthand but in a way that I can't seem to understand. This clamps purpose is to limit a position to an area - the games "camera" follows the _player.position, while making sure the the player never sees the nothingness outside the game map. Here's the function:
CGFloat Clamp(CGFloat value, CGFloat min, CGFloat max)
{
return value < min ? min : value > max ? max : value;
}
Here is the method it's used in, which the method it self gets used inside 'didFinishUpdate' method:
-(CGPoint)pointToCenterViewOn:(CGPoint)centerOn
{
CGFloat x = Clamp(centerOn.x, self.size.width/2, _backgroundLayer.layerSize.width - self.size.width/2); //Value, Min, Max.
CGFloat y = Clamp(centerOn.y, self.size.height/2, _backgroundLayer.layerSize.height - self.size.height/2);
return CGPointMake(-x, -y);
}
-(void)didFinishUpdate
{
_worldNode.position = [self centerViewOnPoint:_player.position];
}
Can someone explain this?
value < min ? min : value > max ? max : value
I could only partially understand the shorthands beginning:
if (value < min)
{
value = min;
}
else if (value > min)
{
value > max??????
}

Answer 1

Here is the explanation of value < min ? min : value > max ? max : value
if (value < min)
{
return min
}
else
{
if (value > max)
{
return max
}
else
{
return value
}
}

Answer 2

Operator precedence is partially involved here. This would be made a lot nicer with some parentheses to aid reading. The comparison operators bind tighter than the ternary conditional, so you have:
(value < min) ? min : ((value > max) ? max : value)
From there it's just evaluated left-to-right. The only tricky bit is that the else branch of the first conditional operator is itself another conditional operator. This would be the equivalent of an else if were you to expand it. The else branch of the second conditional is thus the else for the whole expression.
To convert this to if statements, then, you would do:
CGFloat retVal;
if( value < min ){
retVal = min;
}
else if( value > max ){
retVal = max;
}
else {
retVal = value;
}
return retVal;
You might also prefer this way to clamp a value:
MAX(min_limit, MIN(value, max_limit))
which uses the MAX and MIN macros to evaluate to the lower of max_limit or value and the higher of that or min_limit, producing a result in the range between min_limit and max_limit (inclusive). The effect is the same; I think that's easier to read.