coordinate computation of the image thumbnail - objective-c

Question

This is a code snippet for creating a thumbnail sized image (from an original large image) and placing it appropriately on top of a tableviewcell. As i was studying the code i got stuck at the part where the thumbnail is being given a position by setting its abscissa and ordinate. In the method -(void)setThumbDataFromImage:(UIImage *)image they're setting the dimensions and coordinate for project thumbnail—
-(void)setThumbnailDataFromImage:(UIImage *)image{
CGSize origImageSize= [image size];
// the rectange of the thumbnail
CGRect newRect= CGRectMake(0, 0, 40, 40);
// figure out a scaling ratio to make sure we maintain the same aspect ratio
float ratio= MAX(newRect.size.width/origImageSize.width, newRect.size.height/origImageSize.height);
// Create a transparent bitmap context with a scaling factor equal to that of the screen
UIGraphicsBeginImageContextWithOptions(newRect.size, NO, 0.0);
// create a path that is a rounded rectangle
UIBezierPath *path= [UIBezierPath bezierPathWithRoundedRect:newRect cornerRadius:5.0];
// make all the subsequent drawing to clip to this rounded rectangle
[path addClip];
// center the image in the thumbnail rectangle
CGRect projectRect;
projectRect.size.width=ratio * origImageSize.width;
projectRect.size.height= ratio * origImageSize.height;
projectRect.origin.x= (newRect.size.width- projectRect.size.width)/2;
projectRect.origin.y= (newRect.size.height- projectRect.size.height)/2;
// draw the image on it
[image drawInRect:projectRect];
// get the image from the image context, keep it as our thumbnail
UIImage *smallImage= UIGraphicsGetImageFromCurrentImageContext();
[self setThumbnail:smallImage];
// get the PNG representation of the image and set it as our archivable data
NSData *data= UIImagePNGRepresentation(smallImage);
[self setThumbnailData:data];
// Cleanup image context resources, we're done
UIGraphicsEndImageContext();
}
I got the width and height computation wherein we multiply the origImageSize with scaling factor/ratio.
But then we use the following to give the thumbnail a position—
projectRect.origin.x= (newRect.size.width- projectRect.size.width)/2;
projectRect.origin.y= (newRect.size.height- projectRect.size.height)/2;
This i fail to understand. I cannot wrap my head around it. :?
Is this part of the centering process. I mean, are we using a mathematical relation here to position the thumbnail or is it some random calculation i.e could have been anything.. Am i missing some fundamental behind these two lines of code??

Answer 1

Those two lines are standard code for centering something, although they aren’t quite written in the most general way. You normally want to use:
projectRect.origin.x = newRect.origin.x + newRect.size.width / 2.0 - projectRect.size.width / 2.0;
projectRect.origin.y = newRect.origin.y + newRect.size.height / 2.0 - projectRect.size.height / 2.0;
In your case the author knows the origin is 0,0, so they omitted the first term in each line.
Since to center a rectangle in another rectangle you want the centers of the two axes to line up, you take, say, half the container’s width (the center of the outer rectangle) and subtract half the inner rectangle’s width (which takes you to the left side of the inner rectangle), and that gives you where the inner rectangle’s left side should be (e.g.: its x origin) when it is correctly centered.