Scale circle uivew just big enough to fill screen - ios

Question

I would like to automate the scale factor of many uiviews that have cornerRadius set so that they look like circles. The idea is that these 20 circle uiviews, of varying sizes and location, will scale up to fill the screen no matter their size, location etc when tapped.
My code has a hard coded value that I would like to make intelligent:
[UIView animateWithDuration:0.2 delay:0.0 options:UIViewAnimationOptionCurveEaseInOut animations:^{
self.layer.affineTransform = CGAffineTransformMakeScale(15.0f, 15.0f);
} completion:^(BOOL finished) {
}];
Yes - I could just type in 20 for CGAffineTransformMakeScale but then the bigger circles are scaling larger for no reason - they might need to scale 11 instead.
What would be the way to factor the original size to a fixed, much larger size?
Note: The circle uiview, being rounded, should scale big enough that the rounded edges are not visible - it needs to scale beyond the screen to fill in those gaps at the corners.

Answer 1

Conceptually, you want to center the circle in the screen, then scale it so that the screen rect is inscribed in the circle. Here's a handy diagram:
From the center of the screen, we can draw a triangle to the corner. The hypotenuse of that triangle is your desired circle radius. Here's the code to transform your circle:
[UIView animateWithDuration:0.2 animations:^{
CGPoint screenCenter = CGPointMake(CGRectGetMidX([UIScreen mainScreen].bounds), CGRectGetMidY([UIScreen mainScreen].bounds));
CGPoint circleCenter = [self.window convertPoint:self.center fromView:self.superview];
// Calculate distance from circle's current center to the screen center
UIOffset offset = UIOffsetMake(screenCenter.x - circleCenter.x, screenCenter.y - circleCenter.y);
// Calculate distance from screen center to corner
CGFloat screenRadius = sqrtf(powf(CGRectGetWidth([UIScreen mainScreen].bounds) * 0.5, 2.0f)
+ powf(CGRectGetHeight([UIScreen mainScreen].bounds) * 0.5, 2.0f));
CGFloat circleRadius = CGRectGetWidth(self.bounds) * 0.5;
CGFloat scale = screenRadius / circleRadius;
// Combine scale and translation
CGAffineTransform scaleTransform = CGAffineTransformMakeScale(scale, scale);
CGAffineTransform translateTransform = CGAffineTransformMakeTranslation(offset.horizontal, offset.vertical);
self.transform = CGAffineTransformConcat(scaleTransform, translateTransform);
}];