Resize UIImage with aspect ratio?

After you set your screen rect, do something like the following to decide what rect to draw the image in:

float hfactor = value.bounds.size.width / screenRect.size.width;
float vfactor = value.bounds.size.height / screenRect.size.height;

float factor = fmax(hfactor, vfactor);

// Divide the size by the greater of the vertical or horizontal shrinkage factor
float newWidth = value.bounds.size.width / factor;
float newHeight = value.bounds.size.height / factor;

// Then figure out if you need to offset it to center vertically or horizontally
float leftOffset = (screenRect.size.width - newWidth) / 2;
float topOffset = (screenRect.size.height - newHeight) / 2;

CGRect newRect = CGRectMake(leftOffset, topOffset, newWidth, newHeight);

If you don't want to enlarge images smaller than the screenRect, make sure factor is greater than or equal to one (e.g. factor = fmax(factor, 1)).

To get the black background, you would probably just want to set the context color to black and call fillRect before drawing the image.