Any time you are long gamma, the shape of your P/L curve could be described as a smile shape, or a U shape, or a saucer shape, etc. Any time you are short gamma, your P/L curve could be described as a frown shape, or an upside-down U shape, or upside-down saucer shape. The U or smile or frown or saucer could be tilted to the left or right depending on the position's delta. But any option trader can tell at a glance by looking at a P/L curve if it represents a long-gamma or short-gamma position. My question is this - is there a simple mathematical way of describing a long-gamma (smile) curve vs a short-gamma (frown) curve? Thanks.