I'm developing a game where the player quickly has to tap/click on various shapes such as squares, circles, triangles, stars and so on. I'm now struggling with the following task: I'm searching for a normalized size for each shape, so that every shape is equally difficult to hit. E.g. given a circle with a radius
r, how do I find the length
l of the corresponding square?
At first glance I thought: Easy. Just make all shapes share the same area
A. So, in the example above,
l = sqrt(pi). http://en.wikipedia.org/wiki/Squaring_the_circle
But on second thought, this does not seem to be the best metric. Imagine a star with many long, thin, pointy arms or a very long but thin line. Even if they have the same area as a circle or square, they are still more difficult to hit.
So, what might be a better approach? Maybe something involving the "form factor" (circumference squared divided by area