I'm trying to determine 'how much' (as a percentage) a 2D rectangle fills a 2D circle.
I was comparing the accuracy of some computer game weapons by calculating the max possible dispersion from the weapon's shell origion at a given range. After that, I added a player stand in to help visualize the possible dispersion vs size of the target. Of course I can eyeball the values, but I don't know how to calculate this geometry (as the player's head and feet would not actually be inside the dispersion area, so a basic area calculation is not accurate).
Any guidance is appreciated.
I'm sorry that the question was not more clear, I'll try to elaborate:
In the case of the smaller circle, if you did a basic area calculation of the circle (1.828) and the rectangle (1.6), the result would say that the rectangle fills ~87% of the circle. However, the person cannot be compacted, and their upper body and lower body do not fall within the circle, and therefore the result is not accurate.
Now I think all I need to do is to subtract the difference of the circle's diameter from the max extents of the rectangle (so 2m - 1.526 = 0.474, or in other words, just make the rectangle as tall as the circle's diameter) making the rectangle's new area 1.526 * 0.8. Making the new percentage ~69%, which should be much more accurate. Am I on the right track?
Actual Values from the Test:
Player: 2m tall, 0.8m wide.
Weapon Dispersion Circle A (green): radius = 0.763.
Weapon Dispersion Circle B (red): radius = 1.05.