I want to calculate the area in terms of a real variable.

To begin with, everyone's area is a circle, it has a center point, and a radius. This is all fine and well - the area is directly defined by the parameters at the beginning.

However, this radius can grow and shrink. That too is no problem. But when two players 'boundaries' come into contact, I want the 'stronger' players to maintain control, and the 'weaker' players to shrink.

[b]Is there a formula for say, 'connect each point[1 to 16], return size of area within those points'?[/u]

Will this formula work if the players 'area' was to expand in a manner that wasn't circular?

For example, you have a - fuck dat Imma make pitchers.

Red and Yellow have spawned against the map boundary. How would I calculate their area?

Purple has added two expansions. What is his total radius? Each expansion adds a radius of 6 to your area, but must be constructed within your existing boundary. This means that you only gain a partial increase to your total area.

Yellow has added only one expansion. What is his total radius?

Teal (center) has upgraded his main base and gained +12 radius. I know his total area to be a circle with a radius of 24 now.

Blue has been upgrading his 'strength', and has doubled his radius (like Teal did in the mid-game).

Teal is 'weaker' than Blue (since he has been expanding), and has placed an expansion encroaching his control into Blues area. However, since Teal is weaker, blue maintains his boundary, and teal's is deformed.

Purple used a special ability (I got lazy with paint) and mirror'd his current size, to the North. However, this has made him weaker than Teal, and as such, Purples boundary is deformed while Teal's maintains.

Red and Yellow left the game because spawning at the sides sucks.

Knowns:

Each boundary (initially) consists of 16 units defining the roughly circular area in which you start.

Placing an expansion creates 8 units defining a circular area near your boundary. Of these 8 units, only the ones 'outside' your current boundary are kept, the interior ones are removed.

Unknowns:

The damn area of a polygon - that can become complex as seen in the end-game.

BONUS QUESTION

Blue got attacked by Red and Green at the same time. There 'strengths' are equal, but since blue has 'unoccupied space' (free) to his left and right, his area should maintain the same value. What is his end area?

Post has been edited 1 time(s), last time on May 22 2011, 12:19 am by Cardinal.

None.