Circulation

I wanted to apply some of my schooling to robocode and come up with what I thought was a novel idea, so in the last couple of my bots, I've implemented "circulation" and "rate of circulation" which I have learnt from Calculus III: Vector Calculus. - px

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Basics

For our intents and purposes, circulation is a scalar quantity representing the path of a point in a vector field around another point, or in our case, a target tank around our bot. This value can be used to tell us in what direction the target bot is travelling no matter its heading, and how fast it is circling our bot.

For example, the target can have a positive velocity, and is circling you in a clockwise direction, circulation will be a positive number. Now, if the target changes direction (ie, velocity is negative) but is STILL circling you in a clockwise direction, the circulation will still be positive.

Calculation

Circulation is equal to the dot product of the target's velocity and a circulating vector field around our bot. This equation can be used to determine the value:

circulation = dX*cos(theta) - dY*sin(theta)

This equation assumes that your bot is at the centre of a perfectly circular vector field where,

theta = angle towards target bot, dX = target bot's x displacement, dY = target bot's y displacement

Specific uses