Circulation

Basics

For our intents and purposes, circulation is a scalar quantity representing the path of a target bot 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. After simplifying the expression, 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

> determine whether target is circling clockwise or couter-clockwise

> determine whether or not a bot travels in circular paths around you

> keep track of direction changes independant from target's velocity(+/-)

> other uses? please contribute...

Notes

> positive circulation = clockwise

> negative circulation = counter-clockwise

> zero circulation = target is not moving, or is travelling directly towards or away from you

> Circulation is actually a scalar number representing to what extent a vector is following a vector field. A value of zero is produced when the vector is perpendicular to the field