Calculating points of a circle dynamically in an Android game

Question

Hi there

If my X co-ordinates increment every time a frame is drawn, what formula can I employ from the math library in order to have the Y co-ordinate moving around the circumference of a circle frame by frame, creating the illusion of an orbiting object around a continuously moving central point?

I have seen it may involve sin or cos but am not sure how to adjust the variables accordingly per frame.

Many thanks for your help

Answer 1

You can't make a complete circle if your X coordinate increments every time, because half the time your X coordinate has to be decrementing.

What you want is polar coordinates: theta for angle and r for radius. Your r will remain constant, and your theta will increment continuously. Then your x and y are:

x = r * cos(theta)
y = r * sin(theta)

Answer 2

let ox,oy be the origin of your circle, and px,py be a point on the edge of the circle, with a radius of r

given: (px-ox)^2 + (py-oy)^2 = r^2 definition of circle

solve for py:

(py-oy)^2 = r^2 - (px-ox)^2

(py-oy) = sqrt(r^2 - (px-ox)^2)

py = sqrt(r^2 - (px-ox)^2) + oy <---

So as you increment px with your frames, you can find the appropriate py by recalculating the above formula.