Orbiting multiple objects evenly around a changing radius

Question

I have multiple objects (circles) and I want to place them in a circle, with even distance between each one, and have them orbit the center of the screen.

If I remove one object, I want the orbit radius to reduce and the other circles, as a result, end up getting closer and closing the circle again.

Below are some images to help explain what I'm trying to achieve.

A. is the objects evenly distributed around the center.

B. is after destroying one of the objects, the "circle of objects" need to close in and evenly distribute the objects once again.

C. is just after another object has been destroyed.

I know that the solution is some "basic" math, but it's been a while, and I'm super rusty.

Thanks for the help, if anything further is needed please let me know!!

Cheers!

o7

Answer 1

There are 360 degrees (2π radians) in a circle. Divide that by the number of objects, and that tells you the correct angle between the objects, for even spacing.

If you want to keep the objects the same distance apart no matter how many objects are in the circle, we need to calculate the distance out from the center at which points are that distance apart. That's just trigonometry; we make a triangle from the center to two adjacent objects. Split that into two right triangles, and use the cosin of the half angle to determine the distance from the center to one of the objects.

We can then use the angle and distanceFromCenter to place each object.

So if that calculated angle is a, then: (pseudocode)

float distanceBetweenObjects = 50.0; // or however far apart you want them to be
float distanceFromCenter = (distanceBetweenObjects*0.5)/sin(a*0.5);
float accumulatedAngle = 0.0;
foreach( object )
{
    object.position.x = cos(accumulatedAngle) * distanceFromCenter;
    object.position.y = sin(accumulatedAngle) * distanceFromCenter;
    accumulatedAngle += a;
}

Note that this assumes that the center of the screen is 0,0. If the center of your screen is some other coordinate, then add that to the calculations above. Also note that this doesn't take into account the size of the objects; it's merely trying to place their midpoints a certain distance apart. So your "sistanceBetweenObjects" value needs to include the size of the objects.