Could you explain how this GameObject rotating around another GameObject works?

Question

I'm just learning Unity and I follow a tutorial for a simple game which I want to build up from.

I'm already mostly done with the course and at the end a "boss enemy" gets implemented.

Its special ability is, that it has some other GameObject (a fireball) floating around itself.

It is all done in a single line of code in the update method which I don't quite understand yet, so any explanation would be great.

Here is the code:

private void Update()
{
    fireball.position = transform.position + 
        new Vector3(
            -Mathf.Cos(Time.time * fireballSpeed) * distance, 
            Mathf.Sin(Time.time * fireballSpeed) * distance, 
            0);
}

• fireball is the transform of the object which floats around
• fireballSpeed is a float which indicates the floating speed
• distance is the distance from the boss enemy

I get that we are just updating the transforms position but I don't quite understand the Time.time * fireballSpeed part. I also get that Cos and Sin are returning positions for X and Y but I need to improve my math knowledge to completely wrap my head around it to be honest.

So any explanation would be great.

Answer 1

The purpose of the sine and cosine function is to turn an angle into X and Y coordinates. Here is an animation from Wikipedia (source) which visualizes what these functions do as the input angle is incrasing:

An interesting property of these functions is that they are repeating every 360°. The sine of 10° is 0.17364. The sine of 3600010° (1000 full rotations and then an additional 10°) is also 0.17364. No matter how large the input value gets, the output value keeps oscillating between +1 and -1.

Which means that feeding a continuously increasing timer into the sine and cosine functions is a perfectly valid method to create a continuous rotation.

Although there is one aspect you might want to keep in mind: Floating point accuracy. Time.time is a float. The larger a floating point value gets, the less accurate does it become. This can be a problem in a situation like this where the least significant parts of the number are the most important. So when your game runs for a very long time, then this rotating animation might get a bit choppy.

One possible fix is to use double accuracy instead, which means that you use Time.timeAsDouble instead of Time.time and System.Math instead of Unity.Mathf:

-Math.Cos(Time.timeAsDouble * fireballSpeed) * distance