Math questions (Game math)

[PoetPhilosopher]

I have some math questions for RF, some easy, some harder - kind of more High School level as the math I faced when I was in college, I found harder:

1. Consider a graphics processing system that operates at 60 frames per second. It requires a memory bandwidth of 30GB to move around up to 500MB of graphics data in RAM efficiently. Additionally, it has a fillrate of 24 gigapixels, which initially demands 24GB of memory bandwidth (just a vague approximation for this example). However, with an improved cache system, the fillrate's bandwidth issue is resolved.

Given this scenario, explain why, despite the improved cache system, the graphics processing system can still only move up to 500MB of graphics data.

And what part of the system is the bottleneck?

Also, here's some more:

2. A processing unit can read and write pixels, and has a max capability of 16 billion pixels total a second. It takes turns reading, then writing. How many pixels can it write a second?

3. In a video game, the framerate is given by the equation: Frame Rate (fps) = 30 + 0.5 * t, where 't' represents the time in seconds since the game started. If the game has been running for 10 seconds, what is the current framerate?

4. In a video game, the player's character can jump a certain height when the framerate is stable. The jump height 'h' in meters is given by the equation: h = 2 * (fps / 30), where 'fps' is the framerate in frames per second.

However, due to fluctuations in the framerate during gameplay, the character's jump height becomes inconsistent. For example, at one moment the framerate is 60 fps, and at another moment, it drops to 20 fps.

If the character jumps when the framerate is 60 fps and then jumps again when it's 20 fps, explain why the two jump heights are different.

Why isn't the jump consistent despite using the given equation?

How do we fix this problem?

Note: I also wanted to apologize in advance if my wording or grammar obscures any of the math problems. I've looked them over a couple times, but so far, I think they look good.

I'll post the answers after awhile.

 

[PoetPhilosopher]

Spoiler: Answers

1. Though there's more than one technical answer, there's a 'best and most likely answer', it's:

The graphics processing system can still only move up to 500MB of graphics data because that is the limit of its RAM bandwidth capacity. The improved cache system can reduce the memory bandwidth needed for the fillrate, but it cannot increase the amount of RAM bandwidth available for storing graphics data. The bottleneck in this system is the RAM bandwidth, which limits the amount of graphics data that can be processed at once.

2. A processing unit that can read and write pixels, and has a max capability of 16 billion pixels total a second, can write half of that amount per second, assuming it takes equal time to read and write. So, it can write 8 billion pixels per second.

3. The current framerate is 35 fps.

4. The jump is not consistent despite using the given equation because the equation depends on the framerate, which is not constant.

One way to fix this problem is to use a fixed timestep method, which updates the physics simulation at a constant rate regardless of the framerate. This way, the jump height will be independent of the framerate.

I hope people didn't mind me joining in on the math questionnaires.

 

[Subduction Zone]

Let me try again. I messed up my prior post:

Spoiler

Obviously the problem lies in the Gonculator:

 

[PoetPhilosopher]

Let me try again. I messed up my prior post:

Spoiler

Obviously the problem lies in the Gonculator:

View attachment 81015

I feel your pain.