oozinator
Well-Known Member
Hello friends!
To start off, I’d like to first say that I’m not sure whether this should be a blog or a thread, since it could go either way. The blog format is suitable for the type of in-depth coverage you’re about to read, but it’s lacking in the collaborative, “back n’ forth” idea-sharing that I want to see. If it turns out that I get such feedback, I’ll make it a thread. But anyway…
One of the things I most often hear from gamers is how school subjects suck. To ease the boredom of school/homework and make it more relevant to their hobbies, some have tried blending the two. But in general, the consensus is that school sucks. In particular, my favorite subject has been at the forefront of assaults - math.
Being Asian, this makes me a sad oozi.
But it’s understandable. While art, music, literature, history, social sciences, and heck, even science lends itself easily to creative gaming media, math has been the boring one that usually tells you what you can/can’t do. “You can’t buy that gun because if you subtract the cost from your current funds, you'll end up with a negative number”; “At the rate that you’re grinding these mobs, it’ll take you 6 hours to get to the next level”; “My single warrior has a 33% chance of victory against that elite spearman, but attacking with 2 of them boosts those odds to just under 50%”; and so on. The point is that math is the boring accountant with a bland image. (Seriously, when was the last time you saw an interesting audio-visual representation of math in a game?)
Whoa! This game is teaching me math?! I seriously couldn’t tell!
But being a math and gaming nut, I often think about how math can be used creatively to enhance my gaming experience. One such idea happened when I was brainstorming my last major Minecraft survival project: the crater.
Of the giant holes you see in Minecraft survival (ravines, caves, player-made sand quarries etc.), very few of them look like a crater and those that do, aren’t really all that big. My first thought was: “Wouldn’t it be cool if someone made a massive, perfectly round crater?”
My second: “How do I make it look good, and what will it take?”
The answer to the first was an immediate “Yes!” but the answer to the second took a bit of thinking and tinkering.
While I love math, I usually don’t think about it right away in the design phase. My first planning instinct was to figure out a shape and depth that I liked by drawing a vertical plane profile of the crater like this:
A crater of blood? That's f***ing awesome!
Oh what? That just represents the volume of the crater?
Oh okay...
I soon realized that because the volume of a crater is nothing more than a portion of a sphere, I could use calculus, specifically disc integration about the y-axis, to estimate the volume I’d have to remove. My first attempt was with a crater depth of 40 blocks and a “1/4 bottom fraction of radius”, which resulted in a crater volume that was much too big. To be honest, there was nothing methodical about my approach beyond the math, and I was arbitrarily picking values for the limits (and making tons of mistakes with each calculation along the way).
I eventually referred to game mechanics (according to minecraftwiki.net) to at least set up some boundaries for the variables I was playing with. I knew that there would be a higher chance of encountering indestructible and unsightly monster spawners below Y:40, so my crater should be no more than 30 blocks deep (since at surface, Y:65). I knew that the default normal render distance was set at 128 blocks, so in order to see the crater from one edge to another, the crater diameter must be less than 128 blocks. Yet still, this left a lot of room for experimentation, and I wasn’t a number crunching machine (despite being Asian). So how could I make calculations for a bunch of possible models in a short time?
By making a custom “Crater Calculator” of course!
I made a spreadsheet in Excel that allowed me to enter the desired variables (in this case, “Bottom Fraction of Radius” and “Desired Depth”) to generate all sorts of useful design and logistical data and even draw a rough shape of the crater profile on a graph.
Dem double chests. Kinda obvious that I didn't go with this model
I could've sworn it was gonna look like a kitty cat.
This allowed me to design a crater that optimized aesthetics, considered game mechanics, and minimized materials and work.
Once I found this ideal model, I took the data, fired up MSPaint, and got working generating plans like these:
I swear I didn't do shrooms or drop acid when I came up with this.
If I hadn’t used the math (and spreadsheet) skills that I learned in school, I’d most likely be digging and gradually widening a small pilot hole somewhere in the desert and hoping it comes out looking remotely like a crater.
So yeah, school ain’t useless. And hopefully, some of you have applied what you've learned in school to gaming too! If you have, please comment below.
If anyone wants to know more about the math behind the crater, let me know as well.
To start off, I’d like to first say that I’m not sure whether this should be a blog or a thread, since it could go either way. The blog format is suitable for the type of in-depth coverage you’re about to read, but it’s lacking in the collaborative, “back n’ forth” idea-sharing that I want to see. If it turns out that I get such feedback, I’ll make it a thread. But anyway…
One of the things I most often hear from gamers is how school subjects suck. To ease the boredom of school/homework and make it more relevant to their hobbies, some have tried blending the two. But in general, the consensus is that school sucks. In particular, my favorite subject has been at the forefront of assaults - math.
Being Asian, this makes me a sad oozi.
But it’s understandable. While art, music, literature, history, social sciences, and heck, even science lends itself easily to creative gaming media, math has been the boring one that usually tells you what you can/can’t do. “You can’t buy that gun because if you subtract the cost from your current funds, you'll end up with a negative number”; “At the rate that you’re grinding these mobs, it’ll take you 6 hours to get to the next level”; “My single warrior has a 33% chance of victory against that elite spearman, but attacking with 2 of them boosts those odds to just under 50%”; and so on. The point is that math is the boring accountant with a bland image. (Seriously, when was the last time you saw an interesting audio-visual representation of math in a game?)
Whoa! This game is teaching me math?! I seriously couldn’t tell!
But being a math and gaming nut, I often think about how math can be used creatively to enhance my gaming experience. One such idea happened when I was brainstorming my last major Minecraft survival project: the crater.
Of the giant holes you see in Minecraft survival (ravines, caves, player-made sand quarries etc.), very few of them look like a crater and those that do, aren’t really all that big. My first thought was: “Wouldn’t it be cool if someone made a massive, perfectly round crater?”
My second: “How do I make it look good, and what will it take?”
The answer to the first was an immediate “Yes!” but the answer to the second took a bit of thinking and tinkering.
While I love math, I usually don’t think about it right away in the design phase. My first planning instinct was to figure out a shape and depth that I liked by drawing a vertical plane profile of the crater like this:
A crater of blood? That's f***ing awesome!
Oh what? That just represents the volume of the crater?
Oh okay...
I soon realized that because the volume of a crater is nothing more than a portion of a sphere, I could use calculus, specifically disc integration about the y-axis, to estimate the volume I’d have to remove. My first attempt was with a crater depth of 40 blocks and a “1/4 bottom fraction of radius”, which resulted in a crater volume that was much too big. To be honest, there was nothing methodical about my approach beyond the math, and I was arbitrarily picking values for the limits (and making tons of mistakes with each calculation along the way).
I eventually referred to game mechanics (according to minecraftwiki.net) to at least set up some boundaries for the variables I was playing with. I knew that there would be a higher chance of encountering indestructible and unsightly monster spawners below Y:40, so my crater should be no more than 30 blocks deep (since at surface, Y:65). I knew that the default normal render distance was set at 128 blocks, so in order to see the crater from one edge to another, the crater diameter must be less than 128 blocks. Yet still, this left a lot of room for experimentation, and I wasn’t a number crunching machine (despite being Asian). So how could I make calculations for a bunch of possible models in a short time?
By making a custom “Crater Calculator” of course!
I made a spreadsheet in Excel that allowed me to enter the desired variables (in this case, “Bottom Fraction of Radius” and “Desired Depth”) to generate all sorts of useful design and logistical data and even draw a rough shape of the crater profile on a graph.
Dem double chests. Kinda obvious that I didn't go with this model
I could've sworn it was gonna look like a kitty cat.
This allowed me to design a crater that optimized aesthetics, considered game mechanics, and minimized materials and work.
Once I found this ideal model, I took the data, fired up MSPaint, and got working generating plans like these:
I swear I didn't do shrooms or drop acid when I came up with this.
If I hadn’t used the math (and spreadsheet) skills that I learned in school, I’d most likely be digging and gradually widening a small pilot hole somewhere in the desert and hoping it comes out looking remotely like a crater.
So yeah, school ain’t useless. And hopefully, some of you have applied what you've learned in school to gaming too! If you have, please comment below.
If anyone wants to know more about the math behind the crater, let me know as well.
