See kids, this is why you need to learn Pythagoras and trig at school. Those normal vectors won't calculate themselves ;-)

@crestfallensunbro6001

6 жыл бұрын

James Grimwood Pythagoras Theorem has become somewhat of a meme I'm my maths class, with great effort going into using it as much as possible and the first suggestion for solving every problem is usually Pythagoras.

@dhkatz_

5 жыл бұрын

@youtubeShadowBan Lets hope if you ever get a job, they don't look at your social media

@FrequenzBlog

5 жыл бұрын

@youtubeShadowBan it is not triggering me at all, but your wording and the racist videos just speak for themselves and tell me alot about you as a person. Have a nice day.

@mdejoss1311

2 жыл бұрын

Ah, good quote..

@marcopozzi522

2 жыл бұрын

I now that math is important but that is why some people developed libreries that with some easy functions can automatically do the raycasting or the raytracing 🧐

Great video, but please make your graphics a bit bigger. You’re barely using 30% of the available space. On a cell phone, this does not help.

@MattGodbolt

6 жыл бұрын

Mahj thanks for your feedback. Definitely will use bigger graphics in future. Sadly KZread won't let me edit a video, only replace it...hopefully you can find a way to zoom to see these.

@MattGodbolt

6 жыл бұрын

An Enemy thanks for your constructive comment. I'd rather not replace. I'll consider adding another with a more zoomed view

@panguin7803

6 жыл бұрын

An Enemy, People like you discourage new creators and old ones alike from making fresh and innovative content. I hope you're proud of yourself.

@ragnarokofborg

5 жыл бұрын

@Panguin > "An Enemy, People like you discourage new creators and old ones alike from making fresh and innovative content. I hope you're proud of yourself." I assume from context that "An Enemy" is a screen name for a previous comment, to which "Panguin"'s comment is a reply. But what was that comment? I only see 3 replies to "Mahj"'s constructive comment about the video only using 30%. Was it deleted, or did YT delete it on it's own, or sort it into God-Know-Where in the comment "stream/blizzard/whatever-the-heck-comment-"discussion"-forums-these-days-are-called". I'm confused..

@fluent_styles6720

5 жыл бұрын

Panguin People like them rather help new and old creators improve the quality of their content, helping them to communicate information easily to their audience, increasing their retention. So they should be proud of themselves

As advanced as wolfenstein's engine is, I find it just makes Doom more impressive. Doom's engine is so much more sophisticated than Wolfenstein, it's actually insane to think only one and a half years passed between Doom's release and Wolfenstein 3D's release

@daishi5571

2 жыл бұрын

@etresevo It helped that that they were targeting a much higher system specification.

@robertforster8984

2 жыл бұрын

@@daishi5571 Not really. i486 instead of a i386.

@trashcanman6649

Жыл бұрын

@@robertforster8984 Well a 486dx2 is certainly a lot faster than a 386dx40

@demgreens

Жыл бұрын

@@robertforster8984 Wolfenstein's code is 16-bit; id was targeting 286s. As a side note, it was going to be a 16 color EGA game until late in it's development.

@jonsnow8543

11 ай бұрын

It’s also a lot harder to go from 0 to 1 than it is to make a feature reach version 2+

...I just posted my own raycaster video and fun tutorial! I love how you made your video :)

My algebra teacher would be proud

@sdiv-36b

3 жыл бұрын

this is trigonometry

@ProBarokis

3 жыл бұрын

lol

this just makes me appreciate how powerful even a 286 is. for a person to calculate one frame of wolfeintein by hand with pen and paper it might take a whole week and that little ancient cpu did it in real time. just wow.

@sdsdfdu4437

4 жыл бұрын

Whole week is an overestimate. Might take a couple minutes. But yeah your point is still valid, computers are crazy

@gorgolyt

4 жыл бұрын

@@sdsdfdu4437 You think it would take you "a couple of minutes" to compute an entire frame? Are you sure about that?

@sdsdfdu4437

4 жыл бұрын

@@gorgolyt Yes, we're talking about wolfenstein3d here.

@gorgolyt

4 жыл бұрын

@@sdsdfdu4437 Wow. You're quite dumb, aren't you? It's still 128 pixels across. So you have to do all of the calculations in this video in about one second. 😂 And that's just the first step, ignoring the vertical textures.

@sdsdfdu4437

4 жыл бұрын

@@gorgolyt Jesus fine, so it'll take an hour or two.

This was easy to understand, that is until 2 minutes into the video when my brain failed me.

@frayedsanity

4 жыл бұрын

agreed, I'm fried. I wished I paid more attention in math at school! DAMMIT!

@SummonerArthur

3 жыл бұрын

Same here

If a Wolf3D map has the edges exposed, you can look and go outside the level. In the north and south directions, the wall data repeats. In the west and east directions, it is from other areas of memory, which results in a bizarre world of mixed up blocks, doors, and empty spaces.

This is precisely the kind of video I was hoping existed. I've been dissecting old FPS games. Thank you so much for making this. Know that it is greatly appreciated.

This video has the charme of old educational material and does the job just as precise in a calm yet engaging way. Thank you! Subbed!

now THAT was well elaborated in a very detailed way. Thank you Matt!

Extremely underrated youtube-channel - keep up the good work, the followers will come :)

Everytime I see godbolt I know I'm in for a great time. It's insane how topically everything you post/dev is to me at the time. When I was writing an emulator you did a talk at GOTO. When I was writing a compiler you made godbolt. And now I'm tinkering with primitive 3d graphics and here we are. Thanks for everything Matt really appreciate everything you do. Alot of what determined me wanting to go into a CS degree was stuff you've done. Thanks! PS shout-out to Chicago

@MattGodbolt

6 жыл бұрын

TheVopi wow, thanks for the wonderful support! Very much appreciate your kind words. It's just lucky coincidence I've done things that are helpful to you :-). Great to hear though. And indeed, shouts to Chicago. You should check out the Chicago Open Source Open Mic Meetup, or the Chicago C++ user group if you're into such things!

@TheVopi

6 жыл бұрын

Matt Godbolt I will! Thank you!

@the7th494

4 жыл бұрын

How do you get a degree in Counter-strike?

I implemented something very similar to this recently, without even hearing of raycasting before. I did it using ASCII in command line, and then moved on to actual pixels. It was really laggy, however. I was simply moving my rays thousands of very small steps in the direction of the walls. It also had that strange fisheye effect you mentioned. Nonetheless, It was quite fun to make!

Our geometry teacher taught SOHCAHTOA as "Some Old Hippy Caught Another Hippy Tripping On Acid".

@screamsinrussian5773

5 жыл бұрын

@@rodri_gl how the hell did you reach that conclusion

@rodri_gl

5 жыл бұрын

@@screamsinrussian5773 through Pythagoras'.

@screamsinrussian5773

5 жыл бұрын

@@rodri_gl makes sense

@ThumbsTup

3 жыл бұрын

Same

@samferngamerhd4204

3 жыл бұрын

I live on Brazil and my math teacher told us SOHCAHTOA too. It's so cool it's the same tip on another country.

Thanks for this video, life saver. I was programming a fps game in python using sockets and pygame for fun at school. I kept wondering why I got the fish eye effect until i realised I was not calculating rays with respect to the perpendicular 'p' i.e. 'd'. Great video and really well explained

I don't know anything about advanced math but I was always curious how they made 3D without actual 3D objects. It's really genius, especiallyl since developers at that time had to overcome so many limitations, it's mindblowig. Thanks for the explanation!

thanks, I read an article on this but it took this video for the concept to really sink in.

The explanation in this video is so articulate and easy to follow.

@the7th494

4 жыл бұрын

This is sarcasm

I'm actually going to try and implement something like this inside a more primitive game engine. Maybe even inside a command line using ASCII. Thanks for the detailed explanation!

@Sevendogtags

5 жыл бұрын

If you do decide to do this, please remember to post an update here. Would be cool to see, Thanks!

@Stefan-pd9sl

5 жыл бұрын

Somebody took it even further an created a Raycasting engine in factorio kzread.info/dash/bejne/aaCKo6icdLualbA.html

@mariogamer929

5 жыл бұрын

To be fair, even in the 90s, game engines did exist. But they were often incredibly specific to one project because you can't waste any resources.

@maelstrom2313

5 жыл бұрын

Look up raycasting tutorials. I wrote a raycasting engine in Java last year following one of those. I even added a custom feature to render animated GIF textures. It's super cool and crazy easy to build a simple game engine.

@rjhelms

5 жыл бұрын

This video hints at the genius of the Wolf3D code, but actually implementing a ray tracer really drives the point home. Even on modern hardware, it's not trivial to get the same performance that id software managed to squeeze out of a 286!

Brilliant! Thanks for putting this together. Absolutely fascinating :-)

There is an effort to port Wolf3D to the Commander X-16, an 8 bit 65c02 based machine. Casting all of these rays is time consuming, and complicated by the lack of assembly language commands to do multiplication on 65c02. I found a way to significantly reduce the number of rays cast. Rather than casting rays one column at a time from one side of the screen to another, the screen is first broken up into groups of columns of pixels. There are 304 columns on the screen, so rays are cast to column 0, column 256, column 288, and column 304 (note this column is just off the right side of the screen and not rendered). This breaks up the screen into a group of 255 uncalculated columns, a group of 31, and a group of 15. For each of the rays cast, there are several values saved in RAM: the map block hit, the face of that block (N,S,E or W), the X-intercept or Y-intercept (whichever applies for that face), and the distance in the direction the player is facing. For all the so-far-uncalculated pixel columns, the high byte of that distance is set to 255. For the rest of the columns we do not immediately cast a ray. Instead, we first check to see if the high byte of the distance is still 255. If it isn't, then we skip the column and move to the next one on the list. However, if it is 255 then we look to the left and the right of this column, to find the closest column to the left which has already been calculated and the closest column to the right which has already been calculated. The order we test the pixel columns, the left pointer, and the right pointer can be stored in three precalculated arrays. The first array is the column to test {0,256,288,304,128,64,192,32,96,160, 224, 16, 48, 80,112,144,176, 208, 240, 272, 8, 24, 40, 56...} . The second array is the column already tested to the left {65535,65535,65535,65535,0,0,128, 0, 64, 128, 192, 0, 32, 64, 96, 128...} and the third array is the column already tested to the right {65535,65535,65535,65535, 256, 128, 256, 64, 128, 192, 256, 32, 64, 96, 128, 160...}. After the first four entries, the left-side entries are the largest number lower than the current column before it in the first list, and the right-side entries are the lowest number higher than the current entry in the first list. The column to test next is just the midway point of the largest remaining untested range, from left to right. So the next column to test is 128. To the left we've already calculated column 0 and to the right we've already calculated column 256. Here's where the magic happens: do the column to the left and the column to the right both hit the same map block on the same side? If they do, then we don't need to cast the rays between them. We can just do a linear interpolation on the x-intercept/y-intercept value and on the distance value, as every column of pixels between two that hit the same block and face will be evenly spaced between them. So we just subtract the value for intercept on the left from the value for the intercept on the right to get an intercept range constant, and subtract the value for the distance on the left from the distance on the right to get a distance range constant. Then we add the left value to some fraction times that constant, a different fraction for each column of pixels. Since the difference between the column number of the right one and the left one is always a power of two, we're always interpolating 1, 3, 7, 15, 31, 63, 127, or 255 columns of pixels. It's trivial to keep track of which interpolation routine to use, and the number of calculations in interpolation (two subtractions once for the entire range, plus two multiplication subroutine calls and two additions for each column in the range) is about the same as just the final step of raycasting: converting delta x, delta y, and beta into a distance. On average, this reduces the number of rays that need to be cast down to approximately 305/(log(305)/log(2)) or 37 rays, more or less; about 87% reduction in rays cast on average. If you're standing close to and facing a wall, only the first four rays need to be cast and all the rest can be interpolated.

Hi! I think when I've watched this video a couple of times I'll be able to make a renderer. I plan on using it in my current project. We'll see!

This is really cool, matt

Interesting and easy to follow video. Any chance of a video covering the Doom renderer? :)

Back in 1984, I was 18, and it was the first year (83-84) that my school was offering a Computer Studies O Level, so I did it along with A Levels my last year of 6th form. Never one to be sensible, I decided one of my three projects (the other two were a version of Missile Command in BASIC (heh) and an "address book") would be a program to draw 3D graphics. It's only looking back now that really it's amazing I achieved anything at all. It drew wireframes, and there was no internet and no books on computer graphics available so I had to work it all out myself, and I remember long hours with pencil and notebook trying to work out how to do it. Your mention of learning Trigonometry with "SOHCAHTOA" brought back memories of that. We never learned the acronym though. In the end my program did work. It could draw simple wireframes. My maths led me to a strange implementation where I had something like a vanishing point but at a fixed distance and objects with negative coordinates appeared beyond it, but getting bigger again the further away they were. I don't needless to say have the source code now so precisely what I did I don't know. I feel quite proud to have got that far though. The machines were British school standards- Research Machines 380Z and 480Z, with a networked floppy disk pack of 4 drives. Which felt like something from Star Wars. At home, I had a ZX81. 3D graphics of any kind were a long way beyond it...

@greenaum

5 жыл бұрын

Except for 3D Monster Maze!

@ian_b

5 жыл бұрын

@@greenaum Indeed, how could I forget that? :)

I love the videos where someone more knowledgeable explains the algorithms used in old games and software.

Definitely one of the better explanations I've heard, nice job! This is a little unrelated, but are you the guy that made the Godbolt compiler explorer?

@MattGodbolt

6 жыл бұрын

Jakob thanks for the kind words. I am indeed the same chap :)

@greenaum

5 жыл бұрын

Not as many Godbolts in the programming world as you might've thought, funny old world eh?

matt: explains how wolfenstein 3d's engine works me: ikr is crazy

Wolfenstein was so awesome. I was so addicted to it. I moved on to Doom then Heritc then Hexen. Hexen was my favorite. Awe so many wonderful memories. Thanks for the video. (liked)

I clearly remember the night I downloaded it off of Compuserve. While standing in the cell, I hit the cursor key to spin around and thought "We're not in Kansas anymore". Some of the other tricks your noticed straight away was using flat images for the "rewards" and other items you collected during play. The movable walls were another great trick. Thanks for the "maths" explanation.

Super concise and easy to follow!

@the7th494

4 жыл бұрын

Sarcasm.

Amazing video!

It's funny to stumble upon a video by the guy who made the Compiler Explorer. Thanks for giving the tools and ideas for tinkering! =) And thanks for the notes on self-modifying and self-generating code: made me really want to dig into Wolf3D's internals Why does the fisheye effect occur with the naive hit distance calculation? Geometric intuition suggests that everything should be ok if you choose field of view correctly

@MattGodbolt

5 жыл бұрын

I obviously didn't explain myself well about the fisheye. Field of view doesn't come in to it. Imagine a wall directly 10 feet from you. If you were to take a photo, the wall would appear in the photo as a rectangle, right? No fish eye. However, if you measured the distance from your eye to the wall directly in front of you you'd get (say) 5 feet. But it's further to the left and right edges of the wall, maybe 7 feet away (depending on how long the wall is). If you scaled the left hand as 7 feet away, the middle as 5 feet away and the right as 7 feet you'd draw something like a fish-eye wall. So -- the takeaway is, the scaling distance can't be the straight-line distance from the eye to the object, but rather the perpendicular distance away from a plane at the screen. I hope that's (maybe) a bit clearer! I've seen engines use the straight-line distance and then "fudge" it to undo the fisheye effect instead of calculate it properly as Wolf does. Changing the field of view only changes the angles between each ray cast out, it doesn't create or remove the fish eye effect (although if you have a very large field of view you see something similar).

@agma

5 жыл бұрын

@@MattGodbolt thanks, got it! But what if I aim not to simulate a flat non-distorted picture, but to make the screen "transparent"? In this setup the source of the rays matches the viewer's position, and the virtual screen FOV matches the real one. Will the straighforward approach be more appropriate then? And why isn't it used in game engines? Too narrow FOV? What I want to overcome by this approach is the unnatural view stretching. It's noticeable when you rotate the camera: everything looks way smaller in the center of the screen than on its periphery (yay, I know the reason of this warping now)

It’s interesting to finally learn how similar & different my own attempt at raycasting back-in-the-day was. I don’t think I ever realized the proper way to eliminate the fish-eye effect. I think I ended up with something much more complex. I also remember that I adapted the Bresenham algorithm for drawing lines for the scaling routine.

@greenaum

5 жыл бұрын

There is a way of eliminating fish-eye, Doom uses a specific technique to do it. Buggered if I can remember how! Doom is actually really similar to Wolf3D. One secret of Doom's speed, is that all walls are dead vertical. No slanting walls at all, just straight up 'n' down. You probably wouldn't notice that unless you knew to look for it. There's a few little genius shortcuts like that, that give the illusion of a world with much more freedom to the level design than there actually is. Doom is drawn as vertical strips from top to bottom. Starts at the ceiling, down to any wall, then maybe some more ceiling and wall. Then eventually starts hitting floor and wall partway down each column. Each point on the map in Doom has one floor height and one ceiling height. No floors above other floors. No bridges, no multi-storey buildings. Though there's some bits that look that way particularly in Doom II. The real genius (well, some of it, there's a lot of genius) in Doom is setting up compromises where the machine could generate each frame fast enough, while having more freedom of level design than the simple flat grid of Wolf 3D. The second part, is designing levels that hide those compromises so it looks like there are less limits than there really are.

When i was a kid i looked at these games and thought how crazy intelligent it all looked. That there are people who understand it. And now that i can understand it it just impresses me even more than it did before.

Gets a bit too trigonometric a bit too quick. It might be easier if you actually drew in the triangles, when you talk about SOHCATOAH. People are much better at understanding maths visually, usually, as shapes, human brains work better with concrete examples than abstract theory. I'm sure to you it's all the same thing cos you learned it so long ago you don't even think about it any more, but an important part of teaching something is knowing where the learner's brain is at, and bridging the gap between that, and understanding.

@programaths

3 жыл бұрын

Depends what you want to achieve. Abstract material is transferable while reified material is not. As an example, a common caveat in teaching fractions is using cake and pies. It's very visual and most student can understand that taking two of four parts is the same as taking one of two parts. Going for cake to pie then to enumerable objects is a real struggle. But with practice, student end up building a simple model...which doesn't transfer well! That shows when student are asked to convert a fraction into a real number. Struggle comes back as they didn't internalize that it is a division in the first place and that they are simply asked "do the division". It's also why most adults struggle with ratio. (Problems like "It take 100 hours for 100 people to build 100 houses. How how long does it take for one person to build one house ?") When taught using abstract concept, it takes much more time for students to grasp. But once they do, they can solve any problems involving cake, pies and jugs and even convert fraction into reals. This is not taught that way because people do not need to have profound knowledge and it's OK most people struggle with ratio all their life. It's the practical side which won. But it also limit discoveries we are making. The same with reading has been observed. People lack vocabulary and are not proficient at reading because syllabic reading has been abandoned for the global method. Global method works through repetition. Through a lot of reading, students remember words and even expressions. The issue is that it obfuscate patterns within words. Again, pragmatism won. People seldom use words like "hydrophobic", so it's fine if they have to look it up. Schools "dumbed down" because there is not enough resources, but demand increased. Even 30 years ago, you could end up in a one to one session or in very small group with the teacher. It was also quite normal to have hours of preparation work between two lessons and be interrogated from the get go! What you can do, and that's what I did in the past, is explore and illustrate by yourself. It's very different because your anchor is the abstract subject and not the other way around. But again, starting with abstraction makes everything seems way heavier. But that's the weight of real knowledge!

This needs to be presented as a 70s Open University programme, wearing a kipper tie and drawing on a blackboard.

@skilz8098

4 жыл бұрын

Next up, making the 6502 by hand as they did in the 70s!

great explanation

I can't believe there was no floating point at this time. Really respect them.

Love it Matt :)

Great video!, I have a question : at 5:09, we can already find the coordinate of the first horizontal intersection. But in raycasters, we need to check both horizontal and vertical intersections. The question is, in that case, how do we find the x,y coordinate of the first vertical intersections?

@MattGodbolt

Жыл бұрын

At 6:19 I show the first vertical intersection. I wasn't clear: there's also a dispatch on which of the four quadrants the ray is being cast on, which sets the scene for which direction to check first.

This is amazing, why is youtube showing me this 3 years too late

If you are interested for more information, I recommend the book of Fabien Sanglard he describes in a very descriptice language the whole magic of Wolf3D. The whole engine, not only the rendering. Loved reading it and looking forward for his next book about Doom. Love your awesome vid about rendering of Wolf3D too @Matt! A pictures worth a thousand words. A video is worth a thousand pictures. Looking forward for your further videos!

@khangdao8119

Жыл бұрын

Thanks for recomending the book, but I can't find the chapter in the book that describes the engine of wolf3d, can you help?

I remember playing a game like this on the Gameboy Advance and having my mind blown.

Now imagine the amount of calculations in a modern game. Mind boggling🙌

@pasijutaulietuviuesas9174

5 жыл бұрын

Which is why you have abstraction and automation. In other words - engines.

@ct275

5 жыл бұрын

@@pasijutaulietuviuesas9174 he said calculations.. not how hard it was to code. If anything the engine adds more things to calculate.

@pasijutaulietuviuesas9174

5 жыл бұрын

@@ct275 I know that, I also was specifically referring to calculations. Automation and abstractions reduce the amount of calculations the developers need to make themselves. For example, if you want to find the sum of two integers, you perform a calculation - a+b. You want to find a quotient, you perform a calculation - a/b, where b=/=0. Soon, you find that you require to find the sum and quotient so often that you define functions - sum(a, b) and division(a,b). Later, you need to find averages, so you use your functions - division(sum(a,b)). You find that you need to find averages quite often, so you define a function for it - average(a,b). The more and more you automate and abstract your operations, the less calculations you need to perform. The computer still performs every single calculation, but the video shows how developers THEMSELVES needed to perform these calculations in order to make it happen. Nowadays, you download an engine full of APIs and plugins, you barely need to perform as many calculations. That's the point I'm making.

@briankarcher8338

Жыл бұрын

If you haven't looked into it, you have no idea, haha. Even something simple like a shader is incredibly complex. You have lighting (multiple light sources mind you), texture mapping, even various techniques to pick from. PBR for example. So you need to calculate Metallic, Glossiness, etc. Diffusion, Specular. Fresnel. Just to draw one dot on the screen.

@krozareq

Ай бұрын

Knowing how to optimize code is still very important. Even a game with relatively low graphical fidelity can bring down the FPS if someone doesn't know what they're doing. Even high fidelity modern games can vary a lot in performance due to someone really understanding GPUs and CPUs at low level in their code. A problem is we rely on frameworks and advancing hardware to take up the slack. But software has not advanced anywhere near as much as hardware has. We still rely on a lot of frameworks and libraries with code written decades ago. There's also a lot of room for software optimization in machine learning ("AI").

Hey Matt, great video. Also additional thumbs up for a dark background!

Excellent video. Thank you for the interesting and clear explanation of Wolf-3D's ray-casting, wall-rendering technique, such that even I, a non-coder, found it enlightening.

This is the older video and I don't know if there was a comment on the following issue... At the time stamp 04:55, you are showing that "dx" is the distance of the starting point from the LEFT side of the square field. But at the time stamp 06:20, "dx" is suddenly the distance from the RIGHT side of the square field. Which "dx" is used in the final equation? Left or right side "dx"?

fantastic video, very informative. thanks for making this

2D plane world... 2D raytracing... Modified 1D image (image in one line) vision... Looks like it's what 2D creatures would see.

@haph2087

5 жыл бұрын

well, what a 2D creature would see indexed against another 2D plane of textures.

@puppergump4117

2 жыл бұрын

Actually it's a 1d image with 2d projection.

13:07 why is the height constant/p? Isn't the apparent size of an object arctan(size / distance)? Is it just an approximation that works fine?

@MattGodbolt

11 ай бұрын

I think the angle subtended is that, but the height itself is inversely proportional to distance alone.

The use of the square grid to leverage CPU power was pretty genius on id's behalf. I wonder how was the trig handled without floating point arithmetic?

@rich1051414

5 жыл бұрын

It was built into the compiler, they didn't even need to think about it, but of course, it is always better to avoid using floating point, as doing floating point math without an FPU is expensive.

@MattGodbolt

5 жыл бұрын

I think I explain in the video (it's been a a while...) - everything used fixed-point arithmetic with look-up tables to handle the trig functions.

Cool vidoe. You have a badass last name, man

What grade school did you go to that taught trigonometry? Great video though. Hope you keep doing videos in this style!

@MattGodbolt

6 жыл бұрын

asdf asdf haha, more a mixup in my understanding of school systems. I went to school in the UK and so it would have been "fourth year" of senior school or something like that...

@HailAnts

5 жыл бұрын

I always think that the American system is pretty simple: In total there are 12 grades, 1-5 is Grade School, 6-8 is Middle School, 9-12 is high school. Anything after is college of some kind...

i will use this, thank you!

@11.05 if I am not mistaken.. one lone coder perform this (calculate p) the easier way.. first initialize player position at the midpoint of the map for example if the map is 16x16 we initialize the player position as: float playerX=8.0f float playerY=8.0f so p is 8.0

I did a project on explaining this exact thing about a month before this was made. Research for it was extremely difficult. This would have been "very useful"

Thanks for the great video, very interesting. Have you seen the Game Engine Black Book: Wolf 3D by Fabien Sanglard? it goes into a lot of this detail, it's a great read.

Thanks man it helps a lot

It's really 2D with depth projection for the x/y map. No height changes whatsoever.

I'm sorry but I can't follow this, can you please explain why yIntercept is equal to ( y + dy + dx/tan(θ) ) ? I thought since the space between the Vertical Intercepts is [-dx * tan(θ)], shouldn't it be equal to ( y + dy - dx*tan(θ) ) ?

Where floating points more expensive to compute back then ? And if so, did they use integers for doing all those calculations ? Thanks for a great video btw.

@MattGodbolt

6 жыл бұрын

Igor Mitrovic absolutely! There was no hardware floating point unit. Software routines for floating point had to be written, and software FP is at least 100x slower than hardware. Floating point numbers have to be unpacked, added or multiplied, renormalized and then repacked. Or something like that. These are all integer operations and so can be written using just normal integer instructions. Hardware is more efficient by far at this though. Googling "software floating point" gets you a bunch of guys if you want to look at code, else the Wikipedia article on floating point explains some of the algorithms. You can see how you might build routines but also that they're considerably more complex than just integer addition.

@steefant

6 жыл бұрын

Fun fact: today's x86 int (long) divisions are about 10 times *slower* than float (double) divisions (possibly other operation too but I did not check; for div it's about 10 vs. 100 cycles) making fixed-point algorithms slower than simply using floats! Blew my mind when we stumbled upon that while trying to figure out why our fixed-point port of an algorithm was way slower on x86 than the original.

@im95able

6 жыл бұрын

If anyone is interested, there are great lectures on KZread by Alexander Stepanov(the guy who wrote STL in c++, and invented concepts) about many programming topics. In one of the lectures he talks about cost of fixed and floating point operations used on different data structures. You will find that lecture here : kzread.info/dash/bejne/ZX9mrs-nka-ydps.html Basically today, it looks like, floating points have pretty much caught up to integers, if you look at the speed of computation.

Came for a neat video filled with trivia and cool stuff, got a math lesson. Negged.

This tells how proficient Carmack as a programmer about 3 years into professional game programming, starting from a couple of Ultima spin-offs (Shadowforge and Wraith for Apple ][) in 1989. Jeez that guy is a beast and he probably programmed non-stop 12 hours 7 days.

nice explanation, thx

Dude.. I learned a lot with this! Thanks for making it!

Great video. Just wonder why you say that techniques used on wolf3d are outdated and you use goto on your code.

There's a better way to calculate how large the column of pixels for the wall should be than calculating the normal distance. Calculate the square of the normal distance, and use that directly.

I'd be really interested in seeing that fisheye effect you mentioned at 3:38.

@MCSteve_

5 жыл бұрын

Just search up "raycasting fisheye effect." It just looks like the player is looking through a fish bowl. When facing and far from a wall, the lines (top and bottom) slowly converges at the ends of the screen; this is more apparent when the Fov is relatively wide.

@callsignseth7679

5 жыл бұрын

Check out the coding train Livestream for a demonstration of that on P5 js kzread.info/dash/bejne/X2qdq8VvXbyTm84.html

@rszec

5 жыл бұрын

@@callsignseth7679 The middle section of the stream of Daniel is about 3D representation of ray casting and the fish eye effect when we don't take in consideration this geometrical adjustments.

@mattj2217

5 жыл бұрын

Ultima Underworld and I think Catacomb Abyss both have this issue.

@shifter65

4 жыл бұрын

There's a picture of the effect in the book "Game Engine Black Book Wolfenstein 3D" by Fabien Sanglard.

a 286 with no floating point was certainly NOT "state of the art" in 1992!

@MichaelPohoreski

5 жыл бұрын

Tom P. Agreed. I still have my 386SX-16 from 1990. A 486DX2 was state of the art in 1992!

@danpowell806

5 жыл бұрын

It wasn't 'state of the art', but it was met the minimum system requirements.

@robertforster8984

2 жыл бұрын

I think he met to say i386.

I'm pretty curious about the self-modifying code of the ray casting loop. How was it even done? And was this common practice when writing tight loops? It's seriously cool to think about, but in hindsight, I can see how much of a pain in the ass it could be for someone who doesn't know about it.

@MattGodbolt

6 жыл бұрын

I'm not sure how common it was, but Wolfenstein did it here: github.com/id-Software/wolf3d/blob/05167784ef009d0d0daefe8d012b027f39dc8541/WOLFSRC/WL_DR_A.ASM#L235 patched the `jge` etc :)

@bhargavvoleti2647

6 жыл бұрын

Wow, that was way simpler to understand that I thought it would be. Guess I'll be reading the wolfenstien source code this weekend.Amazing video as usual!

@thulinp

6 жыл бұрын

The technique is fairly common in assembly code, which forces a fair level of spaghettification anyway. The speed critical bits like 3D rendering would be where you invested in assembly coding, which is far slower to develop.

Great video thanks. :)

I'd like to know how the lookup tables work and how the precision works with fixed point numbers.

@MattGodbolt

5 жыл бұрын

Something like this: instead of having 360 degrees in a circle, have 256 of them. Prepare (for eaxmple) a table of sin() by having sin(0/256), sin(1/256), sin(2/256)... etc. Now you can get sin(angle) by looking at entry "angle" in the sin table. For the entries: we know that sin() ranges between -1 and +1. So, we use a signed number between -128 and 127 to mean -1 to +1: we store (sin(angle) * 128)) in our tables, as an integer. So now we have a 256-byte table of sin. To multiply by sin(angle), we take a number like "150" and multiply it directly with the sin value. Then we shift it down by 7 (to account for the 128-scaled sin()). That way we get an answer in the right domain. Later you can note that there's a close relationship between sin() and cos(), and can reuse parts of the table. tan is a little trickier, as is tan-1. But hopefully this gives a little taste!

Wolfenstein 3d has always fascinated me. For the longest time I have wanted to understand how it was made and after this video... I still don't. That is not the video's fault. I was never good at math. Its a start though and thanks for that. I feel like there could have been some more information on screen once the explainations started. The drawings were great but some supporting text maybe. Just a thought.

Alright, but what about rendering the texture on the walls?

@MattGodbolt

5 жыл бұрын

Henry H. I was hoping I covered that when I said about the scaled renderers. I didn't go into too much detail I guess. There were "JIT" compiled routines to scale all possible output sizes of a vertical slice of texture. And the textures were stored sideways to make that more efficient. Sorry I didn't get into details there!

ID software took this several steps further with the followup game Doom , featuring much richer 3D map rendering, while still not requiring any 3D rendering or math coprocessor, although they needed more CPU power.

@MattGodbolt

6 жыл бұрын

thulinp absolutely. I have plans to cover Doom and Quake too :)

@SweetHyunho

6 жыл бұрын

thulinp If today's engines were this efficient, wouldn't movie-like games run smoothly on ten years old hardware?

@totara3463

6 жыл бұрын

Sounds exciting! Can't wait to see how Id Software pulled off such a great 3d engine for Quake

@kangarht

5 жыл бұрын

define 3d rendering ? all rendering happens in 2 dimensions. hence you are plotting pixels on a screen.

@SerBallister

5 жыл бұрын

@@SweetHyunho Today's engines are very efficient, the whole area of realtime rendering is advancing all the time, what makes you think they aren't optimised ?

I'm sorry, but this has become sort of a pet-peeve of mine (especially with all the videos about real-time raytracing around these days): Raycasting is simply the process of "firing" (or casting) a ray from one position in one direction into a scene and checking what it hits. That's all there is to it. It's still in use in almost every single game you play today, for example to check what enemy a bullet hits. In itself, it has about as much to do with rendering as a hammer has to do with building a house. Raytracing generally describes algorithms that use raycasting to render an image. Everything beyond that is not included in the terms on their own. Two other things I noticed: 1. You're only using about a quarter of the screen. I imagine that's a bit annoying for people watching this on a smaller device. 2. The step done around 12:35 might have been easier to follow if you circled the terms replaced by delta X and delta Y in the equation for p. Still, very nice and to the point explanation of the algorithm.

@MattGodbolt

5 жыл бұрын

Thanks for the comments. You're not the first to point out my mistakes here :). If I were to redo things, I'd use more of the screenspace and make clearer the definition of what ray casting is.

@barrybathwater4877

5 жыл бұрын

hammers have a lot to do with building houses, Lol

@Clairvoyant81

5 жыл бұрын

@@barrybathwater4877 Well... yeah... they are definitely used while building houses, but using a hammer does not mean you're building a house... which was the point.

@barrybathwater4877

5 жыл бұрын

@@Clairvoyant81 using the toilet means you squeeze poopies out

Now I see why Carmack was so resistant to adding "push-walls" when John and Adrian pestered him to. That breaks the grid stepping. I wonder how he went about it in the end?

@nickwallette6201

5 жыл бұрын

Good point. Maybe it used 2D sprite tricks to move it further away by just decrementing its height and width.

@SerBallister

4 жыл бұрын

@@nickwallette6201 You could fudge the intercepts on tiles that contain the shifted wall.

@shifter65

4 жыл бұрын

If still curious, checkout the "Game Engine Black Book Wolfenstein 3D" by Fabien Sanglard. There's a section talking about how it was done

@Domarius64

4 жыл бұрын

@@shifter65 thank you!

6:14 and 6:31 no, when stepping to the next cell you have to add +1 or -1 to the initial computation dx/tan(θ) or dy/tan(θ), as you correctly describe later based on source code.

How does the programming compare to Catacombs 3-D?

@MattGodbolt

5 жыл бұрын

I'm afraid I don't know! I'll be honest I'd not heard of Catacombs 3D!

@jeffyp2483

Жыл бұрын

pretty sure its very close if not the same. wolf3d used an evolution of the cat3d engine, which if memory serves is itself an evolution of the hovertank3d engine.

Nice Video. :-)

what's the BNC->RCA converter for? PVM? :)

@MattGodbolt

6 жыл бұрын

Tangent it's a 10baseT ethernet terminator...it's an attempted visual pun with the title "oh no it's the Terminator". It has failed ... And I'd forgotten to update it hehe

Here in the US I wasn't taught trigonometry until college. I have a feeling you learned it a lot sooner...

8:24 this is what makes it extra good. thx for sharing.

@techeadache

5 жыл бұрын

Good and unstructured code. It works but it is insane. It applies 16-bit arithmetic on 32-bit words. It is not portable because it requires an old C compiler that defaults to unsigned comparisons. There should be a disclaimer.

@kentlofgren

5 жыл бұрын

@@techeadache woaaa did you just use _knowledge_ to elaborate on my initial argument!! O_O :-)

@techeadache

5 жыл бұрын

@@kentlofgren I think a lot of people will try to implement this craziness on a different compiler. Ofcourse without knowing that (-dx) means static_cast(static_cast((1L

I don’t know. I remember Wolfenstein running pretty poorly on a 286. You would want a state of the art i386 to play Wolfenstein well.

@blakegriplingph

2 жыл бұрын

Plus around that time, the 486 was generally available anyway.

Another high quality video with excellent explanation, as usual with your content. Thank you! One small note though: the graphics were perhaps a bit too small, the lines thin and faint, and the annotations a bit tiny. On mobile, I could see them fairly okay, but someone with a smaller screen and/or less good vision could have a hard time. And especially thanks for adding captions (to whoever created them, if it was submitted, and not made by you), on top of your already clear and understandable speech!

@MattGodbolt

6 жыл бұрын

Thank you for the feedback! I'm still learning how to best record these, and getting the screen zoomed up appropriately is something I just worked out how to do! Sorry the diagrams suffered from being too small here!

Please, make a classic doom engine analysis, thanks

a detailed code review would be much appreciated.

Wait, THE Godbolt?

Why is the Ubuntu font so popular ? Edit: Lucida Console too OMG r u using Libre Office ? High-5 !

@MattGodbolt

5 жыл бұрын

I'm using reveal.js

Interesting, I'm assuming the example they created was in C, however, how would one achieve this via java? Just curious

@marijnstapert9036

5 жыл бұрын

I think you can implement this in any language

It's actually not that hard when you think about it but coming up with it in 1992 when nobody has done it before is the actual achievement. I was 15 at that time and it took me years to figure out how it works. There was no stackoverflow that you could consult at that time.

It should be noted; Ken Silverman's Build Engine could actually do room-over-room tracing, even though it was primarily a raycasting engine. I'm not exactly sure how it worked, except that doorways and windows that you could pass through worked by teleporting the player to different places in the map.

@navithefairy

Жыл бұрын

The build engine wasn't geometrically correct though, try looking up and you will see everything looks distorted!

@Roxor128

8 ай бұрын

@@navithefairy It's the same trick used by Rise Of The Triad: treat the view like it's really tall and slide the screen up or down, then render the bit that'll actually appear. Unlike a proper perspective-correct 3D rendering, it will keep the walls dead-vertical when you look up and down, whereas a proper rendering will have them turn into diagonals.

I actually expected the raycasting routine to be written in assembly.

Well I didn’t understand that (sitting here munching breakfast), but it looked really interesting, so I’ll definitely watch it again

@iisky1

5 жыл бұрын

trig is a high school subject.

@____________________________.x

5 жыл бұрын

IndiiSkies - And I’ve studied Engineering at Degree level you little snot nosed spod, but that doesn’t mean I can design a bridge before I’ve even drunk my coffee.

@denoww9261

5 жыл бұрын

@@____________________________.x yikes

@LKRaider

5 жыл бұрын

IndiiSkies - and its been 20 years since I last used any of this.

@____________________________.x

5 жыл бұрын

@Tommy Hopps - actually, zero tolerance for numpties is generally how we all turned out.

I'm pretty sure that either when or VERY shortly after that game came out I had a 386-sx 33 MHz with a separate external FPU I got a few weeks later, 2-4 MB RAM & a 40MB(lol) Hard Drive. & I felt Boss because of it. I am more certain that I had that same system for playing Doom. NO Q these things were like literal magic at the time. id/Carmack are Legends imo, I'm sure these things were ripe for discovery & implementation but he/they were the 1st to do it in a way that reached millions. I used to do modem to modem deathmatches with my uncle. But imho Quake was thE defining moment in history where everything really came together for 1st person 3D multiplayer gaming.

@Roxor128

8 ай бұрын

Don't forget Ken Silverman. Cloned Wolf3D as a teenager to make Ken's Labyrinth, then went on to make the BUILD engine that powered Duke Nukem 3D, Shadow Warrior, and Blood plus a number of less well-known games in the mid-1990s, and which got a revival for Ion Fury in 2019.

@realcygnus

8 ай бұрын

@@Roxor128 Yup, I haven't really seriously gamed since but the evolution of technology has been almost as interesting as the the tech itself.

The 486 was released in 1989, 386 in 1985. A 286 would not have been "state of the art" in 1992, but rather a paperweight.

@MattGodbolt

6 жыл бұрын

Patrik Lindström a fair criticism! Thanks for the correction. It was in fact the minimum spec!

@jamesgrimwood1285

6 жыл бұрын

A 486 might well have been out 3 years before Wolf3D, but they were super expensive and only really affordable for business use. A 286 was a realistic "home PC", but yeah, not state of the art. Mine was made by ICL and had a whole megabyte of RAM and a 40MB hdd. It was a massive upgrade from my Atari ST - it did VGA! ;-)

@kebman

6 жыл бұрын

I knew many people who still used the 286 in 1992. In fact some even used older PCs for accounting and such. It wasn't a paperwheight unless you were a hardcore gamer. Edit: Atari ST

@KuraIthys

6 жыл бұрын

we got our first 486 in 1993. Wasn't cheap as such, but considerably cheaper than the 286 we got in 1990. That does give you some idea of when the 486 started to common. I mean, there's sometimes a big gap between something first being available and it being common. there were computers with a recognisably modern GUI in the mid-70's, but it's not until the mid 90's that it was common enough to be the norm, and not something of a niche thing...

@SweetHyunho

6 жыл бұрын

I played Wolf on 286 and my next computer was 586 in 1996.

I'm going to have to make a raycaster now.

You are a saint