How Isometric Coordinates Work in 2D games
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- เผยแพร่เมื่อ 15 พ.ค. 2024
- Isometric games often use hand-drawn 2D sprites to add depth to a game without having to deal with full 3D rendering.
In this video, I cover how it works, the math you need to render isometric sprites on the screen, and how to find the isometric tile from a screen coordinate.
0:00 Intro
0:21 Orthographic projection
1:16 Tiling a sprite
1:40 Transforming tile coordinate to screen
2:55 Accounting for sprite size
3:39 Correcting offsets
4:00 Transforming screen coordinate to tile
4:46 Adding depth
4:52 Outro
Music: Snake Hips - Lucas Pittman (via epidemicsound.com) - วิทยาศาสตร์และเทคโนโลยี
A few people have been asking for code and how to invert the matrix. Here's some (untested) code I've put together in TypeScript, although it should be similar in other languages. Hopefully this gives an idea of how the math translates to code.
gist.github.com/jordwest/8a12196436ebcf8df98a2745251915b5
Thanks, the inversion was tricky to implement from the formula. The one thing I added was rounding the results from to_grid_coordinate(), but besides that it worked like a charm. Thanks for the interesting video.
EDIT: spoke too soon, for some weird reason the Y from to_grid_coordinate() is off by 1, and I don't know why. I can hard code the fix, but it's ugly. Also, the multipliers on the code are all 0.5 and in the video some were 0.25. It works but the mismatch is disconcerting. I tried to change the numbers to match the video and the results are crazy.
@@rafaelrosafu If something's stored as an int somewhere and it's being divided, it will be rounded which could explain the error consistently being off by 1
@@metallsnubben good point, I'll double check. thanks.
It now has 101K views
@@rafaelrosafu Hmm not sure about the Y being off by one, but the 0.25 is after halving the iy and jy (to account for sprite size: 0.5 * 0.5 = 0.25). In the code above I left it unsimplified for clarity, but I suppose in doing that made it more confusing haha.
This is an incredible and polished explanation, going through the steps, the problems you face, and then how to solve it. It helps the viewer to reslly understand how we got to the final solution.
Well said!
I agree!
This is the best type of tutorial. No fluff, no information that's potentially unnecessary, reference to where to find more information if it *is* necessary. I'd been trying to do this on my own with no help for two days (pride's a troublesome thing) and I'm glad to see it's not something super obvious that I was missing, but not daunting either. Thanks for the video
That's awesome, so glad it helped :)
I especially value such vibeos!
This is such a great, high quality video, hitting just the right spot between learning and reference.
While remaining entergaging (/hj) as well!
(the /hj is the ironic use of the term, but the genuine meaning behind it)
(tho yk. ik that effective educational content is also entertaining haha. it's also very pretty~)
Wow, I already knew all this, but this video is EXTREMELY polished. I especially like how you went through some potential problems people might run into while doing this, such as the offset. Well done!
@@marianmotorina chillax dude
I said "i knew all this" to emphasize that I still got something from the video, even if the concepts were familiar. this is a compliment
@@marianmotorina ratio bozo
@@kingbroseph9773 lol he really did go for it after a literal year
I can't believe that this video only has 574 views with this amazing content.
Thanks, and here I am amazed it's even getting a hundred views :)
@@JordanWest you deserve much more than that
I’m still amazed
I’m sure it will blow up at some point
@@UndeadAlv f-four hours ago??? Is that a /j as in u came across it and it had 37k views as it did for me (and abt 1/10th as many likes)? Or did it seriously explode in _four hours??_
@@foul-fortune-feline well, we are all here right now
I love how game developers create amazing things, when dealing with hardware limitations.
isometric view was developed out of limitation, but turned out so appealing that its still used in indie games to this day
PS: great video, its very well explained, i think the possible "errors" one might encounter when creating such view did the best job at explaining things to me. Too few people show possible errors you might encounter, and just say "you type this here, or it wont work"
Helped develop an isometric engine about 20 years ago. The 3d nature of isometric games can be surprising. It gets real fun trying to sort non tile aligned Arbitrary sized objects for display. Ordering can get real complex real fast especially if you get cyclic dependencies between objects.
That sounds fascinating, I wonder at what point is it easier to just go to 3D? I guess there's always a tradeoff, especially if you want hand drawn sprites instead of rendering triangles.
this just makes me think of what a nightmare chris sawyer must've had with rollercoaster tycoon
That’s the most concise and easy to understand video that I found on TH-cam about isometric grids!
I'm glad to see my linear algebra class is paying off now... haha
But, this is an amazing video!! (almost even a tutorial it's so thorough)
You just decided to drop an amazing tutorial out of nowhere ?
I love how there's no code involved so it's applicable in any environnement we want, isometry rocks !
that wavy isometric had me hypnotised, great vid!
This is an amazing video, great job! Love the visualization and maths explained.
This is wonderful, thank you for the clean explanation and resources.
what an elegant explanation and visuals. great job Jordan!
this one of my favorite videos of all time. It combines everything I love into one video. Applauds to you jordan! 👏 👏
I saw it done a different way before. Take a 2D grid, but every odd number of Y is shifted to the left half a space. When you want to move a particular direction, you'd want to check if the current Y position is odd or even and then decide whether or not to change the X value as well as decide whether to increment or decrement the Y value.
I loved this video! It's a simple and quick explanation on how it works and leaves me satisfied. Great work!
Beautiful visualization and clear explanation!
I am so happy to see an application of the math that I just learned in the linear algebra course at my university. Really cool!
This is a fantastic video! I am working through this to render an isometric field step by step. Incredibly lucid description. Thank you!
Bro i need more from you, the quality is top notch. Keep up the absolute amazing work
this is extremely high quality and straightforward. I am amazed.
I'm going to go ahead and call this the "perfect" illustrative video. Sentences spaced out perfectly, tone of voice is clear and just right, visuals are top-notch, language is simple enough to be understood by a layman but not dumbed down. No awkward pauses, background music not intrusive, the visualization of the problems one might face is really, really smart. The video is quite short but concentrated. I can't find a single flaw. I'm definitely going to study this next time I try to explain something whether in class or otherwise. Have a great day!
I've been out of typical schooling for a while, and honestly this made me remember how much I enjoyed math and liked being able to see how numbers work when previously not being able to work it out. Lovely video - very informative in more ways than its original purpose, overall edited and make concisely, along with a nice calming voice leading you through aptly.
An enjoyable experience - cheers.
That was a gorgeous piece of education you just put together. Bravo!
This is superb, I would love to know more about this! Great job man
This is great timing! I was just thinking of making an isometric adventure game of my own.
Praising the TH-cam algorithm aside, your scripting and editing is great and I feel like you gave the perfect amount of information.
Instant subscribe :)
I love your editing style, such a great tutorial!
Oh GOD that video is so good! Thank you a lot, Jordan! Always wondered how to do this effectively
This video is exactly what I needed! I’m working on an isometric project and was having trouble with the tile picking formula. Can’t thank you enough!
3:35 how are the occlusions being handled here? Like when 2 sprites partially overlap how do you determine which one is drawn in front when they don't have z coordinates?
In this animation the sprites are simply rendered from back to front, left to right. Often you can get away with sorting by the screen y coordinate
@@JordanWest oh *nice*
absolute godly tutorial, very detailed and dynamically useful
Awsome content!!! Keep it up! :D Really well explained, love the fact you showed how it would look like in each step! Kudos!
Wow, I vaguely knew the translation before, but never understood why. This so perfectly illustrates the problem and solution!
I like how you show the problems you could face before getting to the completed code, that gives a lot of insight on this sort of thing
This is such a great video, your channel deserves a lot more attention!
Holy cow that was so cool explained. Even with such easy task, each step error explanation with showcase! Wow
Awesome explanation! This is a great introduction to matrices
I’ve tried making isometric stuff before, but this explains its EXTREMELY WELL. Thank you!
really relaxing and informative, amazing content
Amazing content :) can’t wait for your channel to blow up. Thanks for the good work
I don't know why I was suggested this, but it is certainly a great explanation.
Reminded me of why I hated matrixes so much, but still, it was pretty simple to understand
This is the single most useful isometric tutorial I've ever seen. I will definitely be referencing this a lot.
pure simple. well done explaining, thanks
Really underrated video, it tells you enough to understand whats going on but not so much that you feel overwhelmed.
This channel looks like it's gonna blow up soon, and I'm all here for it :)
Awesome tutorial, and I love the presentation style.
Well-made and informative video, thanks!
really good vidéo :D fun to see each result !!!
This was a great rundown on isometric games setups ...
I've been struggling the whole week and only found this video now. Thank you !
I'm currently working as a teaching at a summer camp as Teaching Assistant and love how simply you explained isometric coordinates with linear algebra. I would love to teach it to my kids, but the camp is only three weeks long, and we just introduced objects recently, but maybe if time permits, I can at least give them the formula and show them how it works in the final week.
This is really good edutainment. I hope your channel soars Jordan. This is the kind of content modern TH-cam needs more of.
This is an incredible and polished explanation
This is just fantastic. Thank you Jordan.
Thank you! One of my favourite games when I was a kid was called Utopia (on the amiga) and as a developer I always wondered how they programmed the layout.
I decided never to try it as I had no idea where to start (other than google). But this video gave me enough information that I can now imagine the solution in my head.
Thats very much appreciated.
great vid
definately deserves way more attention
Definitely one of the best videos on the subject.
Amazing video. And I always being amazed how linear algebra has so many uses in video games and multimedia in general
Immediate like for this channel. You are explaining like a boss!
TH-cam needs more videos like this and you deserve way more views.
Thanks!!!
Exactly what I needed to build my engine, thanks!
This is an amazing resource for me! thank you for making such well a explained video, i'm in your debt!
Thanks for the kind words, glad you found it helpful!
This is a great video. Just showing the process of trial and error very quickly with no fluff you were able to get through the topic very quickly and instructively.
The only slight error is the term: 1/(ad-bc) is not the determinant, but the reciprocal of the determinant. It might seem a bit nitpicky, but it would be like calling 1/2 the number "2"
Ah good catch, thanks
you're the type of guy to correct Albert Einstein, and be right
It was on my suggestion list of TH-cam but it turned out amazing I really love it and it got an idea to try with different things, thank you.
Plus I like and subscribed.
That was a really great explanation of a problem I didnt realize existed but makes a ton of sense!
This is a really good explanation. I have been building something like this for the past month or so and just came across this video.
amazing ! I really like aubjects like this, math , geometry , logic , visuals
Well made video, easy to understand. Please make more video like that.
I just love that this video perfectly matches my youtube search and with such quality content. thanks man
I love that your search perfectly matches my video :) glad it helped!
I only understood about half of this video but it's already answered a lot of questions I had about 2.5D games.
Amazingly well done!
You just tricked 35 thousand people into learning change of basis good job
Got 'em
Very well done video!
With such high quality content you deserve more subs :)
This is a simple, great explanation!
Thank you! This was a great explanation
well well well seems youtube has recommendes me a great channel this time! the explanation was great! thank you!
Phenomenally helpful.
I'm so happy the TH-cam algorithm recommended your video to me. I've liked and subscribed!
Incredible, i love content that shows how maths apply in the context of programing.
Concise, clear and nice looking
honestly this is really good content. even though the aim is supposed to be informative, this is really entertaining. excellent script writing and visuals! would expect this type of content from a 1million subscriber youtuber. now its time to get you there.
This is a very good video and extremely polished
this is so informative !
love
Wonderful! Thanks for this.
Crazy how simple it seems!
I just found this because we have to make a 3d project for uni... and this is super well explained and really well made! Thanks for the quick and amazing explanation
Hey, a good part of the math on doing the tiled grid is done here, this is amazing! Thank you, I need to get back into dragonruby and make an isometric map eventually!
Thank you so much! I was hoping to find a good way to explain how isometric projection works for making a tactical rpg fangame
i love the explanation, I'm a CS student and your video helped me finally understanding reversed matrixes!
I will definitely need this when I start programming soon
Thank you so much
This is really helpful, thank you!
in 2 minutes, this makin me feel inspired to make a new iso-game. this is the ideal youtube video :) a quick dose of motivation
this was so good I have to watch it again
Holy shit, I've been trying to find the name of Mystic Towers for years, knowing that I played a game like it as a child. I couldn't remember the name or even exactly what it looked like and here you are just casually showing a clip from it with its name and release year! The search is finally over, thank you!
Although I didn’t really need this for anything, you explained this well, good job 👍
Wonderful animations and math application
The cube wave looks so satisfying
Very nice explanation , thanks a lot! :)
This video was great. I helped me a lot!
Cool quick little tuto, thanks for sharing m8!