A Universe of Triangles - Computerphile 

This dude would make a badass villain in some sort of Sherlock Holme-ish type movie/series. :D

Kudos to whoever does the animations for Computerphile. They are always very helpful.

I am at 00:34 nd have decided already this guy can be leader of my village.

It sounds like james bond is giving me a lesson on co-ordinates, it's awesome.

As a designer I'm never going to be able to use a triangle without being accused of being Illuminati.

Can we have more of this dude in future?

I am very bad at maths, geometry and stuff but this dude's explanation is just crazy. I wish i had a teacher like him.

One of the best explanations I ever see! Thanks a lot.

This dude reminds me of the Tenth Doctor. Also, of caffeine.

1:48 Your coordinate system isn't right-handed. It's good usage to make it right-handed, usually.

That's a lot of triangles for the side of a cylinder! I'm sure you could get away with 2 per side ;)

I wonder if they were sitting on a three legged stool when they figured to model with triangles... interesting that the same reasoning for why to use triangles is the same reason why 3 leg stools are better than 4 legged ones - no wobble.

Quaternion tie-in with Numberphile. Do it! Do it! :)

While triangles are easiest for rendering, displaying a mesh. Quads are more convenient for modelling, creating a mesh

Can I borrow John Chapman to go to a restaurant with me and my friends so he can explicitly and careful describe everything about the food I ordered from the menu and how I plan to consume it and drive all my friends nuts? :)

Looking forward to the next video about moving them about in 3D space.

Have to once again thank you for these videos. it's just so easy to link a playlist instead of spending hours explaining it.

This man is the richard hammond of triangles

Would have saved me so much time if this video existed a few months ago when I learned this all the hard way.

I'm happy to see comments about the animations. They are a fantastic touch to these videos. Keep doing that :)

This is just awesome ! Watch the whole series.

Love this series, I am actually getting a basic and more clear understanding than I ever had. Clear and concise explanation. Much appreciated.

A great summary of how polygons are used and drawn by a computer. Good job!

This is the worlds best video on a particular topic where a topic is explained so clearly and easily that i am beyond impressed and writing the comment in the middle of watching the video

I wish i was this fluent in math and geometry.

Ive noticed in some older video games though that both sides of the triangles are rendered. If you walk too close into a corner in some 3rd person games you could see the inside of the characters body, and its coloured the same way as the outside.

What a lovely video. Thank you!

This was fun to watch. Reminds me of my GameMaker days (the 3d engine in GM is quite simple, and you had to do a lot of the rendering manually)

Really cool stuff, I never learned about it in this way and I think it might come in handy in some of my projects

Thank you! More 3D graphics videos please!

I really enjoyed this one! Loved hearing about those geometry problems. Thank you.

Very well done videos, thanks. I already understood these concepts, but this was perfect to share with friends.

Now I know what models are made of. The more you know. :D Thanks Computerphile!

This is very interesting, looking forward to the next computer graphics video! I always learn new stuff with Computerphile videos, so, thanks a lot, and keep it up ;) !

Amazing presentation! Very well done. Thank you.

Oh, it hurts so much seeing a left handed coordinate system.

I was typing a whole pile of stuff on how triangles are coplanar and how that makes rendering the triangles so much nicer. I failed to notice how long this video is. Thankfully it was mentioned before I finished typing :P

That was a very good video. Thanks Brady.

By far my favorite ***** video yet

Wow great timing! I've actually been working on a 3D renderer myself for the past 2 weeks. It's far past this but still great video.

Excellent as always!

I knew everything this dude is talking about (and much more) a long time ago. Plus actual mathematics of 3 rotation, projection, translation and texturing.

This reminds me of FEM (Finite Element Method) which uses triangles (most of the time) to approximate surfaces in 3D, like he said. It is used to approximate solutions to differential equations.

I think maybe the rectangular piece of paper should have been folded out of the plane (with the fold line intersecting the two opposite vertices), instead of it being bent to create a curve. As you could obviously curve the triangle into a new plane also, but you could not fold the triangle into a new plane.

How do you divide a sphere into triangles??

Wow, you can be a great teacher. This was awesome.

I'd love to see a computerphile - quaternion video ^_^

Ahhh that makes total sense! Great video thank you :D

very cool episode!

This video is awesome thanks!

I never knew how do they distinguish inwards and outwards facing polygons. Cool

This was really cool!

You just made my day

Very good explanation

Great explainatory video guys :D

this explains so much.. thank you!

Quite a nice topic! More on tessellation and maybe game rendering!

P.s. I have enjoyed every single Computerphile vid! My only complaint is that they don't come often enough. :)

Doesn't his coordinate system violate the right-hand rule? I think +z should be out of the paper, not into the paper.

Interesting stuff! Thanks.

The opening comments of this excellent video remind me of the Red Dwarf episode Waxworld and Pythagorus.

As someone who works a lot with FEA, this was terrific.

hope this is going to be a playlist soon... :D

Best description ever thank you so much know I finally get it

The way the z axis is defined is not wrong, but it is not the most conventional one. This might be confusing. According to the right hand rule, +z would point "out" of the plane (towards the viewer) and -z in the opposite direction (just like with the triangle winding). Still, great video!

Very well explained! :)

The important thing about triangles is that they are uniquely and completely determined by the coordinates of their three vertices. Squares are ambiguous; four coordinates may define a square, or they may define a "squaroid" which won't lie in a plane. 3D software will often render a squaroid by jumping back and firth between it's possible renderings randomly, based on floating point rounding errors and such.

This video would have been really useful to me 2 weeks ago xD, very good video.

I'm studying this right now, video was really useful thanks :)

So what you mean by the face of a triangle is basically the side with visible texture?

And that is why triangles are my... MARVELS OF THE SCIENCE

Here's a drinking game for you, a beer and a shot of tequila every time the word "verticies" is used, and no, I'm not responsible for your alcohol poisoning.

Yay. Upcoming video about Linear Transformations... Brady should do a Linear Algebra Numberphile video to go with it.

Maan, this is some real maths-video I have seen in a few days

There are actually many systems for representing 3d objects (meshes), it depends on the "rendering engine" (software that reads the data and presents it to the video card). The most common are.. A list of individual triangles, triangle strips (where each new vertex is assumed to be part of the next triangle in the mesh), meshes (as in the video, where a point list describes how to connect a vertex list), quads & quad strips (similar to triangle and triangle lists, but they use 4 verts), polygons and primitives.. nurbs, (like using a cage of points around a mesh to imply where the surface is). although these all get converted down to triangles by software &/or graphics card at render time. Also, there are terrain maps and bump maps.. which are like a list of numbers (think grey-scale image, with each pixel in the image being a height) that tell a rendering engine how high a point is from a particular plane or distance from the centre of a pre defined primitive. There are undoubtedly other ways to represent 3d objects too. ie, could use angles and distance from a point. Graphics cards themselves are usually what limits what people do (rendering speed etc).. & often have cool features that allow programmers nifty ways to represent model data.

In the case of particles, it's actually easier both to render and to control them if they're rendered as projected raycasted rectangular images rather than a set of 2 triangles because they render much nicer and don't get as distorted or have the sorts of orientation glitches you get when you introduce multiple cameras. Fun fact: the Sega Saturn used strictly tetrahedral based rendering, making it's textures signifigantly less distorted, but also, due to their low-resultution, less smooth and more jaggy. Also, it made developing for the Saturn a nightmare for multiplats since all of the in-game geometry had to be converted to tetragons from the triangular polygonal mesh data of the Playstation, N64, 3DO and PC verisons. Also, he forgot to mention anti-aliasing, which is a post-processing filter applied to polygonal renders that helps eliminate the jaggies and better approximate curved surfaces. It's standard practice in modern video games and part of why modern games don't look as polygonal as their past counterparts. You can disable this filter in most modern PC games and you can see the difference.

Nice video! I have a question. Obviously our brain can create 3D scenes from memories, and the scenes we see in our dreams. So the question is: Do we know how our brain stores such 3D information? I presume it must be done in some very efficient manner. Does it has some correlation with the technique you described in the video.

nice grapichs on the coordinates like it very much

Origami very much works from this principle of triangles using folds and inverse folds - I would recommend all developers take up origami to help physically visualise vectors.

Interesting stuff!

great one

Nice explanation for newcomers or those who want a brief recap

More from dis guy pls.

great informative video...but I have a question for you... Can any single vertex of a triangle can also be on another plane and still be a valid triangle like you explained for other higher polygons e.g., rectangle?

I think I know now why there are so many games with crystals as a central plot element. They're so easy to render with triangles.

It's quite elegant, the way the 3D coordinates are converted to 2D coordinates for rendering on the screen by matrix multiplication. It's all math from the 1980's.

He kinda sounds like Shaun Connery lol

That's one charismatic programmer! I like his style... He's so suave... Like he's about to take you on a dinner, just when he explains about graphics triangles.. lol

@ LucAs Bune: There is a big difference if you use flat shading or Catmull-Clark subdivision.

00:36 Half way into '3D geometry & chill' and he gives you this look.

Weird leftie axis system. I'd have put the +z the other way. :/

cool vid. are you going to be doing videos on rasterization and other render methods such as ray tracing?

Whats interesting is that if you consider the possibility of our existence being that of a computer simulation then you would end up trying put together how the three dimensional objects such as spheres in our universe and/or the concept of a circle aren't plotted in terms of small triangles, and so if you truly believed this was the case, you would be conflicted in coming up with a better way in creating computer models without the use of triangles. i.e, in mathematics we have pi a continuous number that illustrates the circumference of a circle, and so we haven't really fully come up with a definitive way to fit our understanding of round surfaces let alone implement it into a computer simulation.

Triangles are to shapes what sine waves are to periodic signals. You only need the former, in different sizes and at different angles/phases, to construct a representation of the latter.

Blew my mind!

i like this guy

Moiré effect on the shirt... What is the math of the moiré effect?

An interesting sequel would be explaining how voxels work and their advantages (and disadvantages)

Less frequently, but rectangular meshes are also used. You can still restrict the points to be coplanar. Of course, creating the mesh is more difficult.

given how much tessellation is used now and given that modeling is typically done using quads, n-gons or curves I wonder how long triangles will last before we just switch to rendering bezier patches or whatever directly since it doesn't really make much sense to draw a triangle that's smaller than a pixel