The True Power of the Matrix (Transformations in Graphics) - Computerphile

"The Matrix" conjures visions of Keanu Reeves as Neo on the silver screen, but matrices have a very real use in manipulating 3D graphics. John Chapman explains the true power of the matrix.

Graphics series with John Chapman:

5/ Light and Shade in Computer Graphics: Coming Soon

Addendum - at 12:35 the formula should read: x*0+y*0+1*1

This video was filmed and edited by Sean Riley.

[Prime-of]

Don't skip the maths please, that's not a 'cool thing' to do. Presumably we're here because we're interested in the subject, so don't try and hide what it REALLY involves. You're doing the same thing that the profs in the 'Problems with High School Physics' video (on sixty symbols) were talking about - cutting out the maths. It's not boring, maths is beautiful and attractive - it describes the truth of systems (physical and simulated), and I'm interested in the truth.


Thank you

[ApocDevTeam]

and this is just one triangle, now imagine modern video games that consist of tens of millions of triangles all textured, shaded, constantly moving and interacting with eachother at 30+ frames per second. you truly start to appreciate the power of a graphics processor.

[joaza]

You should write matrix-vector multiplication in the correct way of x' = Ax and not x' = xA. Matrix multiplication is not commutative and xA cannot be evaluated. Also, do not teach people to use the 'x' for the dot product, that is for cross product. I know I'm an ass for pointing out how to write stuff but people should learn it the right way, considering this video was made for learning purposes :)

[Xray-Rep]

I realize this video is 9 years old (at the time of this comment) but it is the BEST explanation of matrix transformations that I have seen and heard. Prior to watching this video, I have watched at least 18 or 20 other videos that explain matrix transformations but all of them left me confused. Now I understand details that were skimmed over or simply left out of the other videos. THANK YOU COMPUTERFILE for this excellent tutorial!

[MorreskiBear]

I've tried to make 3D graphics from scratch on my old Commodore 64 before. The best I could do was rotate a stationary cube one point at a time, one axis at a time. Later I learned that somehow you could smush all three rotations together in something called a matrix - but couldn't begin to wrap my head around how or why that worked. Your video might have helped me begin to understand matrices and 3D stuff. Thank you!

[nerdbot]

Nice! Keanu Reeves explaines the Matrix. He knows best

[AbdulrahmanMajash]

At 12:44 I think he made a mistake in the last set of additions. Since it's matrix multiplication it should've been:
xa+yb+1*c
xd+ye+1*f
x*0+y*0+1*1
It wouldn't have mattered in the end (due to multiplying by zero), but this should've confused people who don't know matrix multiplication.
Also, multiplying 3x1 by 3x3 isn't valid (# of columns of the first =/= # of rows of the second). He did it the other way around. It's alright using the formulas he put, but doesn't agree with the "row column" multiplication method which I assume many does it that way. I'm sure he knows what he's doing, but just wanted to clarify some points. Good video btw. Important for signal processing as well c:

[goeiecool]

Why did he have to fast forward the rotation formulas!? I was really interested in seeing him work it out

[carlossoto]

"We're doing a shear operation in 4-dimensional space, which then casts it's shadow back to 3d space as a translation"
am I the the only one that finds that beautiful?

[Sad-Lemon]

You can feel how passionate about graphics the presenter is by listening to him. I hope every single teacher in my country would share that passion for their respective disciplines ;)

[mkaatr]

Looking forward to the video about how to map a 3D object/Surface into our 2D display screen :)

[ScottLahteine]

Ah, this takes me back to the mid-2000's when I did a lot of work directly with OpenGL, and matrices were a real revelation. Happily today we hardly have to think about it, since the work has been done. We can just open up Unity 3D or some other 3D simulation environment and go to town with nary a thought for trigonometry. It's still essential to understand these concepts, since we sometimes need to do some fancy things, and it forms a good foundation to understand the world of 3D, but we no longer have to look at these complicated underpinnings very much today.

[energysage]

To any math nerds who freaked out when he multiplied two 1x2 matrices at 2:30, he did that for clarity for viewers who aren't clear on matrix multiplication (which seems overly complicated when you first learn it). He  clearly applies the transformation which would be the 2x2 matrix given by first row [1, 0] second row [0, 2]. The way he wrote it, though, isn't so much incorrect as it is a different operation... it's element-wise multiplication, which programmers use often.

[finthegeek]

Disappointing, what is the point of going into this complex an idea and skipping out half of the

that said having a decent understanding of it already it was a solid enough video

[yushatak]

WHY DID YOU FAST FORWARD HIS EXPLANATIONS OF THE PARTS THAT CONFUSE ME? O_O

[SimonDouville]

I don't know why i'm watching these videos. I understand nothing to maths. But find it interesting that something that seem so simple to do in photoshop is in fact so complicated. Kinda feel humbled by that.

[isaac]

Computerphile is probably one the best of your channels, Brady.
You can't find such simplicity and good explanations elsewhere, that will give you a foundation to work off of. It is really nice. 

[Mrkol_]

NOOOO! Make a separate video about all complicated math parts! DO IT!

[mrjoehimself]

The ability to teach these topics so eloquently is a real gift, it's truly a joy to watch.

[superearthbender]

I think he's in The Matrix right now.