Intro to Graphics 06 - 3D Transformations

[@emcpadden]

I’m binge watching these videos. Cem does an awesome job at exploring things. I can tell he really enjoys teaching and that is also what makes these visits so engaging! Great job! I will be watching his other content when I’m done with this series. Thanks for making this so approachable. I feel like I could teach someone else this from his excellent explanations. Thank you!!!

[@MrErererererr]

I am glad that I find this lectures. Thanks for great videos.

[@ahmeterencagatay8985]

Hocam Sabancı Üniversitesinde son sınıf CS öğrencisiyim, Computer Graphics dersimin midterm'üne hazırlanıyordum ki videolarınıza denk geldim. Slide'larınız konseptleri görsel olarak sürekli canlandırmanız ve enerjiniz harika, çok güzel anladım çok teşekkür ederim.

[@EnchiridionYT]

Lovely! Thank you Cem! 🙂

[@blanchsb]

I've been studying this topic for a while and have an engineering background. I must say this 2D and 3D explanation of CG matrices for Rot/Trans/Scale is wonderfully done. Thank you very much for posting this to KZbin.

[@oflpoeog]

Thank you again University of Utah and Cem Yuksel for making these intro lessions available for the plebs at www

[@rupeshmandke]

One of the very few easy to understand explanation of otherwise made complex to understand topic! This one helps build the intuition which is very useful. Perspective projection is combination of Perspective transform + Orthographic projection is something explained very well. Looking forward to upcoming videos :)

[@wazabear6916]

Your hard work is appreciated, I can tell you put a lot of effort into these videos. Thank you.

[@santiagofernandogomez4986]

Thank you so much for this content. Please keep uploading more videos, this is gold!

[@jorgecouchet1081]

Beautiful and incredible explanation! Thanks a lot for you really hard work!

[@szabolcsnyeste9666]

Thank you for the video! 3D rotation was very gentle, it alone worth a couple lessons. And when the homogeneous last coordinate gets to be zero - that's where the fun begins :)

[@karmagiel]

Edit: nvm, i think i got it now ^^ could it be there is a mistake in the matrices in min 37:06 ? Because when the far and near plane are both in negative z direction, 2/f-n gives us a negative scalar => would invert our z-coordinates aka change the handedness of the coordinate system. looking at the source code of glm::ortho for example, they put an extra minus sign in front: -2/(far-near) great videos btw :)

[@anuragparcha4483]

Thanks for this great course Cem. I have a doubt at 58:33, why can't the 3rd row of [0, 0, ?, ?] be [0, 0, Pz, 0]? Would that not help with maintaining Pz = P'z? Since Pz^2 / Pz = Pz? Or does this matrix need to be independent of the P vector?

[@saikongz]

At 53:40, I am kind of lost here. Do you mean [α*x, α*y, α*z, α] and [x,y,z,1] are the same point w.r.t the camera view? In 2D dimension, for example, [1,2] and [3,6] are not same point with respect to position, but are the same when it represent direction. Is this the correct understanding?

[@saikongz]

Or another way to understand is that, because the existence of orthographic transformation, these two points ([α*x, α*y, α*z, α] and [x,y,z,1]) will eventually converge to one. Does this make sense?

[@cem_yuksel]

Homogeneous coordinates take a 3D vector and make it 4D. Therefore [ax, ay, az, a] is a 4D vector. The corresponding 3D projection of such a 4D vector is [x,y,z]. Note that the 4D vector [x,y,z,1] (i.e. a=1) has the same projection.

[@smoothrelaxation2870]

Great series so far. I can't say I'm comfortable with the math yet but knowing what we're trying to achieve helps keep me motivated. I make environments in Unreal Engine 5 so understanding perspective has already helped me make better scenes. Cheers.

[@arts2crafts]

Thanks a lot for posting Sir. It is really a useful lecture Is there a downloadable link for the slide deck ?

[@oflpoeog]

53 years old, if i was young again i would study Computer Graphics (at Utah)

[@SreyRc]

So well explained! Can't thank you enough!

[@nikolaitesla4267]

Hi, I’d like to follow these lectures and work on the assignments, but I’m unsure about my JavaScript skills. Is learning JavaScript essential for understanding and retaining the concepts covered in the course? Or are there alternative approaches I could consider? I’d greatly appreciate your guidance. Thank you!

[@cem_yuksel]

No, JavaScript is not essential, but it is not a hard language to learn for anyone with programming experience, and it is a good skill to have.

[@graphics_travelers]

57:11 Pz multiplied by another Pz? Don't you mean divided by Pz or multiplied by 1/Pz, that's the only way one will get a 1?

[@cem_yuksel]

Yes!

[@graphics_travelers]

@@cem_yuksel Thank you for clarifying.

[@caviare8169]

Your illustrations are so great! Thanks for sharing these videos (^ ^)

[@Ryan-ms8bi]

Cem, at 31:15. The Projection Transformation, why 1 represents f and -1 represents n, did I miss something? I like your course very much😃.

[@cem_yuksel]

Good catch! It's a left-handed coordinate frame. :)

[@Ryan-ms8bi]

@@cem_yuksel I see , thanks ！😀

[@MultiHomestead]

Where can I download the slices?

[@karmagiel]

another question: With the orthographic projection we were able to define the location of the view volume ourselfs. Now when we used perspective projection we kinda directly used the vertex-coordinates relative to camera space. that would imply that our view-frustum-box center is at (0,0) in the camera space, wouldnt it?

[@cem_yuksel]

No, it is a transformation from the camera space to the canonical view volume, which has a different center.

[@karmagiel]

@@cem_yuksel thanks!

[@FPChris]

I know you can change It however you want but I was alway most comfortable with your eye as 0,0,0 and -x left, -y up, and -z behind. +Y up is cool too if you think of it as Height. But then I’d prefer +Z moving away as a Distance value. Again do what ya like but be consistent.

[@lavz24]

Great explanations.

[@ic_1234]

Thanks Tom Araya!!!

[@한푼땡전]

I LOVE THIS CLASS

[@rishabhsharma9369]

Cem, at min 54, could you explain why we are dividing the 4th coordinate(previously represented value 1 and for perspective transformation Pz). Looking at 2D transformation video, I thought the value 1 was introduced for the trickery of representing translation as a matrix operation.

[@szabolcsnyeste9666]

The 1 value was enough for the translation part, but not enough for this case. Two things to highlight: one part is that if you take [x,y,z], and multiply by 'α', and do this for all α values in interval (-inf,inf) that gives you one particular line in 3D which goes through the origin. This is useful for us because if the eye is in the origin, we see this line as one point. Second take: we track this 'α' value like this: [α*x, α*y, α*z, α] and this represents the same point as [x,y,z,1] and so [x,y,z]. To get the 1, we divide all by 'α'. To truly understand this I believe you need to go through some calculations by yourself, but I can not help you in the limits of this comment.

[@FPChris]

9:35 yep.

[@spider853]

Thank you

[@BigRubberDucky]

School teaches you such generic things and I really want to niche down into graphics, but man the barrier of entry is very high.