Intro to Graphics 09 - Curves (Part 1)

[@darkarchon89]

I love this video series. Your pedagogical style is great. I appreciate how you emphasize your important points by literally pointing to what you're talking about, and you're using your videos dynamically to talk about graphics in a way that feels far more accessible than the textbooks I have at hand. Not to say that the textbooks are useless, they're still useful and necessary. For instance, Foley et al. has a very good treatment on homogeneous coordinates, and I found the 2nd edition of this book online for a bargain $4. The fundamentals hold up despite the age of the book. Anyway, thanks for these videos. What a gift for any student who wishes to learn more about CG.

[@Mahm00dM0hanad]

Finally I found that hidden gem deep in KZbin, thanks a lot for sharing

[@Benjinx264]

This has been fantastic. A huge help to see this series. I'll be continuing to watch them all. I really hope to see more of these style of videos from you! thanks so much!

[@gegirti]

57:05 such a magical moment!

[@adsick_ua]

I like how the fact that the derivative represents direction is visible from the equation itself: it consists of differences of vectors (p1 - p0), (p2 - p1) and (p3 - p2) which are essentially directions, not positions. Also if you look at it in homogenous coordinates the w coordinate (1) will be eliminated by subtraction and become 0.

[@FMTAZ]

Thanks a ton for your videos Cem! In my experience, many people skim over the fundamentals really quickly, which makes higher level concepts significantly harder to grasp. I appreciate the slow and steady pace, and the clear explanations :) Quick question/comment: I worked the derivative of Bezier curve, and I'm getting (2 * (1 - t) * t * 3 * (P2 - P1)) (no ^2), which makes sense, since the power2 will make this a quadratic term. Am I missing something? Edit: looks like the ^2 is blacked out in the next lecture!

[@cem_yuksel]

You can find the derivatives of Bezier curves on Wikipedia: en.wikipedia.org/wiki/Bezier_curve

[@viper5326]

seriously you are awesome! explanation and presentation are incredible. ty from germany :)

[@burakcanik01]

These courses are intuitive and awesome! Congratulations and many thanks. I found one error: The derivative of the cubic Bezier has an error where the term (P₂-P₁)3 is pre-multiplied with the term 2(1-t)²t, whereas it should have been 2(1-t)t (without the square/power of 2). I realize there is one other comment already mentioning this (which I upvoted) but I figured it would be better (more visible) if I also mentioned it. It seems to be fixed (smeared) in the next video (Part 2) but it is not mentioned explicitly as far as I could see from a quick glance. It would be nice if you post-humously edited the video or at least mentioned this in the description and/or comments. I was picking my hair wondering what I'd done wrong for quite some time 😁 Also I wish universities in my country had more teachers like you 🤘🚀

[@saikongz]

Thank you so much for the content! One question though, if two Bézier curves are split from one Bézier curve, do they have C2 continuity?

[@cem_yuksel]

Yes, indeed, as long as you are careful with the curve parameter. In fact, if you split a Bezier curve into two curves, you get C-infinity continuity at the splitting point (i.e. all derivatives on either side of the splitting point match).

[@lavz24]

Great lecture!

[@aurag1760]

I'd add a tiny bit of info on bezier and casteljau : their companies are both french and rivals (still to this day!)

[@Semtex777]

Thank you very much Cem ! ((please improve the audio (lapel mic ?) it will be perfect !))

[@cem_yuksel]

These are previously recorded lectures, so I'm afraid there isn't much I can do to improve the audio quality without recording them again. :(

[@metabast]

Hello, thanks you very very much ! It is very usefull and very clear and much more ! ( good mood )

[@ergis8004]

Math + Computer Science = Magic 💫

[@ashutoshtiwari3931]

Not related but its way to hard to believe that both bazier and casteljau got the same idea at same time. Sounds like both stole idea from someone else.

[@cem_yuksel]

So you are suggesting a mysterious third person came up with the same idea at the same time? :) Actually, this is more common than you'd think. Scientists at the cutting edge of human knowledge often see the same next step around the same time. In the case of Bezier and de Casteljau, their thinking was not identical but mathematically equivalent.