Vector Rotation (Derivation & Geometric Proof)

[@samuelgibson780]

This kind of thing is why the internet is awesome. I've never taken a trig class, and these kinds of quick overviews are priceless

[@mrsajjad30]

I can feel the amount of effort and hard work you have put in making this explainer video just to make it so simple for us. Thank you so much Sir. I really appreciate it. I am making a top down tank game and I wanted to implement the rotation logic myself that brought me to your channel. Thank you Sir!

[@pikuma]

That's very kind. Thank you. :)

[@gcpezzi]

Remember that a rotation matrix is basically the same as that initial formula you see in the slides. :)

[@omnis8240]

Thank you so much. I'm glad you asked us to find the proof for y' prime Very satisfying.

[@samhighfield]

This is by far the best explanation of vector rotation I have ever found. Most books and people just gloss over the derivation of this and frustratingly just accept the formula to be the truth, not even mentioning the great lengths that go into creating these short, simple formulas. Thank you so much!!

[@danilaushamburg2975]

This is the best explanation of rotation matrix I ever saw, for sure :)

[@azaxmaj2629]

Great explanation. Helped a lot. All the best for future similar topics. We will be waiting. Thank you .

[@unsolvedmystery7408]

This is really really helpful, I am going to buy your course as well 😊

[@parinamais]

being able to find y' at the end made me so happy 😄 you are an awesome teacher!

[@pikuma]

Told you! :) Great one.

[@archaicmagnongaming3796]

Finally I found a video that don't use cos(A+B) and sin(A+B) formula

[@aidanflannery1934]

You're a good teacher

[@hapboyman]

This is an excellent explanation, Gustavo. However, I know a more straightforward approach. I studied it on the Brilliant online school, on a Vector course. You need to cut out of paper a right triangle whose hypotenuse is the length of the initial vector and the legs are its components. Then attach it to the graph and rotate it and everything will become clear.

[@katsusanw-game-ch]

Your description is so easy to know.😀

[@kooroshtorabi8773]

Thank you so much! All of your videos are PERFECT.

[@giggles8593]

Thank you for this invaluable information!

[@carljeffersondelfin4210]

you deserve more views!

[@rodolfoc.nascimento6301]

Wow what a amazing explanation!

[@khaledx4964]

you show us the truth that vector rotation is simple👌👌👌👌👌 Don’t forget me when you get famous

[@Lord_Biyoma]

great and complete explanation thank you !

[@contentprogramming]

good work , i love it

[@EgorChebotarev]

interesting and accurate explanation

[@TheALEXMOTO]

All such explanations do not explain the magic of the transition from point G to point F. It may seem strange, but I was helped by an example with a light source that shines at 100 percent and behind it are two obscuring glasses each of which gives a dimming of 50 percent. that results in a brightness of 25 percent.

[@japhethjay4880]

Thanks so much for the video

[@japhethjay4880]

I need to get into game dev at some point

[@joachimschmidt7662]

Every sub is hard won. Here, take mine :-) Very good lecturer.

[@leeoiou7295]

Very useful video

[@haidergilani1423]

I love this video

[@eduardomacedo2504]

Thank you for the great video!

[@dandnnn]

Great video!

[@MrKlaygomes]

Parabéns! Excelente material!

[@maxgin3728]

thank you so math, very useful🙂

[@sic111]

very cool video

[@alexandern9353]

what is D a projection of? like I don't see where its y-coordinate came from, it's neither y nor y'

[@lksxxtodin5292]

Thanks!!! ❤

[@xKeray]

quaternions next?

[@tjalferes]

Thank you.

[@tecnolog7933]

As I could understand, if I use the formula I mot only rotate, but I move the vector or I can use this formula to rotate, but keep the position in cartesian plane. Also, grade A content, really cool.

[@pikuma]

The rotstion assumes that the pivot point is always the origin (0,0). If you want to translate (move the vector around) you should do that after the rotation.

[@tecnolog7933]

@@pikuma Thanks, i was with this question because the dots are away from origin.

[@mohokhachai]

Good tuts

[@slca]

Thanks 🙏

[@mr.chindo8570]

how to write in terms of beta

[@ian.ambrose]

I appreciate the explanation but that derivation seriously is so long. There's a 5 minutes long derivation by Pen and Paper Science but with the same mathematical approach.

[@pikuma]

Hi Ian. There are many ways of deriving the rotation components. I believe the most common one out there is the one where people rotate both axis keeping 90° between them and projecting their cosine and sine. I tried to add the actual geometrical *proof* of the problem, hence the length of the video.