Vector Rotation (Derivation & Geometric Proof)
Вставка
- Опубліковано 10 жов 2021
- Most game programmers know that we can use a matrix to rotate a vector around the origin.
They also probably know that a vanilla rotation matrix looks something like this:
[ cosθ -sinθ ]
[ sinθ cosθ ]
But, do you want to understand where these formulas come from?
In this video, we'll learn how to derive the formulas for vector rotation in 2D, including the mathematical geometrical proof of how to find the new rotated values of x and y.
I hope you enjoy it! :)
For comprehensive courses on computer science, programming, and mathematics, visit: www.Pikuma.com.
Don't forget to subscribe to receive updates and news about new courses and tutorials:
/ @pikuma
Enjoy! - Наука та технологія
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
Remember that a rotation matrix is basically the same as that initial formula you see in the slides. :)
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!
That's very kind. Thank you. :)
Great explanation. Helped a lot. All the best for future similar topics. We will be waiting. Thank you .
This is the best explanation of rotation matrix I ever saw, for sure :)
Thank you for this invaluable information!
Thank you so much! All of your videos are PERFECT.
great and complete explanation thank you !
Parabéns! Excelente material!
Finally I found a video that don't use cos(A+B) and sin(A+B) formula
Wow what a amazing explanation!
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!!
good work , i love it
Thank you for the great video!
Thanks!!! ❤
Your description is so easy to know.😀
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.
interesting and accurate explanation
you deserve more views!
Great video!
Very useful video
thank you so math, very useful🙂
Good tuts
Thanks so much for the video
I need to get into game dev at some point
Thank you.
Thanks 🙏
very cool video
what is D a projection of? like I don't see where its y-coordinate came from, it's neither y nor y'
you show us the truth that vector rotation is simple👌👌👌👌👌
Don’t forget me when you get famous
quaternions next?
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.
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.
@@pikuma Thanks, i was with this question because the dots are away from origin.
Every sub is hard won. Here, take mine :-)
Very good lecturer.
how to write in terms of beta
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.
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.