❖ Rotating Points Using Rotation Matrices ❖

In this video I justify the formula used involving matrices to help find the new coordinates of a point after a counter clockwise rotation. There is one quick example as well at the end! The formula is pretty easy to use so long as your remember matrix multiplication so I spent more time on the justification part since it is more interested!
This topic would be useful for people in animation or design if you want to understand the mathematics occurring in the background.

[@patrickjmt]

Hi all! Wanna help a RUclips education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

[@kseshan731]

I am a chemist (retired professor) and I am trying to understand how animation works (matrices and graphics). You are a wonderful teacher. Thanx for helping me to come to this solution for rotating vectors using mathematics I learned at school (and remember still). Brilliant lesson.

[@patrickjmt]

thanks for the kind words. good luck in your studies!

[@GoatDirt]

MAD respect doing explainers in SHARPEE. NO mess ups. Great work!

[@cheatman05]

Finally I can think of something when someone says "transformation matrices", because those were nothing but a bunch of vectors for me till now. Thank you for making this great, clear explanation.

[@varus7993]

I watched your videos since I was an undergraduate student, now I am studying in Ph.D and still watch your videos XD. Thank you so much for everything you have made for us. I am really appreciated

[@yupitzmeeee]

I am like 15 years old and in my country this comes in when you’re like 17. And I am still doing it lmao.

[@ian.ambrose]

@@yupitzmeeee That means you are very smart! Congrats!

[@AlexMcClung97]

Great explanation, thanks! It would be great to see a derivation of the 3D case (3x3 rotation matrix) also.

[@delandoduggan7698]

Please

[@vijaishankar3942]

​@@delandoduggan7698 It's the same for 3D, here we are rotating along the z-axis, so if you want to rotate along the y axis then substitute x and y with x and z. So it's just a matter of changing the axis.

[@dhanush.n290]

@@vijaishankar3942 I need full answer for 3×3 matrix

[@susius4211]

@@dhanush.n290 the Z stretches out of the plane, so rotating the other two does not affect it. Therefore, you would append a Z’(0) to the end of the pre-existing equations. For the third equation, you are rotating/performing transformations with the Z-axis directly, not the other two. Therefore, they are x’(0) y’(0) by the logic used previously. Z would be Z’(1) because it is now being transformed.

[@fxckingjapanese]

Thank you so much Patrick!! I had an assignment of this. You almost saved my grade of Engineering Mathematics :D

[@mustafasiddiqui8203]

Almost?

[@hoodiegamer9256]

We pay a million bucks in tuition but the guy from RUclips teaches way better for free OMG thank you very much Sir

[@patrickjmt]

hey! i have a name! :)
glad you like the video :)

[@hoodiegamer9256]

@@patrickjmt no problem man. I appreciate you taking the time to teach this Patrick

[@codebitcookie8053]

You just made my life easier, I can't thank you enough!

[@spicesmiles]

soo clear!! thank you!!
no fancy tricks, just clarity...sigh
again thank you!

[@obensustam3574]

I am a robotics software engineer and use rotation matrix for differential robot position estimation in my code. However, I was not aware of the mathematics behind it. Thank you so much for this great explanation.

[@souraneelchattoraj1293]

Dude you have no idea how much this video helped me understand the -sin theta, i forgot about trig identities and this is just what I needed to carry on my 2 link manipullator research. Thank you

[@yunweneric5528]

Quite eloquent and straight to the point.
I find this quite helpful
Thanks

[@Haligonian]

You are shockingly good at freehanding straight lines.

[@keithturner1069]

Hey mate, I'm currently doing a mathematical exploration of matrices as part of a teaching degree. I stumbled upon the rotation matrix through some guess work, but I didn't understand where it came from until your video, what a great explanation! I would have never gave thought to use that trig identity. Cheers and keep up the good work :)

[@guy6567]

never thought id need this so when i learnt in school i didnt understand, now i need it for my code, funny how that works, im so interested this time, last time didnt even care enough to remember

[@veronicagonzalez5411]

thanks for all the help, you have saved me many times in my time of need and i just wanted to say thank you

[@mridulk81]

Made the topic so clear
thnk u man

[@password6975]

Some of the best material on youtube

[@MuksEmmaN]

You explained in 9 mins what my lecturer tried explaining in a week

[@pathummudannayake6947]

Thank you. Awesome explanation. Some class just gave the matrix for 3D without saying how it got there. Your explanation is spot on.

[@FreeMayaTutorials]

Amazing lecture! You are a great teacher.

[@patrickjmt]

Many thanks!

[@lukas7966]

nice video! if you aren't interested in the derivation, start at 10:50 and for the "shortcut" start at 15:21

[@georginihrizov9317]

I have been banging my head the whole day trying to rotate a triangle and if it were not for you I would have lost my sanity. Thank you!

[@PopDeek23]

Spectacularly clear explanation! Thank you!

[@gloystar]

Dude, you're the best! This is indeed the best and simplest explanation and derivation of that rotation matrix. Other guides on the net just complicate things. I love your videos. Perhaps you could make a video demonstrating how, using this formula, the y=1/x curve is actually the hyperbola [(x^2)/2 - (y^2)/2 = 1] rotated 45 degrees counter-clockwise.

[@imme.8736]

I love this video. It's super clear. Thank you a lot.

[@IrocZIV]

As always, a very helpful video.

[@ShahbazKhan-rg7fd]

Thanks man, really helped with understanding some Matlab code for my uni project

[@mohamadhafizulazwanmohamad3333]

Great video. Very easy to follow.

[@patrickjmt]

Glad it was helpful!

[@gopinadhvuchuru1399]

Its a wonderful explanation Mr. Patric.... thanks man

[@djgulston]

You are saving lives, sir!

[@unsolvedmystery7408]

Very very helpful seriously very helpful thankyou so much, i was working on an HTML canvas project and this helped me alot

[@patrickjmt]

glad it helped :)

[@ItsNotAllRainbows_and_Unicorns]

I was able to work it out after the half way mark, but thank you. The way it's taught in books left me wanting more. I never felt it was properly explained. Was it sin(theta) or -sin (theta). Utilizing trig identities, it explains where one places the minus sin.

[@NikOG3]

Water clear explanation, thanks!

[@wayneruan7711]

You are way better at explaining this than Khanacademy. Praise the lord!

[@vestafarhan7580]

Really thank you 🙏 best teacher 👨‍🏫

[@lakshraja4831]

Thanks, great vid really helped me with the spinning donut

[@ReversedFootage]

Absoluting amazing explanation, kudos!

[@marxregis]

Thank you for the great explanation!

[@aramh3376]

Thank you mate.It's been useful.

[@dr.sudharsanaraopotturu1380]

Excellent explanation, thanks for your efforts. Keep it up sir

[@rajeshramachander4799]

Fantastic explanation!

[@rahulnaryal7739]

Thanks buddy

[@lifematch]

Can you please do 3D rotational Matrices!!!!!! Honestly your way of teaching is the only way I can understand!

[@sam90o48]

tysm for showing me this ,it will help me. in solving many problems

[@ignaciomora8317]

Great explanation thanks fella

[@gidonkessler1799]

just what i needed for my programming :)

[@adamtongi427]

Thank you very much. I didn't know how to represent a point in matrice form.

[@avinashjha7848]

Thanks sir for this great explaination

[@Stella-yv2ns]

Thank you very much, very good explanation!

[@k_dery0928]

finally I can understand now thank you so much

[@wellbangok8959]

I don't know why I'm here but DIFF EQ is a nightmare.

[@roycas3]

this explanation helped me a lot thanks.

[@leah.2520]

thank you very much, i always wondered where this matrix came from !!!!!!

[@ahsansher1059]

thanks for sharing it with us very nicely explained

[@debarshiroy2939]

Thank you so much for the video

[@davidnguyen4353]

thank you so much!!! my prof didn't show this on her slides

[@hi6747]

Thank you for your lecture.

[@b0606089]

True content, no bullshit.

[@hartonianwar3607]

wow I like this video.
very good at explaining the material

[@dioutoroo]

Sheeeeshh!! You're excellent!

[@wisdom_wellness365]

Great explanation! Thanks

[@ivanurbina2422]

Beautiful explained

[@magicteen1]

This is gold!

[@Nanba91]

YOU ARE A LIFE SAVER THANK YOOOOOOOOOOOOOOOOOU

[@weisu1427]

Thanks Patrick, this was really helpful!

[@patrickjmt]

perfect! glad i helped!

[@tarikalansari5521]

amazing, thank you so much!

[@jonas26a]

Very helpful and explained well. Thank you

[@TheCharbMusic]

Very good explanation, thank you very much !!

[@dangkhanhlinh476]

This is exactly what i need. Thanks you

[@geromeponch6248]

great video. thanks

[@daqiangsz]

讲解很清晰，感谢

[@JimmyGray]

Great demo!! Thanks!

[@nabeelkamal92]

Thank you so much Patrick. Its great.

[@nircoren8161]

amazing! thank you

[@Jafar-is6te]

When - sin is in the second row, that makes a clockwise rotation.
When it is in the first it will be counter-clockwise.

[@domenicodifraia7338]

Great video man, thanks!

[@HabibKhan-jr9id]

Thanks. That was very helpful.

[@ProfDiaz-19]

Excelente explicación hermano se gano un seguidor.

[@EverydaySimulations]

Love it if you'd do the 3 dimensional version! Thanks pat

[@diegohiroshiysusvideos2909]

Nice video for my surface orientation system from game character on slope. I love trigonometrics 7w7

[@nooshax1]

thank you so much

[@kemibello6812]

Very helpful, thanks

[@shashwat4299]

Bull eyes explanations dude you have logic great

[@sathishkumarpalani6364]

Awesome Buddy.

[@spoofvideo2361]

Hey friend, Very helpful video => Gret
Perfect 2D Rotation.

[@electricengine8407]

my program actually works yay
now i just need to figure out how to rotate vectors in 3d

[@taihatranduc8613]

thank you a lot

[@nehalahmed2515]

Love you Bro

[@boratsagdiyev3936]

I love you, man...

[@MuhammadSohailKhan]

its really helpful :)

[@srinathsri4365]

nice one..

[@elnurvalikhanli7056]

thank you so much !!!

[@frankmsigwa6674]

Thank you sir

[@MdAbdullahAlMuyid_nowho]

Thanks yo. A lifesaver : )

[@mariamgarba1416]

thanks for this, is there a 3D (X,Y,Z) explanation of this videos?

[@mathguy4264]

perfect. Thank you.

[@CarlaLud]

Great explanation, thank you! But how would I change this method to rotate around an arbitrary point, instead of the origin?

[@krishpatel9139]

Add the value of the point to the end result.

[@sitinurbaya6157]

Awesome video! very clear explanation ...thank you so much !
would like to ask... how do you get the left side matrix if you know the initial and final coordinates... thank you so much!