I can't hear êx or êy anymore after making this video. Somewhere in the future, I'll probably make a part two which will discuss more advanced matrix operations e.g. determinant, inverse, ...
FloatyMonkey always! It’s only a matter of time before these blow up, they are too good not too, this type of content is sorely missing in the indie community imo. Game dev maths from theory to practice is a void that definitely needs filled!
Great video. Only have one question. If you first shear and then rotate, to project it into the first coordinate system, you first have to multiply with rotation matrix and then shear matrix. You did it reverse. Why?
Questions at 15:00 : (1) Should those three rotation matrices also have the fourth columns and rows as the previously shown scaling and translation matrices have? (2) I thought there was a matrix that could rotate around any arbitrary axis, is that not a thing?
1. They're not required but you could write them. In that case you add a row of zeros to the right and bottom but have to make sure the bottom-right element is a one. Essentially you 'paste' the 3x3 rotation matrix into a 4x4 identity matrix. 2. You get this matrix by multiplying the shown three primary rotation matrices. The result is still a 3x3 matrix but writing it symbolically with sines and cosines gets really long and would've been a mess to put in the video ;)
@@FloatyMonkey 2. Thanks for the reply!! So, then would those three component rotations actually be the projection of theta into the planes perpendicular to those axes? I was trying to multiply them out as you said, but then I realized that I didn't know if those were all the "same theta", and I found this insanity on wikipedia en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle and en.wikipedia.org/wiki/Transformation_matrix#Examples_in_3D_computer_graphics , I'm trying to figure out how this actually works so i can try to program higher dimensional rotations lol, it just keeps getting worse and worse hahaha
Yep, don't tell me about those rabbit holes ;) The formulas you found on Wikipedia are both the same and are used to rotate around an arbitrary axis (given by a unit vector). Another way to create arbitrary rotation matrices is by multiplying the 3 elementary ones from my video. In that case theta is different for each matrix. You basically construct a rotation matrix from Euler angles instead of an axis and an angle as in the Wikipedia articles. Hope this clears things up.
this video is really good, you cleared many of my questions I'm still not sure how all of this will be applied to game deving tho, if anyone could give me an example I'd be very glad
When rotating, why does the green vector x coordinate is -1 * sin instead of sin? is it because it ended up in the negative side of x axis? Is there another rule to explain this?
Im sorry. Cant read math notations. Does anyone has a similar practical example using some C# math library instead? Would help me as a gamedev more than this.
Thank you professor. I didn’t know how importan were the matrices in game development. You forgot to mention what software you used to make those amazing 2D and 3D graphics.
I can't hear êx or êy anymore after making this video.
Somewhere in the future, I'll probably make a part two which will discuss more advanced matrix operations e.g. determinant, inverse, ...
I know it’s been a year but this series is super helpful! Hopefully one day we will get a part 2.
Can you tell me what program do you use for your videos please?
This is some Khan Academy / 3blue1brown quality content right here. Amazing work. The visualizations are incredible.
Actually a Khan Academy and 3blue1brown combination
this is truly a goldmine, i love it so much
These videos are so helpful, they are amazing at describing these concepts! I'm so sad you aren't making them anymore.
This video is just perfect. Thank you very much for your effort to teach
I was pining for another entry into the series, can’t wait to watch this when I get home from work! Thanks for awesome content as always!
I'm sorry it took me so long. Thank you for always being so supportive!
FloatyMonkey always! It’s only a matter of time before these blow up, they are too good not too, this type of content is sorely missing in the indie community imo. Game dev maths from theory to practice is a void that definitely needs filled!
Exactly the video I was looking for, super useful stuff!
I had 100 doubts, and u sir reduced it to NONE
omg this might be the best explanation video for the rotation matrix... i wonder why it has so few likes...
Im clapping with my ears. You made me understand them so easily. Forever thankful, thank you so much mate. Insta subscribed, awesome content.
Excellent video! I love it. How did you make it?
Thanks! It's all made in PowerPoint, the morph transition does a lot of the heavy lifting.
I absolutely love your explanations!!!! This is just what I was looking for!!!!! How did you do the visuals?
Great video. Only have one question. If you first shear and then rotate, to project it into the first coordinate system, you first have to multiply with rotation matrix and then shear matrix. You did it reverse. Why?
Thank you. This was very illuminating.
9:25 Why is that? If we think about vector as a point it is ok. But if the vector is vector in 3d then it wil be scaled and not translated.
Lol only 200 views? I mean this is very special content but very well made. Thanks a lot.
Questions at 15:00 :
(1) Should those three rotation matrices also have the fourth columns and rows as the previously shown scaling and translation matrices have?
(2) I thought there was a matrix that could rotate around any arbitrary axis, is that not a thing?
1. They're not required but you could write them. In that case you add a row of zeros to the right and bottom but have to make sure the bottom-right element is a one. Essentially you 'paste' the 3x3 rotation matrix into a 4x4 identity matrix.
2. You get this matrix by multiplying the shown three primary rotation matrices. The result is still a 3x3 matrix but writing it symbolically with sines and cosines gets really long and would've been a mess to put in the video ;)
@@FloatyMonkey 2. Thanks for the reply!! So, then would those three component rotations actually be the projection of theta into the planes perpendicular to those axes? I was trying to multiply them out as you said, but then I realized that I didn't know if those were all the "same theta", and I found this insanity on wikipedia en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle and en.wikipedia.org/wiki/Transformation_matrix#Examples_in_3D_computer_graphics , I'm trying to figure out how this actually works so i can try to program higher dimensional rotations lol, it just keeps getting worse and worse hahaha
Yep, don't tell me about those rabbit holes ;) The formulas you found on Wikipedia are both the same and are used to rotate around an arbitrary axis (given by a unit vector). Another way to create arbitrary rotation matrices is by multiplying the 3 elementary ones from my video. In that case theta is different for each matrix. You basically construct a rotation matrix from Euler angles instead of an axis and an angle as in the Wikipedia articles. Hope this clears things up.
Does multiplying different translation matrixes work? Because they aren’t linear?
this video is really good, you cleared many of my questions
I'm still not sure how all of this will be applied to game deving tho, if anyone could give me an example I'd be very glad
Awesome Video. Which software do you use for the visuals and animations?
Amazing work! you saved me, Thanks a lot!
Super useful stuff. THANKS
Excellent video! But do these rotaion matrices has gimbal lock?
For translation matrix
what is the difference between t and v
Is this useful for programming games😇
When rotating, why does the green vector x coordinate is -1 * sin instead of sin? is it because it ended up in the negative side of x axis? Is there another rule to explain this?
Ya, I think that's the reason there's no other.
omg, u are my heaven today.
I have 0 experience with coding and this video opened my eyes to such a range of possibilities and optimiations THANKS
Which applications did you use to make the graphical contents?
It's all made in PowerPoint, the morph transition does a lot of the work.
Excuse me, why didn't you include matrix reflection?
My word! This is it!!
Great stuff
Im sorry. Cant read math notations. Does anyone has a similar practical example using some C# math library instead? Would help me as a gamedev more than this.
Thank you professor. I didn’t know how importan were the matrices in game development. You forgot to mention what software you used to make those amazing 2D and 3D graphics.
Please become a teacher u are good
My brain sucks.
♥
why no one explain visually transpose Matrix 😭
Me studing this in 8th grade😢
not everyone will come here for game dev.
Nope. I def have a linear algebra final in a few weeks
Your mouth asmr sound is irritating
And disturbing .
If you are willing to you should improve your audio setup qualities or change it.
Thankyou .
You already lost me at the hats, which you didnt bother much to explain. What is transformed, the coordinate system or the arrow? Gibberish
Bruh watch his vectors video. He mentioned that in the beginning.