Linear Algebra for Computer Scientists. 14. 3D Transformation Matrices

Most real time animated computer games are based on 3 dimensional models composed of thousands of tiny primitive shapes such as triangles, and each vertex in a model is encoded as a vector. In this computer science video you will learn how matrices are used to transform these vectors in three dimensional space. You will meet some new types of transformation matrix, the translation matrix, the scaling matrix and three variations of the rotation matrix. You will learn how a single transformation matrix can be composed from several transformation matrices by calculating their dot product, to create a single transformation matrix that encodes multiple 3D transformations at once.

Chapters:
00:00 Recap 2D computer models
00:54 2D Transformation Matrices
01:53 Apply a 2D Transformation Matrix to a 2D Vector
02:22 Transformations in Three Dimensions
03:12 3D Transformation Matrices
05:34 Apply a 3D Transformation Matrix to a 3D Vector
07:12 Composing 3D Transformation Matrices
07:53 Transform a 3D Model
08:13 Local and Global Coordinate Systems in a 3D world

[alaanasser]

Oh man... tears of joy because of this joyful of an explanation... Despite reading books on application of LA, nothing comes close to this visual explanation....Love from Syria brother

[blanchsb]

I am actually trying to wrap my head around matrix math in blender while writing some python scripts and I found out you are using blender to explain matrix math! I watched the entire series just so I could understand this last video best and I am really glad I did. You built on the topics really well. Thank you.

[bluewillowjiankaameilu]

I wish u are my university faculty. I've never seen such explanation and the importance of it for CSE students.
Thank you so much respected sir.

[thenixboy]

I watched the whole series in a blink, which is unsual given I get bored quite fast, but I learned every bit of this very series and feel I should go through it a couple more times and take notes. Great content.

[informatiker]

Best video about 3D transformation ever!! Thanks!

[glowstonedust]

Yo this guys sick if you wanna learn matrix applications watch this video its too easy to understand

[hobart]

Fantastic series, unbelievably well explained. Thanks for all your effort.

[SKHooligan]

So clearly explained. Thank you for this.

[colonelfreelance]

Well That was cristal clear !! Thank you sooo much !!!

[fadlialim]

Amazing explanation! A question: What do you use for your animations?

[amblypygi]

You're doing god's work, thank you!

[pictzone]

Thank you so much for this mind-blowing video! Although you made it quite clear how most computer graphics are rendered on the fundamental level, I'm wondering how distorsion effects work in the same context. Because those don't seem as simple as doing some holistic operations on the entire plane. You're basically affecting a local group of vectors that kind of propogate (dictated by some kind of algorithm) a certain way and distance to nearby vectors, depending how far it's pre-programmed to propagate.

How come these kind of effects don't violate the uniformity of linear transformations that are usually applied?
Because they certainly can't be linear anymore if they apply only a limited amount of space.

[stephenhemingway]

Have you finished the series or will you be continuing with more LA videos? They're really good.

[cohenbore]

Mega thanks...wat abt other transformations sheer, reflection..

[febifebriansyah]

could you explain about homogeneus coordinat system?

[anudarienkhbayar]

What's program do you use for 3d?

[prometheusli]

so why i need the fourth row? i just delete it, anyhow the fourth result is always one, i just type fourth param & result equal one

[super_jo_nathan]

What's going on with all the reuploads?