Quick Understanding of Homogeneous Coordinates for Computer Graphics

Graphics programming has this intriguing concept of 4D vectors used to represent 3D objects, how indispensable could it be so that every 3D graphics API force it on its users ?

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[guilhermecampos]

After seeing many videos here on YouTube, I finally understood Homogeneous Coordinates and Projection Matrix thanks to you

[boggybolt]

Came in thinking I'd get an explanation on why we have 3D and 4D vectors (already knew), instead got an explanation on how the math behind 3D rendering works (did not know). Amazing!

[Tsura]

This summarized in 7 minutes what my prof couldn't teach me in 3 days... amazing job!

[thygrrr]

This is a really good explainer that connects some bridges that after 25 years with OpenGL coding I still hadn't built an intuition for.

[Nallu_Swami]

DUDDDEEEE you have no idea how much the video has helped me out to think of multiplications visually, THANKS A LOT

[teharchon]

Hands down, that was the best explanation for this I've ever seen.

[naishalsuvagiya]

Good animation plus explanation, 👊
Keep it up you will surely make great in future😊

[williamwang]

this is the only video for your channel




and it's awsome

[HartleySan]

I think this is the video that finally made all of this click. Thank you so much!

[-AALIYAH]

Purely directional vectors (homogeneous coordinates with w = 0) can also be used to represent points at infinity. This is useful for simplifying intersection computations - the intersection of e.g. two parallel lines is a point at infinity, not "no point". If you really want to go nuts, you can extend the coordinate system to lines and planes (which also get easy intersections and even unions, e.g. find the line passing through two given points), and introduce rigid transformations (quaternions and dual quaternions), which have nice properties for rigid body physics and skeletal animation. The result is called projective geometric algebra, which provides a unified representation and a simple set of operations for all of these objects. Quaternions are not actually magical!

[alonsorobots]

This is so high quality for being your only video uploaded!!! More please!!!

[CoconutKhajiit]

Dude, this video was very clear, while also having all the mathematical details, brilliant!
Make more!

[orphansock]

Wow! What an absolutely outstanding video! This by far the best explanation I've ever come across.

[theman]

Now I understand why the heck they all multiply x and y by w!!

Thank

[Byrns]

Best and most concise explanation I’ve seen yet 🙏

[jahbini]

You explained this topic much better than Jim Blinn

[donnyjoe]

Awesome explanation! Thank you for the effort!

[DahVeeDeeOh]

Thank you so much. I was not making headway understanding homogeneous coordinates either by my professor's lecture or readings. Everything is clear after watching this video.

[dn]

Great video! I’d love to learn more from you. I hope you end up making more videos.

[gianlucanordio]

Crazy quality and explaination for a video of a channel with 497 subscribers (well 498 now). Good job :D