The Dot Product - A Visual Explanation

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Clipped from the super long shaders for beginners stream of two days ago!

Note that this is for two normalized vectors, it's a bit different if only one or none of them are normalized. Regardless - the case of two normalized vectors is very common in shaders!

For example, Lambert shading is the dot product of the light direction and the surface normal

Full video will be up soon!

[xniyana]

This video is literally that meme where "the random youtuber with a small channel has the exact answer to your problem"....Even the bigger channels didn't explain the concept behind dot products so simply. Love this!

[mittensandsnowdrop]

You wouldn't believe how helpful your videos have been for me. Studying games programming and I have a maths module. Your videos have totally saved my life! Thank you so much.

[IMTechnicalAnimation]

Thank you SO much! I only found a lot of mathematical explanations. This little drawing explaining that it's just one vector projected onto another, was all I was looking for.

[luisdfernandez]

In just over a minute you explained to where it finally made sense. Nice!!

[loot]

Far and away the best explanation I've come across. People normally try to make it sound complex but it's not.

[bigevilcorporation]

"Ugh this is doing my head in, I hope there's some Freya-like explanation on YouTu--" AND THERE IT IS

[JaimeBeilis]

you’re amongst my favorite persons now. Great explanation <3

[rustemagayev]

As someone with chronic migraine, which makes thinking about and understanding complicated concept really hard, your explanations are a blessing.

[izvarzone]

most important, not forget normalize both vectors before sending them to dot product, just in case. I had bad results when not normalized, scratched my head before realize why that happened.

[ninthjake]

Really good explanation. Even a simpleton like myself understood it :)

[remon]

this is so cool and useful Freya! I have been working with shaders for a long time but the bigger my mental library gets the more I need to study in order to keep my knowledge. Videos like these are super helpful for this.

[brigsqpr]

TYSM for the video! literally could not find another answer to my question of what the dot product is "saying" and you had it in literally the first 5 seconds.

[jackleu]

The explanation has to be qualified as it is correct iff the first vector is a unit vector. Or, the dot product would be the projected distance x the length of first vector. Actually, it would be nice to start with a unit vector, then generalize into non-unit vectors. Overall, this is a concise explanation.

[Lpoker]

This is a really interesting way to conceptually understand the dot product, thanks!

[lemetamax]

This actually makes perfect sense! Now i perfectly understand how dot products work in my code

[yurkkon]

made my day. happy to find your channel

[arcadiaplanatia]

This is actually such a good video. I've been struggling so long to understand this thank you so much!!

[randomaccount]

Finally someone explaining what the dot product even is instead of just jumping into how it is calculated.

[jasoniswrongabouteverythin]

man, whenever im trying to understand some game dev math stuff i really should come to this channel first

[Ofenkatze]

I wish I could tick a "love" emoji instead of just like. Most concise explanation I've found so far.