I laughed out loud when you said "I wish I had a kitten. Pet the kitten". Never have I been so entertained and educated at the same time. Been watching your videos for a while now. There are so many! I want to thank you so very much for them. They are helping a lot not only with web development (for visual effects), but also game development, and just generally becoming a more well rounded person. THANK YOU!

Sir this is amazing, I studied about 75% of ur videos topic but for the fact I loved the way you explained I just watched the whole video (Clear!) THANK YOU♤♡

Thanks for the great videos. It's rare to see someone actually explains the logic and process behind the code. Can't tell you enough how much I appreciate your videos. Keep it up!

I learned vectors and trigonometric functions again 12 years after graduating from high school to understand your lecture. Thanks for the good class!

You explained very clearly how to calc the dot product, but I didn't feel like I really "got it" until I came across this: "The dot product tells you what amount of one vector goes in the direction of another." It makes more intuitive sense when explained like that. You might've made that clear, but I missed it. In any case, maybe it will help someone!

bruh your grasp of this topic must be so fundemental to you b/c you explained this so fucking well. Cheers brother you helped a struggling physics student.

ooohhh maaan i just realized, this is the weatherman technique!! i swear for some reason it super helps to have an educator physically pointing at the computer, body language is very valuable, nice one dan :-)

You should have a million views. Perfect videos, really well done!

Ah, it was such an interesting, informative, and cozy lecture. I like it :)

God, I love you Dan, thanks for all the tutorials

Angle of a vector is also atan2(vy, vx); which is useful because we generally want to avoid sqrts in our gaming code

This explanations were super clear. Thank you!

Just excellent explanation! Great video

Great explanation. Really enjoyed it.

So well explained and super funny, thank you so much for this video!!!

3:39 Beads, flowers, freedom, happiness 🎉

Holy cow, sir, thanks !!!!

I love your channel

Thanks very useful :)

All your videos are first rate. Thank you so much for making them. I have one questions. How can I use the dot product to determine whether the angle relative to my current vector is negative or positive with respect to the vector I'm comparing it with? Thanks again.

I just sold my soul to obtain those.

Thanks for sharing your knowledge and high content quality videos, sir! I still have one question regarding the vector dot product. I'm trying to perform an orthogonal projection for two points S1 and S2 into an estimated line with the model Ax + By + C = 0. This line was estimated by the least-square method considering a set of points whose start and end points are the points that I want to project to the line (S1 and S2). My approach was to get two points P1 and P2 that lie on the line by providing the x coordinates of the start and end points to the model equation in order to predict the corresponding y coordinates. Then, I computed the vector from P1 to P2 which has the same direction as the line. I normalized the obtained vector to get its unit vector. Moreover, I computed the vectors from P1 to S1 and P1 to S2. Finally, I performed the projections: ProjP1 = (vector P1-S1 dot product unit vector) * unit vector + P1 and ProjP2 = (vector P1-S2 dot product unit vector) * unit vector + P1. However, I am not obtaining orthogonal projections. Do you have any idea how to correctly perform an orthogonal projection for a point into an estimated line with the model Ax + By + C = 0??

Brilliant presentation. Could you please help me with the code for 3D flow field. Thank you

I wish my math teacher teach me like this.

brilliant

Awesome

Why are you still multiplying with b at the end? Isn't A.dot(B) enough if B is normalized?

ok thanks

I would like you to rename this video, or add the sentence "Scaler Projection Explained" :) I have been looking for an explanation for it.

Does this code also works for 3d vectors? Or how can I calculate the scalar projection for 3d vectors?

This video is a brilliant explanation but the code visible at 7:10 doesn't seem to work, and the code linked on github just uses angleBetween(). I think that vector a and b need to be normalised before using the formula to calculate the angle, otherwise d/(a.mag() * b.mag) produces a number greater than 1... so the acos function then produces NaN.

If we could just clone Daniel and fill up our schools with Daniels for every lesson the future would be very bright indeed.

after watching the latter part of the video for the 25th time about projections I also wish I had a kitten.

Hello legend

"You know, I am just locked in a room... with lights... and Processing, [so what else am I supposed to do...?]" Aren't we all? 😂

another great video dan , useful sketch thanks now i have to ask, what determines how the vectors are setup in github.com/shiffman/The-Nature-of-Code-Examples/tree/master/chp06_agents/FlowfieldImage in there you have 3 photos which give diff outcomes, how and why dan? further more i imported my own pic just to test something out and i got diff vectors then all others so what is it that tells vector how and or where to setup shop? more specifically how do i get the vectors to follow this road but not that road? how do i tell vectors to change their magnitud of speed if a condition is met? i see in you face.jpg in the data folder that the vectors are following the face profile pretty good but this is the only photo that vectors line up so neat following that contour that makes up the face , pretty cool dan

This may blow your mind but p5.js etc isn't the only JS thing out there

learn how to make a number 2

You represent everything I despise about maths teachers. Self indulgent show offs, all speeded up, with no regard for the alumni. Calm down, tone down you ego, stop giggling and do keep sharing your knowledge. Thanks