[VEX for Algorithmic Design] E12 _ Vector Basics

This is a new series I've started explaining the basics of VEX for algorithmic design / procedural modeling which I'm using on daily basis.
In this 12th episode, I'm explaining the basics of a vector to get used to the most used vector operations with several small exercises.
I've also started a Patreon, it would be great if I could get your support to continue creating tutorial contents.
00:00:00 Intro / What is vector?
00:06:46 Vector addition
00:15:37 Vector subtraction
00:17:54 Exercise 1
00:30:06 Exercise 2
00:39:02 Exercise 3
00:48:02 Vector multiplication
00:51:50 Vector division
00:54:07 Exercise 4
01:02:32 Normalization and magnitude
01:08:27 Exercise 5
01:13:46 Dot product
01:27:32 Exercise 6
01:37:34 Cross product
01:45:33 Exercise 7
01:53:13 Next topic - Trigonometry
[Project Data Downloads]
github.com/jhorikawa/VEXForAl...
[Patreon page]
/ junichirohorikawa
[Episodes]
Episode 1 - Attribute Basics: • [VEX for Algorithmic D...
Episode 2 - Group Basics: • [VEX for Algorithmic D...
Episode 3 - Parameter Basics: • [VEX for Algorithmic D...
Episode 4 - Variables and Operations: • [VEX for Algorithmic D...
Episode 5 - Array: • [VEX for Algorithmic D...
Episode 6 - Strings: • [VEX for Algorithmic D...
Episode 7 - Loop: • [VEX for Algorithmic D...
Episode 8 - Conditional: • [VEX for Algorithmic D...
Episode 9 - Function: • [VEX for Algorithmic D...
Episode 10 - Volume Basics: • [VEX for Algorithmic D...
Episode 11 - Dictionary Basics: • [VEX for Algorithmic D...
Episode 12 - Vector Basics: • [VEX for Algorithmic D...
Episode 13 - Trigonometry Basics: • [VEX for Algorithmic D...
Episode 14 - Quaternion Basics: • [VEX for Algorithmic D...
Episode 15 - Matrix Basics 1: • [VEX for Algorithmic D...
Episode 16 - Geometry Functions: • [VEX for Algorithmic D...
Episode 17 - Intrinsic Attribute: • [VEX for Algorithmic D...
Episode 18 - Randomness Basics: • [VEX for Algorithmic D...
Episode 19 - Noise Basics: • [VEX for Algorithmic D...
Episode 20 - Solver Basics: • [VEX for Algorithmic D...
Episode 21 - Half-Edge Basics: • [VEX for Algorithmic D...
Episode 22 - Remapping Basics: • [VEX for Algorithmic D...
Episode 23 - SDF Basics: • [VEX for Algorithmic D...
Episode 24 - Force Basics: • [VEX for Algorithmic D...
Episode 25 - Force Extended: • [VEX for Algorithmic D...
Episode 26 - Recursion Basics: • [VEX for Algorithmic D...
[Houdini Related Playlists]
VEX for Algorithmic Design: • VEX for Algorithmic De...
Houdini Tutorial: • Houdini Tutorials
Houdini Algorithmic Live: • Houdini Algorithmic Live
Houdini Snippets: • Houdini Snippets
Houdini Tips: • Playlist
[Portal Page]
Facebook Page: / parametricproceduralho...
[Books]
Algorithmic Design Workbook with Houdini: gum.co/GOZFw
Tiling Pattern with Houdini: gumroad.com/l/OVDgY
Algorithmic Design with Houdini: www.bnn.co.jp/books/9788/
Books on BOOTH: orangejellies.booth.pm/
[Contact]
Twitter: / jhorikawa_err

[@captainjacksparrow947]

if not for you we would have to enroll in some university or take a really expensive course (which most of us can't afford) and still would be left questioning our choices. Thanks, Juni for helping us out. You are a great teacher and an amazing person.

[@KZLR]

You're doing a public service with these. Thank you.

[@abdullaharshak.n7870]

Man you are genius. When ever I watch houdini tutorials on online. They said like if you subtract this vector to that vector you get this output.but they will not explain the core concept behind that how it’s actually works. Now it make more sense.

[@tacoma87x]

Really enjoying these videos! Keep em coming!

[@tradstown]

Very cool knowledge. Thank you so much for explanations!

[@emilmelikov8620]

Thank you for unlocking the mysteries of Houdini math which were previously unaccessible for the ones like me. The format you are teaching is really efficient for the non-math persons. Besides Houdini, it helped me to understand the math itself which I couldn't love (and study) at school, because I didin't then understand where to apply it. Now your theory+practice format helps to understant and immediately apply the gained knowledge making it memorable forever.

[@xanonymous3468]

its easy to understand the knowledge in your class. thank you very much!

[@josefh8782]

This is the best explanation of vectors in Houdini I have come across. FYI, I think you can achieve that same orientation in the last segment by just adding @up = {0,1,0}; to a wrangle, rather than having to use cross product etc.

[@ajithmartin7125]

Really helpful tutorial series, Thanks bro.

[@vladlearns]

That's a solid like, as always. Thank you.

[@sherifmedhat8625]

Amazing series ! these tutorials helped me so much in my career as a 3d artist / unreal game developer.

[@ThermostatB]

Thanks a lot for your tutorials, you are awesome!

[@sumonecalledalex]

These videos are so good. Thankyou.

[@MDA_01]

Thank you Junichiro!

[@bbsoft546]

Hey Junichiro, this one is one of the coolest as always, i wonder if you have tutorial about Dihedral function? because i could not find it in your tutorials.

[@znbk5652]

I would appreciate if you can do full explanatory for matrices and quatrinion in vex it would be a very useful resource for many...

[@peretiatko]

So good, thank you

[@pixelfound]

This is gem :')

[@TheElrachyd]

really nice, thank you

[@phatbuihong4014]

Thank you so much.

[@graphic-nations]

Amazing thank you keep going

[@SK-hj1xh]

Thank you.

[@lst8076]

Thank You

[@jimjimjim5995]

Thanks, btw i think that vectors should be normalized in order to calculate correct dot product

[@MElsadig]

thank you

[@AncienRegimeStudios]

Exercise 1 was fun.

[@rahulbisht396]

This is a gold

[@jisankim948]

Oh, my Teacher!

[@travislrogers]

Hi Junichiro, thank you so much for sharing all this wisdom. I have a question. When I replicate your addition example in H19 my red v3 vector points in the opposite direction and only looks like your example if I invert it (v@v3 = -v3;). Do you know if something changed in how Houdini calculates these directions in H19 or maybe I'm missing something? Thanks!

[@travislrogers]

Haha, sorry, user error! I accidentally set the visualizer for the v3 vector to be a Vector Trail and the other 2 as Vectors 🤦‍♂️

[@HoudiniVFX]

Спасибо за уроки! Аригато!

[@toxicityspb26]

Спасибо! どうもありがとうございます

[@sams_3d_stuff]

Dear Mr. Horikawa, at 1:15:13 you said "the projected length is the dot product" where I think it should be , the dot product is the projected length * the length of the vector projected onto (vector A in this case). so the dot product is : A.B = fA, not f only. Here A and B are 1, so it doesn't matter, but when I scale any of the vectors the dot product isn't only f anymore. I might be wrong, I saw a 3blue1brown video and he said that. Here kzbin.infoUgkx3rL3_AYotoJJaNAfoSPBMQ3KWtHPuC6A Love your videos, thank you!

[@josefh8782]

For those new to the concept of vectors, this is the perfect video to watch before jumping into this: kzbin.info/www/bejne/nH_OkK2wlrKiidU

[@ViralKiller]

It's confusing as a vector can be simply a position coordinate like vector = {0,0,0}, but this is not a traditional vector with an origin point and direction and length....so what we call a vector is actually 2 houdini point vectors, and the direction and distance is calculated from their positions...

[@babajaiy8246]

"It's confusing as a vector can be simply a position coordinate like vector = {0,0,0}, but this is not a traditional vector with an origin point and direction and length....so what we call a vector is actually 2 houdini point vectors, and the direction and distance is calculated from their positions..." You are confusing yourself. "so what we call a vector is actually 2 houdini point vectors, " That's only required to actually plot the vector where we want it; Otherwise the single value of the vector, e.g. {x,y,z} is still inherently there(within those two plotted points) and can still be used as that inherent vector UNCHANGED even if that inherent vector is plotted elsewhere with two different 'houdini point vectors'. It's no different that using graph paper when doing your high school math. Where ever you plot that same vector (same direction and same magnitude) on the graph paper, it will still have a co-ordinate for its 'head' and 'tail' in addition to its inherent magnitude and direction. You use a poor example of {0,0,0} because not even considering Houdini, such a vector is a special vector(exception) called a zero point vector - having no direction and no magnitude.

[@ViralKiller]

@@babajaiy8246 ok so basically my mental model is flawed in the fact that, I am trying to create an origin point for the vector when in fact one is not needed and the vector can be transposed anywhere

[@josefh8782]

Yeah I think it's fair to be confused. The term vector gets used in a few different contexts in Houdini, even though the data itself is the same - it just depends what we want from those numbers. In the case of @P, we are generally just using these three numbers as coordinates. We don't usually desire a magnitude or direction in this instance. But should we wish to visualise them and use them for something, they are there as they are inherently the calculation between the coordinate of the point and it's position from the origin (0,0,0). In the case of say, velocity, we would care about this. If you create a point that is not at {0,0,0}, add a vector as an attribute for this point, and then visualise this vector, you will notice that the line will draw to the point rather than {0,0,0}. However its direction and magnitude is calculated as though the point was at {0,0,0}. Once you move your point away from {0,0,0}, you'll notice that the direction and magnitude of the vector doesn't change, it merely gets translated around with following the point.

[@MDA_01]

@BabaJaiy You might find it helpful to view the video @Josef H posted above - which has a good explanation of the multiple perspectives from which vectors can be considered. '...It all depends on the direction that you look at them from' Jk : )

[@ViralKiller]

@@josefh8782 OK so most of the time @P, say {3,4,5} is actually {3,4,5} - {0,0,0} from the origin, it does indeed have a direction, you could tell it to keep going in that direction...The bit that confused me was, I forgot about the origin so assumed it was just 1 set of values when there are indeed two arrays to provide direction