[VEX for Algorithmic Design] E13 _ Trigonometry 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 13th episode, I'm explaining the basics of trigonometry, aiming to explain how you can practically use it for algorithmic design / computational geometry by understanding the basic logic.
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 trigonometry?
00:03:01 Angle / Degrees and Radians
00:07:02 Angle Conversion Functions
00:13:22 Calculate PI
00:19:14 Sine, Cosine, Tangent
00:31:14 Visualize Trigonometry
00:49:15 Exercise - Draw Circle
00:56:20 Exercise - Circular Animation
01:02:04 Exercise - Draw Wave
01:16:37 Exercise - Wave Animation
01:21:18 Range of Sine and Cosine
01:27:07 Exercise - Scaling Animation
01:33:11 Secant, Cosecant, Cotangent
01:40:34 Inverse Trigonometry (to get angle)
01:59:17 Exercise - Angle between two 3D vectors
02:23:31 Draw arc between vectors
02:44:27 Next Topic - Quaternion
[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

[@Toguro07]

One of the best Houdini series which combine art and technicality

[@sherifmedhat8625]

At the final excersie - i didnt really understand why did we have to normalize the x,y and z Axises to get the result of the arc point positions correctly !? shouldnt the normalize function affect the positions of these points making them shorter or longer than the actual endings of these vectors that I'm trying to create an arc between them ? Edit : I figured that the only vector that needs normalizing was the z axis vector - which was calculated from the cross product of the dir1 and dir2 vectors. This will ensure that the arc doesnt offset slightly inwards from its end point. Not normalizing any other vector would still draw the arc correctly.

[@FaitelTech]

Find an angle and draw an arc between two vectors, those examples are extremely useful. Thank you.

[@axendroo2541]

2:03:04 this moment is soo funny , when houdini crashes. Great tutorial btw, really helpful🙇‍♂

[@rgptr]

Amazing series! Such great content! Your effort is tremendous and amazing too!

[@AncienRegimeStudios]

Tough to slog through but well worth the trouble. Impressive demo/lecture. Thx.

[@m_erdem]

Awesome tutorial as always, thank you.

[@DirkKool]

Like giving the best houdini tutorials isnt enough! he is making lofi beats meanwhile.

[@CallOfMuffi]

Excellent episode as always ! :D Will you make an episode on Matrices in the same series ?

[@graphic-nations]

Thank you for sharing

[@bando-od7yt]

Thanks so much for this maths stuff. You are a god.

[@bando-od7yt]

Can you please make a buymeacoffee.com page so I can support you . Can't support through patreon because I only have a debit card.

[@peterkgeorge8559]

thank u. i completed all the 12 episodes

[@delaskarvfx]

Amazing!!!

[@MadiMisaki]

I love how Pythagoras theorem is everywhere.

[@crcrossraider4162]

Great (super) lesson

[@nobunaga8514]

You are the best!

[@kitma5747]

Thank you very much.

[@nalalarra2230]

Hi, first of all I want to tell you that I love your work and I can't thank you enough for sharing your knowledge with everyone! I've been following the VEX series and I found a doubt in chapter 13. In the last exercise, where you draw an arc between two vectors . When you calculate the virtual axes (2:40:35), why do you multiply the angle cosine by the virtual axis vector ? You would not have to multiply it only by its coordinate? xaxis.x * cos(ang) and yaxis.y * sin(angle), as you did in the exercise of calculating the angle between those two vectors. Sorry for the inconvenience, a greeting!

[@dissonantprotean5495]

Thank you for this tutorial. It's mostly clear, however I don't really understand why you would have to normalize certain vectors e.g. for the cross products and virtual axis

[@sherifmedhat8625]

For the virtual axis example : the dot product formula is mathematically calculated as length of vector 1 x cos of angle x length of vector 2. In this example, we chose vector 2 as the virtual axis, and only one part of this equation gets us the length of the base axis that we want ( meaning we only want length of vector 1 * cos angle only). Therefore, we normalize vector 2 so that we make it equal to 1 and not affect the formula and the result that we are seeking.

[@ViralKiller]

1:31:00 I have just one suggestion... float val = sin($PI * 2 * (@Frame / $FEND)); ^^this should really just be a detail attribute, and then u can use a separate point wrangle to read the f@val value to move the points, otherwise you are re-computing val (which only needs to be computed once), on every single point, when it is in a point wranglw

[@bekabaratashvili3178]

Hey Junichiro, Really great course!!! I like your method for finding angle between Two 3d vectors, but just for interesting, why don't you use that formula? angle=arcos(dot(a,b)/(|a||b|)) The last part - draw arc between vectors was fantastic!

[@bass_journey]

Hello Junichiro, I hope you can see this question. I am following along your course and I in here, for example, 1:23:25 you say C becomes -A. I understand that A cannot be negative, as is the length of the circle, but C = -A or B = -A in other instances is it an arbitrary rule? I don't understand where this move comes from. Many Thanks

[@milosgalovic5583]

"wavenum" from draw wave part is not actually frequency, should be noted

[@sams_3d_stuff]

Master

[@simonepeluffo3742]

I have a grasshopper background, so I love Houdini for animation, but your apporch is exactly what I was looking for, thanks.