Coding Challenge 181: Weighted Voronoi Stippling

Stippling is an artistic technique that uses numerous dots to craft an image. In this coding challenge I attempt to implement a weighted Voronoi stippling algorithm with p5.js along with the Delaunay triangulation package from d3.js. Code: thecodingtrain.com/challenges...
🚀 Watch this video ad-free on Nebula nebula.tv/videos/codingtrain-...
p5.js Web Editor Sketches:
🕹️ Weighted Voronoi Stippling: editor.p5js.org/codingtrain/s...
🕹️ Circumcircle: editor.p5js.org/codingtrain/s...
🕹️ Delaunay Triangulation: editor.p5js.org/codingtrain/s...
🕹️ Voronoi Diagram: editor.p5js.org/codingtrain/s...
🕹️ Voronoi Phyllotaxis: editor.p5js.org/codingtrain/s...
🕹️ Voronoi Diagram colored by area: editor.p5js.org/codingtrain/s...
🕹️ Lloyd's relaxation: editor.p5js.org/codingtrain/s...
🕹️ Weighted Stippling - Size and Color: editor.p5js.org/codingtrain/s...
🕹️ Weighted Stippling - Abstract Pattern: editor.p5js.org/codingtrain/s...
🕹️ Weighted Stippling - Video: editor.p5js.org/codingtrain/s...
🎥 Previous: • Coding Challenge 180: ...
🎥 All: • Coding Challenges
References:
🔗 d3-delaunay: d3js.org/d3-delaunay
🔗 Weighted Voronoi Stippling: www.cs.ubc.ca/labs/imager/tr/...
🔗 Sweep Line Algorithm: en.wikipedia.org/wiki/Sweep_l...
🔗 Lloyd's algorithm: en.wikipedia.org/wiki/Lloyd%2...
🔗 Polygons and meshes by Paul Bourke: paulbourke.net/geometry/polyg...
🎨 Pablo Jurado Ruiz: / pablojuradoruiz
🔗 Stippling: en.wikipedia.org/wiki/Stippling
🔗 Voronoi Diagram: en.wikipedia.org/wiki/Voronoi...
🔗 Delaunay Triangulation: en.wikipedia.org/wiki/Delauna...
🔗 Mike Bostock's Voronoi Stippling: observablehq.com/@mbostock/vo...
Videos:
🚂 Pixel Array: • 11.3: The Pixel Array ...
Related Coding Challenges:
🚂 C4 Worley Noise: • Coding Worley Noise
🚂 33 Poisson-disc Sampling: • Coding Challenge #33: ...
Timestamps:
0:00 Hello!
0:37 What is a Delaunay triangulation?
2:31 d3-delaunay package
2:49 Coding the delaunay triangulation.
6:38 What is a Voronoi diagram?
9:17 voronoi function on the delaunay object
10:25 Things you could try with the Voronoi diagram
10:56 Lloyd's "relaxation" algorithm
12:07 Calculate the average of a polygon's vertices
15:30 Calculate the area of a polygon
16:45 Calculate the proper centroid of a polygon
18:47 What is stippling?
19:45 Draw dots based on brightness value of pixel
21:50 Calculate a weighted centroid
24:51 Using delaunay.find()
27:52 Ideas for you to try!
28:47 Goodbye!
Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound
🚂 Website: thecodingtrain.com/
👾 Share Your Creation! thecodingtrain.com/guides/pas...
🚩 Suggest Topics: github.com/CodingTrain/Sugges...
💡 GitHub: github.com/CodingTrain
💬 Discord: thecodingtrain.com/discord
💖 Membership: kzread.infojoin
🛒 Store: standard.tv/codingtrain
🖋️ Twitter: / thecodingtrain
📸 Instagram: / the.coding.train
🎥 Coding Challenges: • Coding Challenges
🎥 Intro to Programming: • Start learning here!
🔗 p5.js: p5js.org
🔗 p5.js Web Editor: editor.p5js.org/
🔗 Processing: processing.org
📄 Code of Conduct: github.com/CodingTrain/Code-o...
This description was auto-generated. If you see a problem, please open an issue: github.com/CodingTrain/thecod...
#delaunaytriangulation #imagestippling #voronoi #sweepalgorithm #lloydsalgorithm #p5js #javascript

Пікірлер: 193

  • @TheFlimTV
    @TheFlimTV3 ай бұрын

    I love how this feels both like a University Lecture, and a kids educational channel!

  • @DanielMiclos
    @DanielMiclos3 ай бұрын

    I just wanted to drop by and express my heartfelt appreciation for the amazing content you've been sharing on your channel. Your videos are not only educational, but also a huge source of inspiration for me and many others in the coding community. The generosity with which you share your knowledge and passion for coding is truly commendable. Thank you for being such a fantastic resource and for all the hard work you put into making complex concepts accessible and fun. Keep up the incredible work!

  • @tiagdvideo

    @tiagdvideo

    3 ай бұрын

    100%!

  • @Haagimus

    @Haagimus

    3 ай бұрын

    Would like to second this as well Daniel for making both education and programming fun and at the same time. I've watched you for years and years and I have always enjoyed everything that you've made, especially the coding challenges. For a little while, I even replicated some of the coding challenges in Python using the p5 package for python. Keep up the great stuff and don't ever stop Sir!

  • @akardasis

    @akardasis

    3 ай бұрын

    I was going to say "This rules. You rule". But your's is more good words.

  • @xM0nsterFr3ak
    @xM0nsterFr3ak3 ай бұрын

    14:40 "This is lovely, but it's collapsing into an black hole..." That's a very funny quote 😂

  • @justind4615

    @justind4615

    3 ай бұрын

    it looks so organic there

  • @jaredgreen2363

    @jaredgreen2363

    3 ай бұрын

    Accidentally made a gravity simulator…

  • @vcvracarkad
    @vcvracarkad3 ай бұрын

    I'd love to see this done for each R G B channel individually. i think that would create a really cool comic book type of effect.

  • @nicolaswinck9562
    @nicolaswinck95623 ай бұрын

    how fascinating it was to see Gloria Pickle turning into Gloria pixels! you make it look so easy!

  • @radadadadee

    @radadadadee

    3 ай бұрын

    I program for a living and I couldn't agree more. He makes it looks so easy! But I know it's much more complicated, he's just so good at his job.

  • @orangejuice732
    @orangejuice7323 ай бұрын

    In college a was an undergraduate research assistant converting a 2d voronoi lattice simulation to 3d. 7 years later I think I finally have a grasp on what that simulation was actually meant to do because of this video so thank you.

  • @conorohagan9947
    @conorohagan99473 ай бұрын

    I love your enthusiasm and I really appreciate that you show your mistakes and laugh about them. Let's be honest, learning to program is boring. You make it really fun.

  • @sentinelaenow4576
    @sentinelaenow45763 ай бұрын

    The Coding Train is by far the most awesome educational and inspiring coding lessons there is. Thank you so much for sharing your coding adventures, you are the best. ♥

  • @HeadmostCantaloupe
    @HeadmostCantaloupe2 ай бұрын

    I love the new editing style Dan! Feels refreshing to see intros and the Apple ][ jingles being used in the beginning of the video!

  • @menaced.
    @menaced.3 ай бұрын

    This is basically just shader math, you should try doing a video about/using glsl or hlsl, theres some fun stuff you can do with them, maybe use shader toy? (Never used it bc Im a gamedev so use shaders in engine/in opengl)

  • @hamiltonianpathondodecahed5236
    @hamiltonianpathondodecahed52363 ай бұрын

    Every time you introduce some idea, I feel like, "yeah sure, I know the math, that's how that works, no way you can implement it in a single video", then you simply code it up. I am amazed.

  • @MyCodingDiarie
    @MyCodingDiarie3 ай бұрын

    You're doing a fantastic job. Don't ever stop creating!

  • @CocoaBeans660
    @CocoaBeans6603 ай бұрын

    This guy makes me so happy and is such an inspiration for KZread and coding in general. I love it

  • @barco10001
    @barco100013 ай бұрын

    In all my (few) but intense years of learning creative coding I have not had a greater source of learning and inspiration from your channel. Your ways of teaching and exploring deep and complex topics of creative coding are amazing, fun, and highly enjoyable. The coding community cannot thank you enough!

  • @dr_ned_flanders
    @dr_ned_flanders3 ай бұрын

    Wonderful video, Daniel. I love how each video is so visual and leads me to learn a new algorithm or mathematical technique as well as improving my coding.

  • @Rand00mThing
    @Rand00mThing3 ай бұрын

    Wow I admire your coding skills. I could not do what you keep doing. I don't have the passion to always throw myself into new coding problems. I will never forget you, "Coding Rainbow" 🙏

  • @mariovelez578
    @mariovelez5783 ай бұрын

    Can’t believe this guy taught me so many wonders of coding back in the day and he’s still going! Keep up the good work!

  • @TheMasonX23
    @TheMasonX233 ай бұрын

    As a former graphics programmer, I loved this! Also, your enthusiasm and positivity is infectious! Love it man, always happy to hop on board!

  • @RyanMcCoppin
    @RyanMcCoppinАй бұрын

    Dude, you are doing a great job. You are personally entertaining, you are providing problem solving techniques and the projects you are doing are very cool. I'm glad I found this channel.

  • @justind4615
    @justind46153 ай бұрын

    Im so excited! I saw your video on nebula tv but i didnt had any subscription so i couldnt watch i didnt think you would upload it this early

  • @rohitwesley
    @rohitwesley3 ай бұрын

    Hay i been braking my head on this algo for the last yr, was exploring how to go from delaney to nanite 😂 and went as mad as you have, 😅 the fact that u had a hard time, makes me not feel so dumb anymore, not to take anything away from you, love your stuff watch as many as i can, would love to see you experiment with shadertoy constraints and do some crazy stuff 😊

  • @Autopawn
    @Autopawn3 ай бұрын

    Thank you! Your work is inspiring 😄

  • @BillionPlusOne
    @BillionPlusOne3 ай бұрын

    This was super fun to watch, thanks so much!

  • @krepker
    @krepker3 ай бұрын

    Mindblowing His ability to pick some abstract concept and just use it to solve an real problem in minutes

  • @pattvira
    @pattvira3 ай бұрын

    I felt so relaxed watching this 😌with a nice touch of Dan's enthusiastic sounds every time he got the next thing to work. Jokes aside! Got lots of inspiration from this tutorial - thank you Dan!

  • @TheCodingTrain

    @TheCodingTrain

    3 ай бұрын

    Thank you Patt!

  • @69zwaan
    @69zwaan3 ай бұрын

    you have a great program of all time. 😊 I like to watch your own coding. nice.

  • @astropgn
    @astropgn3 ай бұрын

    This has been my favorite channel since I don`t know, 2017

  • @MarioTorre
    @MarioTorre3 ай бұрын

    Pretty good stuff. This seems a very useful method to correctly simulate film grain in a digital photo

  • @dgo4490
    @dgo44903 ай бұрын

    This algorithm is good for relaxing UV maps for unfolded meshes for artist texturing. The "raster dots" effect can easily be achieved by averaging the image into boxes of n by n pixels and drawing a circle scaled to the magnitude of the average value. Instead of scaled the dot can also be proportionally occluded by another offset dot masking it out, or a hole dot within the dot and whatnot...

  • @kasperchristensen8416
    @kasperchristensen84163 ай бұрын

    Thank you for another great video, Mr. Shiffman 😁👍

  • @gazzaka
    @gazzaka3 ай бұрын

    You are brilliant...loving the videos, thanks 🙂

  • @adamgliwa896
    @adamgliwa8963 ай бұрын

    Hard work, and good explanation. Very helpful! 👍

  • @givemeyourmoneynao
    @givemeyourmoneynao3 ай бұрын

    Cool video. I took a computational geometry algorithms class in college where we created voronoi diagrams using a beach line sweep algorithm in nlogn time. One of the more difficult classes I had, but a lot of cool problems too.

  • @JUNGELMAN2012
    @JUNGELMAN20122 ай бұрын

    Hands down....Black belt in coding. I love it.

  • @EkimElectro
    @EkimElectro3 ай бұрын

    Watched this. Gzzz my head did hurt. You do make it look easy.

  • @munzeralseed
    @munzeralseed3 ай бұрын

    Love it! It reminds me of a technique you used before, which is Floyd-Steinberg dithering. However, this one seems more challenging since you used an external library, but it sets a challenge to write the whole algorithm from scratch and optimize it, which I think I will attempt!

  • @TheCodingTrain

    @TheCodingTrain

    3 ай бұрын

    oh, please do! I would love to see it!!!

  • @SianaGearz

    @SianaGearz

    3 ай бұрын

    Floyd Steinberg performs error diffusion in some direction, whatever direction you're scanning towards, say towards bottom right, so if you apply it to a moving image, your start of scan is relatively stable say top left corner but your bottom right is very noisy. This isn't visible in static images, only moving. You could potentially start scanning out from the middle but that doesn't really solve the problem, it will still be obvious where the noise is eminating from. There's a more modern algorithm with a similar visual outcome to Floyd Steinberg but without bias in any direction, where you use a precomputed blue noise as a threshold function, and you can reuse the same across frames or use a spatiotemporal variant, and the way to compute this blue noise, the foundation is in this very video - Lloyd's Relaxation of a random point set. Blue noise sampling is the foundation of a lot of modern stochastic rendering methods in graphics. There's a whole research group at Nvidia concerned with blue noise.

  • @landsgevaer

    @landsgevaer

    3 ай бұрын

    You don't need voronoi for how it was eventually done. You could just determine the point that is closest to the pixel ... (That point's voronoi cell will contain the pixel.)

  • @a.lollipop

    @a.lollipop

    14 күн бұрын

    ​@@landsgevaer the voronoi diagram is necessary for getting the polygons whose centroid the points move to.

  • @landsgevaer

    @landsgevaer

    14 күн бұрын

    @@a.lollipop Like I said, you don't need it anymore the way it was eventually done. I gave the much simpler alternative above...

  • @gfabasic32
    @gfabasic323 ай бұрын

    Such a great series!

  • @soadsam
    @soadsam3 ай бұрын

    babe wake up! new coding train video just dropped!

  • @EXPLAIN_TO_YOURSELF
    @EXPLAIN_TO_YOURSELF3 ай бұрын

    Maybe I should leave a comment on each video you upload. Whenever I'm coding or facing a task, I play one of your challenge videos. They inspire and empower me to overcome the obstacles in my tasks.

  • @HomeofLawboy
    @HomeofLawboy3 ай бұрын

    14:43 God coding the fabric of spacetime

  • @riccardoronconi2146
    @riccardoronconi21463 ай бұрын

    Well. This was pretty amazing

  • @Hamomim1
    @Hamomim13 ай бұрын

    My brain hurt, but I was amazed by the beauty of mathematics and your explanation. I have been following it more or less for years. thanks

  • @paper_airplane
    @paper_airplane3 ай бұрын

    Just wanted to note that there are more sophisticated stippling algorithms, like the one based on power diagrams, which is a generalization of Voronoi diagrams (implementing it _is_ a coding challenge). See "Blue noise through optimal transport" paper for details. Besides, you check whether the center of each pixel is inside the Voronoi cell to calculate its mass center. Considering each pixel as a square and calculating the intersection area with each Voronoi cell will give a significant quality improvement for the Lloyd algorithm.

  • @Flackon
    @Flackon3 ай бұрын

    Back in the day I made a random map generator and the coastlines and elevation features were drawn via voronoi diagrams. I coded the main app in p5 but also imported d3 for the voronoi computations, so, yeah. No shame in that, lol.

  • @aeschynanthus_sp
    @aeschynanthus_sp3 ай бұрын

    The formula for the area of a polygon is the famous shoelace formula! Mathologer, among other people, has a nice video about it.

  • @randospawn7495
    @randospawn74953 ай бұрын

    I like dithering in art, it looks cool

  • @mrmb84
    @mrmb843 ай бұрын

    The black hole! 😯 Unexpected but so cool!

  • @ThugLifeModafocah
    @ThugLifeModafocah3 ай бұрын

    I understood the absolute number of ZERO things. Thank you.

  • @stabilini
    @stabilini3 ай бұрын

    Amazing content, thanks !

  • @Tomtekavler
    @Tomtekavler3 ай бұрын

    I can't and have never coded in my life but i still love your videos!

  • @SianaGearz

    @SianaGearz

    3 ай бұрын

    You can. Just start somewhere and one step at a time.

  • @archi_designer
    @archi_designer3 ай бұрын

    Very nice, with c# will be also useful

  • @anon_y_mousse
    @anon_y_mousse3 ай бұрын

    This does look like fun. I think I'll try it in C with RayLib, and use color. This might make for a really cool image viewer.

  • @vicentesoto1628
    @vicentesoto16283 ай бұрын

    geez xD this is high vibration content Loved it Is it maths, cs or stand up comedy though

  • @DarkoRomanov
    @DarkoRomanov3 ай бұрын

    The black holee is mesmerizing

  • @aleksander5127
    @aleksander51273 ай бұрын

    ​ I love your content. If you allow me, here is a suggestion. You could implement an algorithm to find the path to the goal on the Micro Mouse Race.

  • @xenedon1509
    @xenedon15093 ай бұрын

    well that was awesome

  • @Crazyclay78YT
    @Crazyclay78YT3 ай бұрын

    oh man ive been wanting to do this

  • @kuoyulu6714
    @kuoyulu67143 ай бұрын

    I have no idea whats going on but this is so cool 😃

  • @realcygnus
    @realcygnus3 ай бұрын

    Good one Dan !

  • @sachinsurya007
    @sachinsurya0073 ай бұрын

    You are Bob Ross of programming

  • @f_48irfanshaikh29
    @f_48irfanshaikh293 ай бұрын

    Cool as always

  • @DaleHawkins
    @DaleHawkins3 ай бұрын

    Thanks!

  • @StefanWolfrum
    @StefanWolfrum3 ай бұрын

    Wow, so cool!!! ❤

  • @IgneousGorilla
    @IgneousGorilla3 ай бұрын

    Amazing video!

  • @galzajc1257
    @galzajc12573 ай бұрын

    fun fact: we just had those in our first lecture of solid state physics this monday. i'm deffinitely tempted to make a 3D version of this, and make it efficiently, that seems like a fun geometric problem.

  • @nembobuldrini
    @nembobuldrini3 ай бұрын

    fascinating and relaxing

  • @knevari3952
    @knevari39523 ай бұрын

    You are the best !

  • @aquelaquelaquelaquel
    @aquelaquelaquelaquel3 ай бұрын

    Man.. I really love your videos although I don't code almost at all.. but damn i like how you integrate things that are pure abstractions for me into applicable real projects. You are a true professor.

  • @kevinrichter6503
    @kevinrichter65032 ай бұрын

    Small mistake on 9:07, where the last circumcircle of the right triangle should be. But overall, that was a fun and educational coding challenge! As always ;)

  • @clearwavepro100
    @clearwavepro1003 ай бұрын

    Excellent!! :)

  • @Jova
    @Jova3 ай бұрын

    Awesome!

  • @tyhuffman5447
    @tyhuffman54473 ай бұрын

    Stunning as always!

  • @TheCodingTrain

    @TheCodingTrain

    3 ай бұрын

    Thank you!

  • @programmieraufgaben8391
    @programmieraufgaben83913 ай бұрын

    thats cool!

  • @tiosam1426
    @tiosam14263 ай бұрын

    It's a translation of light and shadow with a circle radius variation.

  • @samable9585
    @samable95853 ай бұрын

    I like ,relax, followed by head scratching 😂😂

  • @HexaflexagonFan
    @HexaflexagonFan3 ай бұрын

    the point where you made the points relax based on the centre of gravity could (maybe) be used for liquid simulation

  • @PumpiPie
    @PumpiPie3 ай бұрын

    amazing :D

  • @flameofthephoenix8395
    @flameofthephoenix83953 ай бұрын

    While unrelated to this particular video, surely this comment section is as good as any! I was thinking about how it may be nice to see what you can do with exclusively bill-boarding in 3d graphics, there's of course traditional bill boarding, but you can also make other bill boarding rendering techniques, like for instance rendering 3d lines, this is where you position your image in-between the projected versions of two points then scale it up according to the distance between them and rotate it to fit between, this works really well for a similar cost to standard bill-boarding, you can also do something similar to traditional bill boarding but where you place the image at the incenter of the projected version of a 3d triangle and of course scale it to the size of the incenter too, though I haven't worked out how you could also try incorporating rotation into that to make it a little better. Regardless, I'm curious just how far you could go with just methods like these, I've already made some interesting things with it like a spider since spiders are mostly just lines anyway that could be made out of the 3d line rendering, similarly skeletons would be easy, but for anything beyond that you may need to get super artistic with both traditional and incenter bill boarding plus possibly making new rendering techniques.

  • @adrinoadrino6832
    @adrinoadrino68323 ай бұрын

    Reminded me of Origami and Crease Pattern

  • @landsgevaer
    @landsgevaer3 ай бұрын

    Instead of converting points to voronoi, and then figuring out which polygon a pixel is in, you could just determine which point is closest to the pixel... (The trick with remembering the previous pixel's index still works, or you could use a k-d Tree to make it efficient.)

  • @flameofthephoenix8395
    @flameofthephoenix83953 ай бұрын

    0:39 Yeah! I kind of am a little confused about that particular thing, currently what I've always thought them to be was when you take a bunch of points with a given radius, then starting with the highest radius and going down just render every circle, then bits closer to a point will be prioritized over ones further resulting in segments being created. But it was never really clear whether this was actually Voronoi or just another simpler method intended to replicate it.

  • @flameofthephoenix8395

    @flameofthephoenix8395

    3 ай бұрын

    8:29 Ah! So, it sounds like the method I learned actually is Voronoi and it's much more efficient for finding the areas than the method of having each pixel calculate their distance.

  • @yertzar775
    @yertzar7753 ай бұрын

    This is actually part of Solid state Physics formulation of the K-Space for electrons

  • @olli3686
    @olli36863 ай бұрын

    Wow! Last week, I wrote a kinetic voronoi algorithm which doesn't require any triangularization

  • @JaafarCherkaoui
    @JaafarCherkaoui3 ай бұрын

    Nice

  • @PeterHellmich
    @PeterHellmich3 ай бұрын

    Could be a beautiful effect to transform from the totally distributed dots to those of the image.

  • @munzeralseed

    @munzeralseed

    3 ай бұрын

    He already did it with the logo at 0:09 and it looks so cool!

  • @PeterHellmich

    @PeterHellmich

    3 ай бұрын

    Okay but how? Simply the reversed process?

  • @munzeralseed

    @munzeralseed

    3 ай бұрын

    Yes I think so

  • @ThankYouESM
    @ThankYouESM3 ай бұрын

    I accidentally created a far simpler solution which is what I call radius occupy (by brightness) whereas it does a scan starting from darkest colors, spacing_radius = 25-(r+g+b)//3//25 or break if less than 1, which it will pop out the var xy array points of the var dot_radius + spacing_radius. meaning the whatever color is within that circle which got popped out will not get scanned. Super simple.

  • @RedHair651
    @RedHair6513 ай бұрын

    I'm currently learning Apps Script for work as a Python person in private, and this video gave me violent flashbacks.

  • @martinsvanda5874
    @martinsvanda587428 күн бұрын

    oooooh man you are really crazy

  • @PaulMurrayCanberra
    @PaulMurrayCanberra3 ай бұрын

    @4:31 Other ways to convert an array of x/y into a flat array of pairwise numbers: const somePoints = [{x:1,y:2},{x:3,y:4},{x:5,y:6}]; const method2 = []; somePoints.forEach(p => { method2.push(p.x); method2.push(p.y); }); console.log(JSON.stringify(method2)); const method3 = somePoints.reduce((vec, p) => vec.concat([p.x, p.y]), []); console.log(JSON.stringify(method3)); .forEach is quite a bit better than writing for loops. .reduce is for functional programming weenies, although it is admittedly cool and tends to be compact.

  • @KeithKritselis
    @KeithKritselis3 ай бұрын

    “Let's put them into an array. And lerp the original points towards the centroid.” It seems weird that I understand that...

  • @kossboss
    @kossboss3 ай бұрын

    lol 😂 your the man. I too need to learn yield and generators better

  • @npexception
    @npexception3 ай бұрын

    This looks like a great way to create something that can be fed to a pen plotter. I imagine a giant stipple plot of a picture of my cat :D

  • @Sama_09
    @Sama_093 ай бұрын

    Now we need this in python

  • @undergraduate6050
    @undergraduate60503 ай бұрын

    It is used in that point me website.

  • @apppples
    @apppples3 ай бұрын

    I feel like maybe you could do this with spatial hashing. Like an oct tree, for each point we get its weight, and we find the nearest seed point at each iteration or something? idk. Sounds like something that'd be quite fast on gpu.

  • @pete_thompson
    @pete_thompson3 ай бұрын

    I hope one of you train enthusiasts can answer this - how did you know the delaunay portion of the d3 library was available from the cdn (with that particular url)? I looked on the d3 site and I couldn't find the option of linking to just portions of the d3 libraries without using import statements etc. I much prefer your method of just putting it as a source in index.html, but don't know how to find that it exists? Great video!

  • @user-zo1kn8ob7h
    @user-zo1kn8ob7h3 ай бұрын

    how did you and the paper fit under your pillow and did you use protection? twofish?

  • @flameofthephoenix8395
    @flameofthephoenix83953 ай бұрын

    Hm, I think the fact that you've once again reverted back to averages instead of properly finding the centroid but weighted, the black hole problem is likely still back at least to an extent. If your image was either consistent brightness or a brightness according to the distance from some vector, then the points would likely all collapse into the same place.

  • @flameofthephoenix8395

    @flameofthephoenix8395

    3 ай бұрын

    Hm, after some thought, here's a potential way to weight the centroid towards certain values, first you compute the normal centroid, then you interpolate each Vertice from itself to the centroid based on its weighting then you recompute the centroid with the new vertices to get the weighted version. I don't know if this is the best method of doing it, but it's worth a shot!

  • 3 ай бұрын

    Would it be possible to use both diagrams and other algorithms shown in this video to let's say, triangulate a person's unknown position? I'm no spy nor stalker of any sort, just remembered I was addicted to tv series called Numbers which used Math to solve crimes (of course in Hollywood style, but you get the point). My idea here is how Math can be used to almost anything in life, rather than drawing (which is awesome too).

  • @geoffwagner4935
    @geoffwagner49353 ай бұрын

    Who ever decided on "ducks" at Columbia Collage was a genius, you'd have to be to pick an animal that just says quack all day long as they walk up and down the sidewalk.