Coding Challenge #130.1: Drawing with Fourier Transform and Epicycles

Daniel Shiffman implements the Discrete Fourier Transform in JavaScript using p5.js to render user-drawn paths with epicycles.

In this coding challenge, I implement the Discrete Fourier Transform algorithm in JavaScript and render a drawing using epicycles derived from the transform. Code: thecodingtrain.com/challenges/130-drawing-with-fourier-trans… p5.js Web Editor Sketches: 🕹️ Fourier Transform: editor.p5js.org/codingtrain/sketches/RfrZibjfL 🕹️ Fourier Transform - user-drawn path: editor.p5js.org/codingtrain/sketches/jawHqwfda 🕹️ Fourier Transform - complex numbers: editor.p5js.org/codingtrain/sketches/ldBlISrsQ 🕹️ Fourier Transform - user-drawn path with complex numbers: editor.p5js.org/codingtrain/sketches/sPvZsg2w4 Other Parts of this Challenge: 📺 Part 2: youtu.be/n9nfTxp_APM 📺 Part 3: youtu.be/7_vKzcgpfvU 🎥 Previous video: youtu.be/X8bXDKqMsXE?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH 🎥 Next video: youtu.be/0j86zuqqTlQ?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH 🎥 All videos: youtube.com/playlist?list=PLRqwX-V7Uu6ZiZxtDDRCi6uhfTH4FilpH References: 🚂 Coding Train Logo: twitter.com/TomFevrier/status/1079437780466520065 💾 p5.FFT: p5js.org/reference/#/p5.FFT 💾 FFT on Algorithm Archive: algorithm-archive.org/contents/cooley_tukey/cooley_tukey.htm… 🗄 Discrete Fourier transform on Wikipedia: en.wikipedia.org/wiki/Discrete_Fourier_transform 🗄 Complex Number on Wikipedia: en.wikipedia.org/wiki/Complex_number Videos: 🎥 But what is the Fourier Transform? A visual introduction: youtu.be/spUNpyF58BY 🎥 Fourier Analysis For The Rest Of Us: youtu.be/2hfoX51f6sg 🎥 Epicycles, complex Fourier series and Homer Simpson's orbit: youtu.be/qS4H6PEcCCA 🔴 Code Train Live 165: youtu.be/0b3R8oWffkw?t=2657s Related Coding Challenges: 🚂 #125 Fourier Series: youtu.be/Mm2eYfj0SgA Timestamps: 0:00 Introducing today's topic: a Fourier transform drawing machine 1:29 Fourier transform algorithm 3:08 Signal processing 5:49 Make a signal array 12:09 Euler's formula 15:34 Write the discrete Fourier transform function 21:50 What do we need for a circular epicycle? 22:47 Calculate the amplitude, frequency, and phase 26:30 Calculate amount of time to move per frame of animation 29:44 Draw an arbitrary path for both x and y 31:07 Write an epiCycles() function 34:30 Have epiCycles() return a vector with an x and y 38:59 Grab the path of the Coding Train logo 41:38 Render the epiCycles by order of amplitude 43:57 Conclusion and next steps Editing by Mathieu Blanchette Animations by Jason Heglund Music from Epidemic Sound 🚂 Website: thecodingtrain.com/ 👾 Share Your Creation! thecodingtrain.com/guides/passenger-showcase-guide 🚩 Suggest Topics: github.com/CodingTrain/Suggestion-Box 💡 GitHub: github.com/CodingTrain 💬 Discord: thecodingtrain.com/discord 💖 Membership: youtube.com/thecodingtrain/join 🛒 Store: standard.tv/codingtrain 🖋️ Twitter: https: