├── .github ├── FUNDING.yml └── workflows │ └── render-video.yml ├── public └── Roboto-Bold.ttf ├── .gitignore ├── src ├── components │ └── fourier-visualizer │ │ ├── utils │ │ ├── types.ts │ │ ├── geometry.ts │ │ ├── fft.ts │ │ ├── extract-epicycles.ts │ │ └── fill.ts │ │ └── index.tsx ├── index.ts ├── Root.tsx ├── FourierVisualizerComposition.tsx ├── AssetManager.tsx └── constants │ └── index.ts ├── .eslintrc ├── .prettierrc ├── tsconfig.json ├── .vscode └── settings.json ├── remotion.config.ts ├── package.json ├── LICENSE ├── README.md └── yarn.lock /.github/FUNDING.yml: -------------------------------------------------------------------------------- 1 | # These are supported funding model platforms 2 | 3 | custom: https://www.patreon.com/reactiive -------------------------------------------------------------------------------- /public/Roboto-Bold.ttf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/enzomanuelmangano/fourier-visualizer-remotion/HEAD/public/Roboto-Bold.ttf -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | node_modules 2 | dist 3 | .DS_Store 4 | .env 5 | 6 | # Ignore the output video from Git but not videos you import into src/. 7 | out 8 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/utils/types.ts: -------------------------------------------------------------------------------- 1 | export type Point = { 2 | x: number; 3 | y: number; 4 | }; 5 | 6 | export type Complex = { 7 | real: number; 8 | imag: number; 9 | }; 10 | -------------------------------------------------------------------------------- /.eslintrc: -------------------------------------------------------------------------------- 1 | { 2 | "extends": "@remotion", 3 | "rules": { 4 | // In Skia, style is either "fill" / "stroke" 5 | "react/style-prop-object": "off", 6 | "max-len": "off", 7 | "@typescript-eslint/no-non-null-assertion": "off" 8 | } 9 | } 10 | -------------------------------------------------------------------------------- /src/index.ts: -------------------------------------------------------------------------------- 1 | import {LoadSkia} from '@shopify/react-native-skia/src/web'; 2 | import {registerRoot} from 'remotion'; 3 | 4 | (async () => { 5 | await LoadSkia(); 6 | const {RemotionRoot} = await import('./Root'); 7 | registerRoot(RemotionRoot); 8 | })(); 9 | -------------------------------------------------------------------------------- /.prettierrc: -------------------------------------------------------------------------------- 1 | { 2 | "singleQuote": true, 3 | "bracketSpacing": false, 4 | "jsxBracketSameLine": false, 5 | "useTabs": true, 6 | "overrides": [ 7 | { 8 | "files": ["*.yml"], 9 | "options": { 10 | "singleQuote": false 11 | } 12 | } 13 | ] 14 | } 15 | -------------------------------------------------------------------------------- /tsconfig.json: -------------------------------------------------------------------------------- 1 | { 2 | "compilerOptions": { 3 | "target": "ES2018", 4 | "module": "commonjs", 5 | "jsx": "react-jsx", 6 | "outDir": "./dist", 7 | "strict": true, 8 | "noEmit": true, 9 | "lib": ["es2015"], 10 | "esModuleInterop": true, 11 | "skipLibCheck": true, 12 | "forceConsistentCasingInFileNames": true, 13 | "noUnusedLocals": true 14 | } 15 | } 16 | -------------------------------------------------------------------------------- /.vscode/settings.json: -------------------------------------------------------------------------------- 1 | { 2 | "editor.tabSize": 2, 3 | "typescript.tsdk": "node_modules/typescript/lib", 4 | "editor.codeActionsOnSave": { 5 | "source.organizeImports": "never", 6 | "source.fixAll": "explicit" 7 | }, 8 | "editor.defaultFormatter": "esbenp.prettier-vscode", 9 | "editor.formatOnSave": true, 10 | "typescript.enablePromptUseWorkspaceTsdk": true 11 | } 12 | -------------------------------------------------------------------------------- /.github/workflows/render-video.yml: -------------------------------------------------------------------------------- 1 | name: Render video 2 | on: 3 | workflow_dispatch: 4 | jobs: 5 | render: 6 | name: Render video 7 | runs-on: ubuntu-latest 8 | steps: 9 | - uses: actions/checkout@main 10 | - uses: actions/setup-node@main 11 | - run: sudo apt update 12 | - run: sudo apt install ffmpeg 13 | - run: npm i 14 | - run: npm run build 15 | - uses: actions/upload-artifact@v2 16 | with: 17 | name: out.mp4 18 | path: out/video.mp4 19 | -------------------------------------------------------------------------------- /src/Root.tsx: -------------------------------------------------------------------------------- 1 | import {Composition} from 'remotion'; 2 | import {FourierVisualizerComposition} from './FourierVisualizerComposition'; 3 | 4 | const FPS = 30; 5 | 6 | const SECONDS = 60; 7 | 8 | export const durationInFrames = FPS * SECONDS; 9 | 10 | export const RemotionRoot: React.FC = () => { 11 | return ( 12 | <> 13 | 21 | 22 | ); 23 | }; 24 | -------------------------------------------------------------------------------- /remotion.config.ts: -------------------------------------------------------------------------------- 1 | /** 2 | * Note: When using the Node.JS APIs, the config file 3 | * doesn't apply. Instead, pass options directly to the APIs. 4 | * 5 | * All configuration options: https://remotion.dev/docs/config 6 | */ 7 | import {enableSkia} from '@remotion/skia/enable'; 8 | import {Config} from '@remotion/cli/config'; 9 | 10 | Config.setVideoImageFormat('jpeg'); 11 | Config.setOverwriteOutput(true); 12 | 13 | Config.overrideWebpackConfig((config) => { 14 | return enableSkia(config); 15 | }); 16 | 17 | // Usually I use this value to set the number of threads to use 18 | // Node -e "const os = require('os'); console.log(os.cpus().length);" 19 | // In this specific case, I'm using 1, because with 2 or more threads 20 | // the result was messed up :/ 21 | Config.setConcurrency(1); 22 | Config.setChromiumOpenGlRenderer('angle'); 23 | -------------------------------------------------------------------------------- /package.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "fourier-skia", 3 | "version": "1.0.0", 4 | "description": "My Remotion video", 5 | "scripts": { 6 | "start": "remotion studio", 7 | "build": "remotion render FourierVisualizer out/video.mp4", 8 | "upgrade": "remotion upgrade", 9 | "test": "eslint src --ext ts,tsx,js,jsx && tsc" 10 | }, 11 | "repository": {}, 12 | "license": "UNLICENSED", 13 | "dependencies": { 14 | "@remotion/cli": "4.0.36", 15 | "@remotion/skia": "4.0.36", 16 | "@remotion/zod-types": "4.0.36", 17 | "@shopify/react-native-skia": "^0.1.191", 18 | "fft.js": "^4.0.4", 19 | "react": "18.2.0", 20 | "react-dom": "18.2.0", 21 | "remotion": "4.0.36", 22 | "zod": "^3.21.4" 23 | }, 24 | "devDependencies": { 25 | "@remotion/eslint-config": "4.0.36", 26 | "@types/react": "^18.0.26", 27 | "@types/web": "^0.0.86", 28 | "eslint": "^8.43.0", 29 | "prettier": "^2.8.8", 30 | "typescript": "^4.9.4" 31 | }, 32 | "packageManager": "yarn@1.22.19" 33 | } 34 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 Enzo Manuel Mangano 4 | Permission is hereby granted, free of charge, to any person obtaining a copy 5 | of this software and associated documentation files (the "Software"), to deal 6 | in the Software without restriction, including without limitation the rights 7 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 8 | copies of the Software, and to permit persons to whom the Software is 9 | furnished to do so, subject to the following conditions: 10 | 11 | The above copyright notice and this permission notice shall be included in all 12 | copies or substantial portions of the Software. 13 | 14 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 20 | SOFTWARE. 21 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/utils/geometry.ts: -------------------------------------------------------------------------------- 1 | import type { 2 | SkContourMeasure, 3 | SkPath, 4 | SkRect, 5 | Vector, 6 | } from '@shopify/react-native-skia'; 7 | import { 8 | fitbox, 9 | processTransform2d, 10 | Skia, 11 | vec, 12 | } from '@shopify/react-native-skia'; 13 | 14 | export const fitRect = (src: SkRect, dst: SkRect) => 15 | processTransform2d(fitbox('contain', src, dst)); 16 | 17 | export const getPointAtLength = (length: number, from: Vector, to: Vector) => { 18 | const angle = Math.atan2(to.y - from.y, to.x - from.x); 19 | const x = from.x + length * Math.cos(angle); 20 | const y = from.y + length * Math.sin(angle); 21 | return vec(x, y); 22 | }; 23 | 24 | export class PathGeometry { 25 | private totalLength = 0; 26 | private contour: SkContourMeasure; 27 | 28 | constructor(path: SkPath, resScale = 1) { 29 | const it = Skia.ContourMeasureIter(path, false, resScale); 30 | const contour: SkContourMeasure = it.next()!; 31 | this.totalLength = contour.length(); 32 | this.contour = contour; 33 | } 34 | 35 | getTotalLength() { 36 | return this.totalLength; 37 | } 38 | 39 | getPointAtLength(length: number) { 40 | const [pos] = this.contour.getPosTan(length); 41 | return pos; 42 | } 43 | } 44 | -------------------------------------------------------------------------------- /src/FourierVisualizerComposition.tsx: -------------------------------------------------------------------------------- 1 | import {SkiaCanvas} from '@remotion/skia'; 2 | import {Group, Rect} from '@shopify/react-native-skia'; 3 | import {interpolate, useCurrentFrame, useVideoConfig} from 'remotion'; 4 | 5 | import {svgPath} from './constants'; 6 | import {durationInFrames} from './Root'; 7 | import {FourierVisualizer} from './components/fourier-visualizer'; 8 | import React from 'react'; 9 | 10 | export const FourierVisualizerComposition: React.FC = () => { 11 | const {height, width} = useVideoConfig(); 12 | 13 | const frame = useCurrentFrame(); 14 | 15 | // Full animation duration is 2 * Math.PI 16 | const time = interpolate(frame, [0, durationInFrames], [0, 2 * Math.PI]); 17 | 18 | return ( 19 | 20 | 21 | 22 | 39 | 40 | 41 | 42 | ); 43 | }; 44 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/utils/fft.ts: -------------------------------------------------------------------------------- 1 | import FFT from 'fft.js'; 2 | import { Complex, Point } from './types'; 3 | 4 | /** 5 | * Compute the Fast Fourier Transform (FFT) of a given set of 2D points. 6 | * 7 | * FFT is an algorithm to compute the discrete Fourier transform (DFT) 8 | * and its inverse. It's used to convert a signal from its original domain 9 | * (often time or space) to a representation in the frequency domain and vice versa. 10 | * 11 | * @param {Point[]} points - An array of 2D points representing the signal. 12 | * @returns {Complex[]} - An array of complex numbers representing the frequency domain. 13 | */ 14 | const computeFFT = (points: Point[]): Complex[] => { 15 | // Determine the number of points in the given data. 16 | const N = points.length; 17 | 18 | // Initialize the FFT object for the given number of points. 19 | const fft = new FFT(N); 20 | 21 | // Create input and output arrays for the FFT operation. 22 | // Since FFT works on complex numbers, each point is represented 23 | // by two values (real and imaginary). Thus, the length is N*2. 24 | const input = new Array(N * 2).fill(0); 25 | const output = new Array(N * 2).fill(0); 26 | 27 | // Map the 2D points to the input array. 28 | // Every even index represents the x (real) value, and 29 | // every odd index represents the y (imaginary) value. 30 | for (let i = 0; i < N; i++) { 31 | input[2 * i] = points[i].x; 32 | input[2 * i + 1] = points[i].y; 33 | } 34 | 35 | // Apply the FFT transform. This converts the input (time-domain signal) 36 | // into the output (frequency-domain representation). 37 | // The output array is modified in-place. 38 | fft.transform(output, input); 39 | 40 | // Convert the output array to an array of complex numbers for easier handling. 41 | const result: Complex[] = []; 42 | for (let i = 0; i < N; i++) { 43 | result.push({ 44 | real: output[2 * i], 45 | imag: output[2 * i + 1], 46 | }); 47 | } 48 | 49 | return result; 50 | }; 51 | 52 | export { computeFFT }; 53 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/utils/extract-epicycles.ts: -------------------------------------------------------------------------------- 1 | import { Complex } from './types'; 2 | 3 | // Define the Epicycle type which represents a circle with a certain frequency, 4 | // amplitude, and phase in the Fourier series. 5 | type Epicycle = { 6 | frequency: number; // The rate of oscillation or rotation of the circle. 7 | amplitude: number; // The radius or size of the circle. 8 | phase: number; // The initial angle offset of the circle. 9 | }; 10 | 11 | /** 12 | * Extract epicycles from a set of complex numbers obtained from FFT. 13 | * 14 | * Epicycles are the set of rotating circles that can be used to approximate 15 | * any periodic curve using Fourier series. In this context, they are used to 16 | * visualize the result of a Fourier transform in terms of circles with different 17 | * frequencies, amplitudes, and phases. 18 | * 19 | * @param {Complex[]} complex - An array of complex numbers representing frequency-domain data. 20 | * @returns {Epicycle[]} - An array of epicycles representing the complex numbers. 21 | */ 22 | const extractEpicycles = (complex: Complex[]): Epicycle[] => { 23 | const numPoints = complex.length; 24 | const epicycles: Epicycle[] = []; 25 | 26 | for (let i = 0; i < numPoints; i++) { 27 | // Indexing logic to retrieve complex numbers in a specific order. 28 | // The reason for this is to sort the frequencies from lowest to highest. 29 | const j = i % 2 === 0 ? i / 2 : numPoints - (i + 1) / 2; 30 | 31 | // Extract real and imaginary parts of the current complex number. 32 | const x = complex[j].real; 33 | const y = complex[j].imag; 34 | 35 | // Calculate the frequency associated with the current complex number. 36 | // It essentially shifts the zero frequency to the center of the array. 37 | const freq = ((j + numPoints / 2) % numPoints) - numPoints / 2; 38 | 39 | // Push the epicycle (circle) data obtained from the complex number 40 | // into the epicycles array. 41 | epicycles.push({ 42 | frequency: freq, 43 | // Calculate amplitude as the distance from the origin to the point (x, y). 44 | amplitude: Math.sqrt(x * x + y * y) / numPoints, 45 | // Calculate the phase angle using the inverse tangent of the ratio of the imaginary to real part. 46 | phase: Math.atan2(y, x), 47 | }); 48 | } 49 | 50 | return epicycles; 51 | }; 52 | 53 | export { extractEpicycles }; 54 | -------------------------------------------------------------------------------- /src/AssetManager.tsx: -------------------------------------------------------------------------------- 1 | import type {SkData, SkImage, SkTypeface} from '@shopify/react-native-skia'; 2 | import {Skia} from '@shopify/react-native-skia'; 3 | import type {ReactNode} from 'react'; 4 | import {useContext, createContext, useState, useEffect} from 'react'; 5 | 6 | type ImagesToLoad = Record>; 7 | type TypefacesToLoad = Record>; 8 | type Images = Record; 9 | type TypeFaces = Record; 10 | 11 | interface TAssetManagerContext { 12 | images: Images; 13 | typefaces: TypeFaces; 14 | } 15 | 16 | const AssetManagerContext = createContext(null); 17 | 18 | interface RemotionCanvasProps { 19 | images: ImagesToLoad; 20 | typefaces: TypefacesToLoad; 21 | children: ReactNode; 22 | } 23 | 24 | const useAssetManager = () => { 25 | const assetManager = useContext(AssetManagerContext); 26 | if (!assetManager) { 27 | throw new Error('Could not find the asset manager'); 28 | } 29 | return assetManager; 30 | }; 31 | 32 | export const useTypefaces = () => { 33 | const assetManager = useAssetManager(); 34 | return assetManager.typefaces; 35 | }; 36 | 37 | export const useImages = () => { 38 | const assetManager = useAssetManager(); 39 | return assetManager.images; 40 | }; 41 | 42 | const resolveAsset = async ( 43 | type: 'image' | 'typeface', 44 | name: string, 45 | asset: ReturnType, 46 | factory: (data: SkData) => T 47 | ) => { 48 | const data = await Skia.Data.fromURI(asset); 49 | return { 50 | type, 51 | name, 52 | data: factory(data), 53 | }; 54 | }; 55 | 56 | export const AssetManager = ({ 57 | children, 58 | images: imagesToLoad, 59 | typefaces: typefacesToLoad, 60 | }: RemotionCanvasProps) => { 61 | const [assetMgr, setAssetMgr] = useState(null); 62 | useEffect(() => { 63 | (async () => { 64 | const assets = await Promise.all([ 65 | ...Object.keys(imagesToLoad).map((name) => 66 | resolveAsset('image', name, imagesToLoad[name], (data: SkData) => 67 | Skia.Image.MakeImageFromEncoded(data) 68 | ) 69 | ), 70 | ...Object.keys(typefacesToLoad).map((name) => 71 | resolveAsset( 72 | 'typeface', 73 | name, 74 | typefacesToLoad[name], 75 | (data: SkData) => Skia.Typeface.MakeFreeTypeFaceFromData(data) 76 | ) 77 | ), 78 | ]); 79 | const images: Images = {}; 80 | const typefaces: TypeFaces = {}; 81 | assets.forEach((asset) => { 82 | if (asset.type === 'image') { 83 | images[asset.name] = asset.data as SkImage; 84 | } else { 85 | typefaces[asset.name] = asset.data as SkTypeface; 86 | } 87 | }); 88 | setAssetMgr({images, typefaces}); 89 | })(); 90 | }, [imagesToLoad, typefacesToLoad]); 91 | if (assetMgr === null) { 92 | return null; 93 | } 94 | return ( 95 | 96 | {children} 97 | 98 | ); 99 | }; 100 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/utils/fill.ts: -------------------------------------------------------------------------------- 1 | import {SkPath} from '@shopify/react-native-skia'; 2 | import {Point} from './types'; 3 | import {PathGeometry} from './geometry'; 4 | 5 | // Extracts and returns an array of points from an SkPath object. 6 | // The whole point of this animation is using the FFT algorithm. 7 | // The FFT algorithm requires an array of points as input. 8 | // But we are drawing simply a Path, which is a collection of points. 9 | // This function extracts the points from the Path. 10 | export const getPoints = (path: SkPath): Point[] => { 11 | const pathGeo = new PathGeometry(path); 12 | const totalLength = pathGeo.getTotalLength(); 13 | const points = []; 14 | for (let i = 0; i < totalLength; i++) { 15 | const point = pathGeo.getPointAtLength(i); 16 | points.push({ 17 | x: point.x, 18 | y: point.y, 19 | }); 20 | } 21 | 22 | return points; 23 | }; 24 | 25 | // Generates linearly interpolated points between each pair of points in the given array. 26 | // WHY? 27 | // Consider this case: we have a Path, which is a collection of points. 28 | // We give to the FFT algorithm the points of the Path, and the FFT algorithm 29 | // returns the epicycles. 30 | // But what if before giving the points to the FFT algorithm, we add more points 31 | // applying a Linear Interpolation? 32 | // Of course the epicycles will be more accurate, because we have more points. 33 | // This is what this function is all about :) 34 | export function generateLinearInterpolatedPoints( 35 | points: Point[], 36 | density = 10 37 | ): Point[] { 38 | const totalPoints = (points.length - 1) * density + 1; 39 | const result: Point[] = new Array(totalPoints); 40 | 41 | let resultIndex = 0; 42 | const step = 1 / density; 43 | for (let i = 0; i < points.length - 1; i++) { 44 | const p1 = points[i]; 45 | const p2 = points[i + 1]; 46 | 47 | const dx = p2.x - p1.x; 48 | const dy = p2.y - p1.y; 49 | 50 | // Interpolate points between p1 and p2 51 | for (let t = 0; t < 1; t += step) { 52 | result[resultIndex++] = { 53 | x: p1.x + t * dx, 54 | y: p1.y + t * dy, 55 | }; 56 | } 57 | } 58 | 59 | result[totalPoints - 1] = points[points.length - 1]; // Add the last point 60 | return result; 61 | } 62 | 63 | // Checks if a number is a power of two. 64 | export function isPowerOfTwo(n: number): boolean { 65 | return (n & (n - 1)) === 0; 66 | } 67 | 68 | // Calculates the next power of two greater than or equal to `n`. 69 | export function nextPowerOfTwo(n: number): number { 70 | let count = 0; 71 | 72 | if (n && !isPowerOfTwo(n)) { 73 | // Count the number of shifts required to get to the next power of two. 74 | while (n !== 0) { 75 | n >>= 1; 76 | count += 1; 77 | } 78 | } 79 | 80 | return 1 << count; 81 | } 82 | 83 | // Fills the array of points up to the nearest power of two with a default point. 84 | // IMPORTANT: 85 | // This function is super important since the FFT algorithm requires 86 | // the number of points to be a power of two. 87 | export function fillToPowerOfTwo(points: Point[]): Point[] { 88 | const targetLength = nextPowerOfTwo(points.length); 89 | 90 | const defaultPoint = points[points.length - 1]; 91 | const filledPoints: Point[] = Array(targetLength).fill(defaultPoint); 92 | for (let i = 0; i < points.length; i++) { 93 | filledPoints[i] = points[i]; 94 | } 95 | return filledPoints; 96 | } 97 | -------------------------------------------------------------------------------- /src/components/fourier-visualizer/index.tsx: -------------------------------------------------------------------------------- 1 | import { 2 | Path, 3 | SkPath, 4 | Skia, 5 | useComputedValue, 6 | useValue, 7 | } from '@shopify/react-native-skia'; 8 | import React, {useMemo} from 'react'; 9 | 10 | // Utility functions to manage and transform path points 11 | import {fillToPowerOfTwo, getPoints} from './utils/fill'; 12 | 13 | // Utility functions for Fourier series visualization 14 | import {extractEpicycles} from './utils/extract-epicycles'; 15 | import {computeFFT} from './utils/fft'; 16 | import {Point} from './utils/types'; 17 | 18 | type FourierVisualizerProps = { 19 | t: number; 20 | strokeWidth?: number; 21 | path: SkPath; 22 | onPathUpdate?: (center: Point) => void; 23 | }; 24 | 25 | const FourierVisualizer: React.FC = ({ 26 | strokeWidth = 1.5, 27 | t, 28 | path, 29 | onPathUpdate, 30 | }) => { 31 | // Shared value to store epicycles computed from the path 32 | const epicycles = useMemo(() => { 33 | // Convert path into linearly interpolated points 34 | const points = getPoints(path); 35 | 36 | // Ensure the number of points is a power of two for FFT 37 | const filledPoints = fillToPowerOfTwo(points); 38 | 39 | // Compute the Fast Fourier Transform on the points 40 | const data = computeFFT(filledPoints); 41 | 42 | return extractEpicycles(data).sort((a, b) => b.amplitude - a.amplitude); 43 | }, [path]); 44 | 45 | // Paths for visualizing the Fourier series 46 | const resultPath = useValue(Skia.Path.Make()); 47 | const circlesPath = useValue(Skia.Path.Make()); 48 | 49 | // Derive the visualization path based on the time evolution of epicycles 50 | const drawPath = useComputedValue(() => { 51 | const skPath = Skia.Path.Make(); 52 | circlesPath.current.reset(); 53 | 54 | let x = 0; 55 | let y = 0; 56 | 57 | // Compute the visualization based on each epicycle 58 | for (const epicycle of epicycles) { 59 | const {frequency, amplitude, phase} = epicycle; 60 | 61 | // Visualize the circles around the path 62 | if (x !== 0 && y !== 0) { 63 | circlesPath.current.addCircle(x, y, amplitude); 64 | } 65 | 66 | // Calculate the position on the circle for the current epicycle 67 | x += amplitude * Math.cos(frequency * t + phase); 68 | y += amplitude * Math.sin(frequency * t + phase); 69 | 70 | // Connect the path to the new position 71 | const lastSkiaPathPt = skPath.getLastPt(); 72 | if (lastSkiaPathPt.x === 0 && lastSkiaPathPt.y === 0) { 73 | skPath.moveTo(x, y); 74 | } else { 75 | skPath.lineTo(x, y); 76 | } 77 | 78 | // Update the center of the visualization 79 | if (onPathUpdate) { 80 | onPathUpdate({x, y}); 81 | } 82 | } 83 | 84 | // Update the resultPath to visualize the overall path over time 85 | const lastResultPathPt = resultPath.current.getLastPt(); 86 | if (lastResultPathPt.x === 0 && lastResultPathPt.y === 0) { 87 | resultPath.current.moveTo(x, y); 88 | } else { 89 | resultPath.current.lineTo(x, y); 90 | } 91 | 92 | return skPath; 93 | }, [t, epicycles, path]); 94 | 95 | return ( 96 | // Render the visualization paths 97 | <> 98 | 105 | 113 | 119 | 120 | ); 121 | }; 122 | 123 | export {FourierVisualizer}; 124 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Fourier Visualizer with React Native Skia in Remotion 🎨 2 | 3 | This is a fancy project done in [Remotion](https://www.remotion.dev/) and [React Native Skia](https://shopify.github.io/react-native-skia/) with the goal of building SVG Path using the Fourier Transform. 4 | 5 | The concept behind this repo is strongly inspired by the following resources: 6 | 7 | - [3Blue1Brown](https://twitter.com/3Blue1Brown): ["But what is a Fourier series? From heat flow to drawing with circles"](https://youtu.be/r6sGWTCMz2k) 8 | - [Jezzamon](https://twitter.com/jezzamonn): ["An Interactive Introduction to Fourier Transforms"](https://www.jezzamon.com/fourier/index.html) 9 | 10 | The idea behind this project is absolutely not mine, and the algorithms are wrappers of [fft.js](https://www.npmjs.com/package/fft.js). 11 | I simply used the same algorithms to run it using **React Native Skia** and render the output with **Remotion**. 12 | 13 | ## How to Run 14 | 15 | Install the dependencies: 16 | 17 | ```bash 18 | yarn install 19 | ``` 20 | 21 | Execute in dev mode: 22 | 23 | ```bash 24 | yarn start 25 | ``` 26 | 27 | Render the video: 28 | 29 | ```bash 30 | yarn build 31 | ``` 32 | 33 | Before doing that you might want to change the `settings` in the `remotion.config.ts` file. 34 | 35 | ## How it Works 36 | 37 | At its core, a Fourier Transform allows us to express any function (in this case, a path) as a sum of sinusoids (sines and cosines). Each sinusoid has a specific frequency, amplitude, and phase. In the context of this visualizer, think of them as individual contributors that, when combined, recreate the original path. 38 | 39 | ### The Process 40 | 41 | 1. **Path to Points**: The `SkPath` is converted into a set of linearly interpolated points using the `generateLinearInterpolatedPoints` function. This function ensures that the path is represented as a series of discrete points that can be processed further. 42 | 43 | 2. **Preparing for FFT**: For the Fast Fourier Transform (FFT) to work effectively, the number of points must be a power of two. The `fillToPowerOfTwo` function ensures this by possibly adding extra points, guaranteeing compatibility with FFT. 44 | 45 | 3. **Fast Fourier Transform**: With our points ready, they undergo the FFT process using the `computeFFT` function. The FFT transforms our spatial data (points in space) into frequency data. This is where we identify the sinusoids that best represent our path. 46 | 47 | 4. **Extraction of Epicycles**: Post-FFT, we use the `extractEpicycles` function to determine the epicycles' properties (frequency, amplitude, phase). These are the circles you see in the visualization. 48 | 49 | 5. **Visualization**: 50 | 51 | - **Circles (Epicycles)**: As time (`t`) progresses, each epicycle rotates based on its frequency. The radius of the circle represents its amplitude, and its starting position is adjusted by its phase. 52 | - **Path Tracing**: Starting from the center, each epicycle contributes to a point in space. As we sum the contributions of all epicycles, we trace the original path. 53 | 54 | The visualization involves both showing the rotating circles (epicycles) and the path they trace. The `circlesPath` and `resultPath` are used for these purposes. 55 | 56 | 6. **Rendering**: Finally, the visualizations are rendered using the Skia paths. The epicycles, the path being traced, and the final traced path are all displayed in real-time as the Fourier Transform evolves. 57 | 58 | ### The Result 59 | 60 | What you witness is a mesmerizing dance of circles, collectively working to draw the original path 🕺🏻. 61 | 62 | ## Feedback & Contribution 63 | 64 | This is a demo project, but if you have suggestions, feedback, or want to show how you've expanded on this idea, feel free to open issues or submit pull requests! 65 | 66 | ## License 67 | 68 | MIT 69 | 70 | --- 71 | -------------------------------------------------------------------------------- /src/constants/index.ts: -------------------------------------------------------------------------------- 1 | import {Skia} from '@shopify/react-native-skia'; 2 | 3 | const svg = 4 | 'M978.141,416.063c7.732-7.25,21.793,1.315,26.098,1.45 c14.066,0.442,28.632-1.293,34.314-0.725c9.666,0.966,32.381,0.725,39.147-3.142c0,0-2.9-0.967-6.767-1.45 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