From 11c3e90c57dd090b025b6f46d599c52cb841b8f0 Mon Sep 17 00:00:00 2001 From: newt Date: Wed, 9 Oct 2024 18:02:46 +0100 Subject: [PATCH] feat: halley's method + pdf -> img --- .husky/pre-commit | 2 +- .husky/scripts/cleanMaths.js | 73 - .husky/scripts/pdfToPng.sh | 22 + maths/halley's method.png | Bin 0 -> 58537 bytes maths/halley's method.tex | 53 + maths/nth root.png | Bin 10194 -> 2482 bytes maths/style.cls | 3 + maths/trigometric functions/cos.png | Bin 37370 -> 8329 bytes maths/trigometric functions/cot-1.png | Bin 25957 -> 0 bytes maths/trigometric functions/cot-2.png | Bin 26863 -> 0 bytes maths/trigometric functions/cot.png | Bin 0 -> 10792 bytes maths/trigometric functions/csc-1.png | Bin 38988 -> 0 bytes maths/trigometric functions/csc-2.png | Bin 4964 -> 0 bytes maths/trigometric functions/csc.png | Bin 0 -> 10322 bytes maths/trigometric functions/sec-1.png | Bin 39959 -> 0 bytes maths/trigometric functions/sec-2.png | Bin 4751 -> 0 bytes maths/trigometric functions/sec.png | Bin 0 -> 10035 bytes maths/trigometric functions/sin.png | Bin 39318 -> 9186 bytes maths/trigometric functions/tan-1.png | Bin 20990 -> 0 bytes maths/trigometric functions/tan-2.png | Bin 26367 -> 0 bytes maths/trigometric functions/tan.png | Bin 0 -> 9992 bytes package.json | 5 +- pnpm-lock.yaml | 1344 +---------------- .../raspberry pie game/Instructions.pdf | Bin 3850948 -> 0 bytes .../raspberry pie game/Instructions.png | Bin 0 -> 1396309 bytes 25 files changed, 120 insertions(+), 1382 deletions(-) delete mode 100644 .husky/scripts/cleanMaths.js create mode 100755 .husky/scripts/pdfToPng.sh create mode 100644 maths/halley's method.png create mode 100644 maths/halley's method.tex delete mode 100644 maths/trigometric functions/cot-1.png delete mode 100644 maths/trigometric functions/cot-2.png create mode 100644 maths/trigometric functions/cot.png delete mode 100644 maths/trigometric functions/csc-1.png delete mode 100644 maths/trigometric functions/csc-2.png create mode 100644 maths/trigometric functions/csc.png delete mode 100644 maths/trigometric functions/sec-1.png delete mode 100644 maths/trigometric functions/sec-2.png create mode 100644 maths/trigometric functions/sec.png delete mode 100644 maths/trigometric functions/tan-1.png delete mode 100644 maths/trigometric functions/tan-2.png create mode 100644 maths/trigometric functions/tan.png delete mode 100644 school/gcse/year 10/raspberry pie game/Instructions.pdf create mode 100644 school/gcse/year 10/raspberry pie game/Instructions.png diff --git a/.husky/pre-commit b/.husky/pre-commit index d0a8bed..cf03b66 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -2,5 +2,5 @@ . "$(dirname "$0")/_/husky.sh" npx pretty-quick --staged -node .husky/scripts/cleanMaths.js +.husky/scripts/pdfToPng.sh git add . diff --git a/.husky/scripts/cleanMaths.js b/.husky/scripts/cleanMaths.js deleted file mode 100644 index 99170a5..0000000 --- a/.husky/scripts/cleanMaths.js +++ /dev/null @@ -1,73 +0,0 @@ -const fs = require('fs'); -const path = require('path'); -const { pdfToPng } = require('pdf-to-png-converter'); -const Jimp = require('jimp'); - -const mathsDir = path.resolve(__dirname, '..', '..', 'maths'); - -const cropBuffer = buffer => - new Promise((resolve, reject) => { - Jimp.read(buffer) - .then(cropped => { - cropped.autocrop(); - - new Jimp( - cropped.getWidth() + 100, - cropped.getHeight() + 100, - '#ffffff', - async (err, image) => { - if (err) reject(err); - - image.blit(cropped, 50, 50); - - resolve(await image.getBufferAsync(Jimp.MIME_PNG)); - } - ); - }) - .catch(err => reject(err)); - }); - -const crawlDirectory = async dir => { - const dirents = fs.readdirSync(dir, { withFileTypes: true }); - - const files = await Promise.all( - dirents.map(dirent => { - const res = path.resolve(dir, dirent.name); - return dirent.isDirectory() ? crawlDirectory(res) : res; - }) - ); - - return files.flat(); -}; - -(async () => { - const files = await crawlDirectory(mathsDir); - - files.forEach(file => { - const [filePath, fileDirectory, fileNameWithExt] = file.match(/(.*)\/((?:.(?!\/))+)$/); - const [fileName, fileExtension] = fileNameWithExt.split('.'); - - if (file.endsWith('.pdf')) { - pdfToPng(filePath).then(async output => { - const pageCount = output.length; - - if (pageCount > 1) - output.forEach(async (page, i) => - fs.writeFileSync( - path.join(fileDirectory, `${fileName}-${i + 1}.png`), - await cropBuffer(page.content) - ) - ); - else - fs.writeFileSync( - path.join(fileDirectory, `${fileName}.png`), - await cropBuffer(output[0].content) - ); - }); - } - - if (fileExtension !== 'tex' && fileExtension !== 'png' && fileExtension !== 'cls') { - fs.rmSync(filePath); - } - }); -})(); diff --git a/.husky/scripts/pdfToPng.sh b/.husky/scripts/pdfToPng.sh new file mode 100755 index 0000000..3a2a04d --- /dev/null +++ b/.husky/scripts/pdfToPng.sh @@ -0,0 +1,22 @@ +#!/bin/bash +find . -print0 | while IFS= read -r -d '' file +do + if [ -f "$file" ]; then + if [[ $file == *pdf ]]; then + mkdir temp + gm convert "$file" +adjoin temp/temp%02d.png + + for temp in ./temp/*.png + do + gm convert "$temp" -fuzz 80% -trim +repage -bordercolor white -border 50x25 "$temp" + done + + readarray -d . -t arr <<< $file + + gm convert -append ./temp/*.png "${arr[1]:1}.png" + + rm -rf temp + rm "$file" "${arr[1]:1}.synctex.gz" + fi +fi +done diff --git a/maths/halley's method.png b/maths/halley's method.png new file mode 100644 index 0000000000000000000000000000000000000000..bec432b78cf62620607e7a98577ecf386ec4455a GIT binary patch literal 58537 zcmd43cT`i+_b(Wwi6WrVM4E{7Zcsp~2uKM?3DS`&AV}{`P(ea3f`lG=Ku|z>QwRu= 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(n-2)c_{n-2}x^{n-3} + ... + c_{1} = \sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1} + \end{dmath*} + + And the second derivative is + + \begin{dmath*} + f''(x) = n(n-1)c_{n}x^{n-2} + (n-1)(n-2)c_{n-1}x^{n-3} + (n-2)(n-3)c_{n-2}x^{n-4} + ...+ c_{2} = \sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2} + \end{dmath*} + + After starting with an initial guess, the next iteration of Halley's method is given by $x_k - \frac{2f(x_k)f'(x_k)}{2[f'(x_k)]^2 - f(x_k)f''(x_k)}$. + + This means that we must first find $f(x)f'(x)$, $[f'(x)]^2$, and $f(x)f''(x)$. These all consist of the multiplication of two series - there is a nice general form to this problem stated below + + \begin{dmath*} + (\sum_{i=0}^{n}x_{i})(\sum_{j=0}^{m}y_{j}) = \sum_{i=0}^{n}\sum_{j=0}^{m}x_iy_j + \end{dmath*} + + \newpage + From this, we can conclude that: + + \begin{dmath*} + f(x)f'(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1} + \end{dmath*} + + \begin{dmath*} + [f'(x)]^2 = (\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j} + \end{dmath*} + + \begin{dmath*} + f(x)f''(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2}) = \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j} + \end{dmath*} + + And all that is left to do is to plug it into the formula for Halley's method, leaving us with the following: + + \begin{align*} + x_{k+1} = x_{k} - \dfrac{2\sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1}}{\splitdfrac{2\sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}{- \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}} + \end{align*} +\end{center} +\end{document} diff --git a/maths/nth root.png b/maths/nth root.png index 20e02691d70e8cae16898e7d496283b824afbab3..72b7276fb389f4883a3d2f45e3c6c220176d3751 100644 GIT binary patch literal 2482 zcmd5;{X5eOAO0dN*&>P=nd)c~X{tF(BnlDono2edtIV>EHs+mTR43$ZB%YSHMP4_e zhEyvrDetM&X@)pX*=!?@bDryZ{(Jd(f#AgELWV(rEKc99fvU$fFSXw{sH4aAUf(;Ex-1>q0Z55smp;0 ze9MT7IJJ*0(m;b8-Y;oNpN3`@%IhL6W_4^3ZCD+oB24a8u3+-&ex}!&*r7|QLbb3? 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