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art/LaTeXWriter-Kosei/index.js

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+/*
+@title: LaTeXWriter
+@author: Kosei Tsukamoto
+@snapshot: example1.png
+*/
+
+/*
+This program parses a subset of latex to write math out with polylines
+- The latex parser was all written by me (Kosei)
+- It supports:
+  - numbers
+  - + - * / ^
+  - \sqrt{}, \int, \times, \cdot, \frac{}{}, 
+  - letters
+- Impactful and useful since it is something that I and some
+of my friends will actually use for practicing
+- Infinite possibilites! Technically complex (took 10+ hours, see code lol) and visually engaging
+- It is as efficient as I could make it (speed of drawing finish)
+- To use it, comment out the "random expression" section
+and input your own latex! Just use the
+renderLatex(yourLatexStringHere) function call!
+
+TODO
+- show example of ALL features
+- handle nested square roots by making outer ones bigger
+- add more commands (https://blog.writefull.com/the-100-most-frequent-latex-commands/)
+- center shorter one in fractions
+*/
+
+
+const width = 125;
+const height = 125;
+
+setDocDimensions(width, height);
+
+
+
+// RANDOM EXPRESSION SECTION START (this code is for demo purposes only)
+
+// renderLatex(String.raw`b \int c \sqrt{b}f \times g \cdot e \frac{a}{b}c+-*/^dmmogus`);
+{
+  renderLatex(String.raw`\int x \sqrt{x^2 + 24} dx`, [10, 5]);
+  renderLatex(String.raw`latex\,\, renderer
+infinite \,\, possibilities!`, [5, 115]);
+}
+{
+  // U SUB
+  let pn = []; // random polynomial
+  let pn2 = []; // polynomial for u sub!
+  let pd = bt.randIntInRange(2, 4);
+  for (let i = pd; i > 0; i--) {
+    let n = bt.randIntInRange(1, 9);
+    pn.push(n + 'x' + (i == 1 ? '' : '^' + i));
+    pn2.push(n * i + (i == 1 ? '' : 'x') + (i - 1 <= 1 ? '' : '^' + (i - 1)));
+  }
+  renderLatex(String.raw`u-sub
+\int (${pn2.join('+')})
+  \times\sqrt{${pn.join('+')}} \, dx`, [10, 88]); // random integral
+}
+{
+  // PARTIAL FRACTION DECOMP
+  let pn1 = [bt.randIntInRange(1, 9) + 'x', bt.randIntInRange(1, 9)]; // random polynomial
+  let pn2 = [bt.randIntInRange(1, 9) + 'x', bt.randIntInRange(1, 9)]; // polynomial for u sub!
+  let pn3 = [bt.randIntInRange(1, 9)]
+  renderLatex(String.raw`partial \, \, fractions
+    \int \frac{${pn3.join('+')}}{(${pn1.join('+')})(${pn2.join('+')})} \, dx`, [10, 55]); // random integral
+}
+{
+  // INTEGRATION BY PARTS
+  let pn = []; // random polynomial
+  let pd = bt.randIntInRange(1, 3);
+  for (let i = pd; i > 0; i--) {
+    let n = bt.randIntInRange(1, 9);
+    pn.push(n + 'x' + (i == 1 ? '' : '^' + i));
+  }
+  renderLatex(String.raw`int by parts
+\int (${pn.join('+')})\cos (x) \, dx`, [10, 30]); // random integral
+}
+
+// RANDOM EXPRESSION SECTION END
+
+
+/*
+format: [
+  Node (CommandNode || TextNode) {
+    type: 'command' || 'text',
+    data: 'commandName' || 'textChar',
+    body?(only if type=='command'): [Arg [Node {}, ...], ...],
+  },
+  ...
+]
+*/
+function parseLatex(latex) {
+  let parsed = [];
+  for (let i = 0; i < latex.length; i++) {
+    let s = latex[i];
+    if (s == '\\') {
+      let o = {
+        type: 'command',
+        data: null,
+        body: [], // array of argument arrays
+      };
+      let startI = i + 1;
+      while (i < latex.length) {
+        i++;
+        let s = latex[i];
+        if (('a' <= s && s <= 'z') || s == ',' || s == '.') {
+          // o.data += s;
+        } else {
+          break;
+        }
+      }
+      o.data = latex.substring(startI, i);
+
+      if (o.data == 'sin' || o.data == 'cos') {
+        // just convert to text
+        o.type = 'text';
+        delete o.body;
+      } else {
+
+        while (i < latex.length) {
+          let s = latex[i];
+          if (s != '{') {
+            break;
+          }
+          let startI = i + 1;
+          let nest = 1;
+          while (i < latex.length) {
+            i++;
+            let s = latex[i];
+            if (s == '{') {
+              nest++;
+            } else if (s == '}') {
+              nest--;
+              if (nest == 0) {
+                break;
+              }
+            }
+          }
+          o.body.push(parseLatex(latex.substring(startI, i)));
+          i++;
+        }
+      }
+      i--;
+
+      parsed.push(o);
+    } else if (s == ' ') {
+      // whitespace, do nothing
+    } else if (s == '^') {
+      // exponent (command with optional brackets)
+      i++;
+      let startI = i;
+      if (latex[i] == '{') {
+        let nest = 1;
+        while (i < latex.length) {
+          i++;
+          let s = latex[i];
+          if (s == '{') {
+            nest++;
+          } else if (s == '}') {
+            nest--;
+            if (nest == 0) {
+              break;
+            }
+          }
+        }
+      } else {
+        i++;
+      }
+
+      let o = {
+        type: 'command',
+        data: s,
+        body: [parseLatex(latex.substring(startI, i))], // array of argument arrays
+      };
+
+      parsed.push(o);
+      i--;
+    } else if (s == '\n') {
+      let o = {
+        type: 'command',
+        data: s,
+        body: null
+      };
+      parsed.push(o);
+    } else {
+      let startI = i;
+      while (i < latex.length) {
+        i++;
+        let s = latex[i];
+        if (s == '\\' || s == ' ' || s == '^' || s == '\n') {
+          break;
+        }
+      }
+      parsed.push({
+        type: 'text',
+        data: latex.substring(startI, i),
+      });
+      i--;
+    }
+  }
+  return parsed;
+}
+
+function renderParsed(parsed, originalOrigin, scale, spacingV) {
+  let origin = [...originalOrigin]; // clone origin since it will be mutated
+  // console.log(origin)
+
+  let spacing = spacingV[0];
+  let spacingY = spacingV[1];
+
+  const textSize = 2; // size of text only (still needs to be multiplied with scale)
+  const spacingSize = spacing - textSize; // size of spacing only (still needs to be multiplied with scale)
+  const textSizeY = 4; // size of text y (still needs to be multiplied with scale)
+
+  const lines = [];
+  for (let i = 0; i < parsed.length; i++) {
+    let p = parsed[i];
+    if (p.type == 'command') {
+      switch (p.data) {
+        case 'times': {
+          lines.push([
+            [origin[0] + (spacingSize) * scale, origin[1] + (spacingSize) * scale],
+            [origin[0] + (spacingSize * 3 + textSize) * scale, origin[1] + (textSize + spacingSize * 3) * scale],
+          ], [
+            [origin[0] + (spacingSize) * scale, origin[1] + (textSize + spacingSize * 3) * scale],
+            [origin[0] + (spacingSize * 3 + textSize) * scale, origin[1] + (spacingSize) * scale],
+          ]);
+          origin[0] += (spacing + spacingSize * 4) * scale;
+          break;
+        }
+        case 'cdot': {
+          const t = new bt.Turtle();
+          let r = 0.25;
+          for (let i = 0; i < 5; i++) {
+            t.jump([origin[0] + (spacingSize * 1 + textSize / 2) * scale, origin[1] + (textSizeY / 2 - r) * scale]);
+            t.arc(360, r * scale);
+            r -= 0.05;
+          }
+          lines.push(...t.lines());
+          origin[0] += (spacing + spacingSize * 2) * scale;
+          break;
+        }
+        case 'int': {
+          const t = new bt.Turtle();
+          t.jump([origin[0], origin[1]]);
+          t.up();
+          // t.arc(270, 0.25 * scale);
+          t.right(90);
+          t.down();
+          t.arc(180 - 15, 0.25 * scale);
+          t.forward((textSizeY / Math.cos(Math.PI/180 * 15) + 2 * 0.25 * Math.sin(Math.PI/180 * 15)) * scale);
+          t.arc(-(180 - 15), 0.25 * scale);
+          lines.push(...t.lines());
+          origin[0] += (spacing - spacingSize) * scale;
+          break;
+        }
+        case 'sqrt': {
+
+
+          /*
+          // DOESNT WORK FOR NESTED (ENLARGES OUTSIDE)
+          let oldOriginX = origin[0];
+          origin[0] += 1.5 * scale;
+          let newOrigin = renderParsed(p.body[0], origin, scale, spacing);
+          const t = new bt.Turtle();
+          t.jump([oldOriginX, origin[1]]);
+          t.up();
+          // t.arc(270, 0.25 * scale);
+          t.right(90 - 15);
+          t.down();
+          t.forward(0.25 * scale);
+          t.left(180 - 15 * 2);
+          t.forward((textSizeY / Math.cos(Math.PI/180 * 15) + 0.25 * 2) * scale);
+          t.right(90 - 15);
+          t.forward(newOrigin[0] - origin[0]);
+          lines.push(...t.lines());
+          */
+
+          // SHRINKS INSIDE
+          let oldOriginX = origin[0];
+          origin[0] += 1.5 * scale;
+          let newScale = scale / 1.1;
+          let newOrigin = renderParsed(p.body[0], origin, newScale, spacingV);
+          const t = new bt.Turtle();
+          t.jump([oldOriginX, origin[1]]);
+          t.up();
+          // t.arc(270, 0.25 * scale);
+          t.right(90 - 15);
+          t.down();
+          t.forward(0.25 * scale);
+          t.left(180 - 15 * 2);
+          t.forward((textSizeY / Math.cos(Math.PI/180 * 15) + 0.25) * scale);
+          t.right(90 - 15);
+          t.forward(newOrigin[0] - origin[0]);
+          lines.push(...t.lines());
+
+          origin = newOrigin;
+          break;
+        }
+        case 'frac': {
+          let newScale = scale / 2.1;
+          let bottomOrigin = renderParsed(p.body[1], [origin[0] + spacingSize / 2 * scale, origin[1]], newScale, spacingV);
+          let topOrigin = renderParsed(p.body[0], [origin[0] + spacingSize / 2 * scale, origin[1] + (textSizeY) * (scale / 2 + scale / 2 - scale / 2.1)], newScale, spacingV);
+          const t = new bt.Turtle();
+          t.jump([origin[0], origin[1] + textSizeY / 2 * scale]);
+          let newOrigin = [Math.max(bottomOrigin[0], topOrigin[0]) - (spacingSize * newScale) + spacingSize / 2 * scale, origin[1]];
+          t.forward(newOrigin[0] - origin[0]);
+          lines.push(...t.lines());
+
+          newOrigin[0] += spacingSize * scale;
+          origin = newOrigin;
+          break;
+        }
+        case '^': {
+          // old
+          /*
+          let newScale = scale / 2;
+          let newOrigin = renderParsed(p.body[0], [origin[0], origin[1] + textSizeY * scale - (textSizeY / 2) * newScale], newScale, spacing);
+
+          origin = [newOrigin[0] - spacingSize * newScale + spacingSize * scale, origin[1]];
+          */
+
+          // keep consistent height for roots!
+          let newScale = scale / 2;
+          let newOrigin = renderParsed(p.body[0], [origin[0], origin[1] + textSizeY * scale - (textSizeY) * newScale], newScale, spacingV);
+
+          origin = [newOrigin[0] - spacingSize * newScale + spacingSize * scale, origin[1]];
+          break;
+        }
+        case '\n': {
+          origin[1] -= spacingY * scale;
+          origin[0] = originalOrigin[0];
+          break;
+        }
+        case ',': {
+          origin[0] += spacingSize * 2 * scale;
+          break;
+        }
+        case '.': {
+          origin[0] += spacingSize * scale;
+          break;
+        }
+        default: {
+          console.log(p.data + ' not implemented yet');
+        }
+      }
+    } else if (p.type == 'text') {
+      let d = p.data;
+      lines.push(...bt.text(d, origin, scale))
+      origin[0] += spacing * scale * d.length;
+    }
+  }
+
+  // 3. draw
+  drawLines(lines);
+
+  return origin;
+}
+
+function renderLatex(latex, originalOrigin = [10, 10], scale = 2, spacing = [2.5, 4.5]) {
+  // 1. parse latex
+  let parsed = parseLatex(latex);
+
+  // 2. draw
+  return renderParsed(parsed, originalOrigin, scale, spacing);
+}