feat: plotcutter

src/plotcutter/bezier.ts

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+export type Pt = [number, number];
+
+export function cubicBezierCommand(pts: Pt[], p1: Pt, p2: Pt, p3: Pt){
+    const p0 = pts[pts.length - 1];
+    if (!p0) return pts;
+
+    const [b1p0, b1p1, b1p2] = getMidPoints(p0, p1, p2, p3);
+    const [b2p0, b2p1] = getMidPoints(b1p0, b1p1, b1p2);
+    const [b3p0] = getMidPoints(b2p0, b2p1);
+
+    const a1 = Math.atan2(b3p0[1] - p0[1], b3p0[0] - p0[0]);
+    const a2 = Math.atan2(p3[1] - b3p0[1], p3[0] - b3p0[0]);
+    const d = a2 - a1 - Math.round((a2 - a1) / Math.PI / 2) * Math.PI * 2;
+    if (isNaN(d)) {
+        console.error('NaN found', { d, a2, a1, p0, p1, p2, p3 });
+        return pts;
+    }
+
+    const d03 = sqdist(p0, p3);
+    if (d * d * d03 < Math.PI * Math.PI / 18 / 18) {
+        pts.push(p3);
+        return pts;
+    }
+
+    cubicBezierCommand(pts, b1p0, b2p0, b3p0);
+    pts.push(b3p0);
+    cubicBezierCommand(pts, b2p1, b1p2, p3);
+
+    return pts;
+}
+
+function sqdist(pt: Pt, to: Pt) {
+    const x = pt[0] - to[0];
+    const y = pt[1] - to[1];
+    return x * x + y * y;
+}
+
+function getMidPoints(...pts: Pt[]){
+    const mps = [] as typeof pts;
+
+    for(let i = 1; i < pts.length; i ++){
+        mps[i-1] = [
+            (pts[i][0] + pts[i-1][0])/2,
+            (pts[i][1] + pts[i-1][1])/2,
+        ];
+    }
+
+    return mps;
+}

src/plotcutter/index.ts

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+export * from "./bezier";
+export * from "./vector";
+export * from "./plotter";

src/plotcutter/normalize.ts

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+// pts is a point loop
+// reorder the points, such that:
+// 1. the points are in counter-clockwise order
+// 2. the first edge(pts[0] to pts[1]) points to the (0,1) direction, as much as possible
+export function normalize(pts: [number, number][]){
+    if (pts.length < 3) {
+        return pts; // Need at least 3 points to form a polygon
+    }
+
+    // Calculate the signed area to determine winding order
+    let area = 0;
+    for (let i = 0; i < pts.length; i++) {
+        const [x1, y1] = pts[i];
+        const [x2, y2] = pts[(i + 1) % pts.length];
+        area += x1 * y2 - x2 * y1;
+    }
+
+    // If area is negative, points are in clockwise order, so reverse them
+    if (area < 0) {
+        pts.reverse();
+    }
+
+    // Find the best starting point to maximize alignment with (1,0) direction
+    let bestIndex = 0;
+    let maxDotProduct = -Infinity;
+
+    for (let i = 0; i < pts.length; i++) {
+        const [x1, y1] = pts[i];
+        const [x2, y2] = pts[(i + 1) % pts.length];
+        
+        // Calculate the direction vector of the edge
+        const dx = x2 - x1;
+        const dy = y2 - y1;
+        
+        // Normalize the vector
+        const length = Math.sqrt(dx * dx + dy * dy);
+        if (length > 0) {
+            const normalizedDx = dx / length;
+            const normalizedDy = dy / length;
+            
+            // Dot product with (1, 0) is just normalizedDx
+            const dotProduct = normalizedDy;
+            
+            if (dotProduct > maxDotProduct) {
+                maxDotProduct = dotProduct;
+                bestIndex = i;
+            }
+        }
+    }
+
+    // Rotate array to start with the best edge
+    if (bestIndex !== 0) {
+        pts = [...pts.slice(bestIndex), ...pts.slice(0, bestIndex)];
+    }
+
+    return pts;
+}

src/plotcutter/plotter.ts

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+import {normalize} from "./normalize";
+
+export function pts2plotter(pts: [number, number][][], width: number, height: number, px2mm = 0.1){
+    let str = init(width * px2mm, height * px2mm);
+
+    // sort paths by x(long) then by y(short)
+    const sorted = pts.slice();
+    sorted.sort(function (a, b) {
+        const [ax,ay] = topleft(a);
+        const [bx,by] = topleft(b);
+
+        if (ax !== bx) return ax - bx;
+        return ay - by;
+    });
+
+    let lead = true;
+    for(const path of sorted){
+        for (const cmd of poly(normalize(path), height, px2mm, lead)) {
+            str += cmd;
+        }
+        lead = false;
+    }
+
+    str += end();
+
+    return str;
+}
+
+function topleft(pts: [number, number][]){
+    let minx = NaN;
+    let miny = NaN;
+    for(const pt of pts){
+        if (isNaN(minx) || minx > pt[0]) minx = pt[0];
+        if (isNaN(miny) || miny > pt[1]) miny = pt[1];
+    }
+    return [minx, miny] as [number, number];
+}
+
+function init(w: number, h: number) {
+    return ` IN TB26,${plu(w)},${plu(h)} CT1 U0,0 D0,0 D40,0`;
+}
+
+function end() {
+    return ' U0,0 @ @';
+}
+
+function* poly(pts: [number, number][], height: number, px2mm: number, lead = false){
+    function cutpt(down: boolean, pt: [number, number]) {
+        return ` ${down ? 'D' : 'U'}${plu(pt[0] * px2mm)},${plu((height - pt[1]) * px2mm)}`;
+    }
+
+    if (lead) {
+        yield cutpt(false, [0, 0]);
+        yield cutpt(true, [0, 1]);
+    }
+
+    yield cutpt(false, pts[0]);
+    for(const pt of pts){
+        yield cutpt(true, pt);
+    }
+}
+
+function sqrlen(x: number, y: number) {
+    return x * x + y * y;
+}
+
+function lerp(s: [number, number], e: [number, number], i: number) {
+    return [s[0] + (e[0] - s[0]) * i, s[1] + (e[1] - s[1]) * i] as typeof s;
+}
+
+function plu(n: number) {
+    return Math.round(n / 0.025);
+}

src/plotcutter/vector.ts

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+import { cubicBezierCommand, Pt } from "./bezier";
+
+export function frame2preview(pts: Pt[][], width: number, height: number, px2mm = 0.1) {
+    return `<svg viewbox="0 0 ${width} ${height}" width=360 height=220>
+        <rect x=0 y=0 width=${width} height=${height} fill="#8001" stroke="#f008"></rect>
+        <path d="${pts2command(pts)}" fill="#0001" stroke="#0008">
+        </path>
+      </svg><span>${ (width * px2mm).toFixed(1)}mm x ${(height * px2mm).toFixed(1)}mm</span>`;
+}
+
+function pts2command(pts: Pt[][]){
+  return pts.map(
+    path => {
+      const pts = path.map(pt=> `${pt[0]} ${pt[1]}`).join(' L ');
+      return `M ${pts} Z`;
+    }
+  ).join(' ');
+}