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src/geometry/polygon.ts

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+import type { Point } from '../types';
+
+export function pointInPolygon(p: Point, poly: Point[]): boolean {
+  if (poly.length < 3) return true;
+  let inside = false;
+  for (let i = 0, j = poly.length - 1; i < poly.length; j = i++) {
+    const a = poly[i];
+    const b = poly[j];
+    if (onSegment(a, b, p)) return true;
+    const intersect = a.y > p.y !== b.y > p.y && p.x < ((b.x - a.x) * (p.y - a.y)) / (b.y - a.y) + a.x;
+    if (intersect) inside = !inside;
+  }
+  return inside;
+}
+
+function onSegment(a: Point, b: Point, p: Point): boolean {
+  const cross = (b.x - a.x) * (p.y - a.y) - (b.y - a.y) * (p.x - a.x);
+  if (Math.abs(cross) > 1e-9) return false;
+  const dot = (p.x - a.x) * (b.x - a.x) + (p.y - a.y) * (b.y - a.y);
+  if (dot < 0) return false;
+  const len2 = (b.x - a.x) ** 2 + (b.y - a.y) ** 2;
+  return dot <= len2;
+}
+
+function closestOnSegment(a: Point, b: Point, p: Point): Point {
+  const dx = b.x - a.x;
+  const dy = b.y - a.y;
+  const len2 = dx * dx + dy * dy;
+  if (len2 === 0) return { ...a };
+  let t = ((p.x - a.x) * dx + (p.y - a.y) * dy) / len2;
+  t = Math.max(0, Math.min(1, t));
+  return { x: a.x + t * dx, y: a.y + t * dy };
+}
+
+export function nearestPointInPolygon(p: Point, poly: Point[]): Point {
+  if (poly.length < 3) return { ...p };
+  if (pointInPolygon(p, poly)) return { ...p };
+  let best = poly[0];
+  let bestD = Infinity;
+  for (let i = 0, j = poly.length - 1; i < poly.length; j = i++) {
+    const q = closestOnSegment(poly[j], poly[i], p);
+    const d = (q.x - p.x) ** 2 + (q.y - p.y) ** 2;
+    if (d < bestD) {
+      bestD = d;
+      best = q;
+    }
+  }
+  return best;
+}
+
+export function rectanglePoints(width: number, height: number): Point[] {
+  return [
+    { x: 0, y: 0 },
+    { x: width, y: 0 },
+    { x: width, y: height },
+    { x: 0, y: height },
+  ];
+}