Carried, stamped and pasted markup geometry

export function carryMarkups(markups, toKey, { from, to, skipClosed = false } = {}) {
  const items = [], sources = [];
  let left = 0, scaled = 0, closed = 0;
  const same = !from || !to || sameSize(from, to);
  const k = same ? 1 : Math.min(to.width / from.width, to.height / from.height);
  const fx = (p) => (same ? p : [to.view[0] + (p[0] - from.view[0]) * k, to.view[1] + (p[1] - from.view[1]) * k]);
  for (const m of markups) {
    if (m.type === 'foreign' || m.locked) { left++; continue; }
    if (skipClosed && CLOSED.has(m.status)) { closed++; continue; }
    const c = clone(m);
    delete c.id;
    c.sheet = toKey;
    c.src = null;
    if (c.pts) c.pts = c.pts.map(fx);
    if (c.rect) { const a = fx([c.rect[0], c.rect[1]]), b = fx([c.rect[2], c.rect[3]]); c.rect = [a[0], a[1], b[0], b[1]]; }
    if (!same) {
      scaled++;
      c.style = { ...c.style, width: Math.round(c.style.width * k * 100) / 100, fontSize: Math.max(4, Math.round(c.style.fontSize * k * 10) / 10) };
    }
    c.replies = (c.replies || []).map((r) => ({ ...r, id: undefined }));
    items.push(c);
    sources.push(m.id);
  }
  return { items, sources, left, scaled, closed };
}

export function supersededStamp(page, { label, author = '', sheet }) {
  const [x0, y0, x1, y1] = page.view;
  const W = x1 - x0, H = y1 - y0;
  const rot = page.rotate || 0;
  const across = rot % 180 ? H : W;                       // the page's width as it reads
  const w = Math.min(across * 0.4, 432), h = Math.max(36, w * 0.18);
  const dx = rot % 180 ? h : w, dy = rot % 180 ? w : h;   // the rect in user space (y up)
  const m = Math.min(W, H) * 0.04 + (rot % 180 ? dx : dy) / 2;
  // "top middle" in user space for each turn of the page
  const c = rot === 90 ? [x0 + m, (y0 + y1) / 2] : rot === 180 ? [(x0 + x1) / 2, y0 + m] : rot === 270 ? [x1 - m, (y0 + y1) / 2] : [(x0 + x1) / 2, y1 - m];
  return {
    sheet, type: 'stamp', rot, author, label,
    rect: [c[0] - dx / 2, c[1] - dy / 2, c[0] + dx / 2, c[1] + dy / 2],
    style: { color: '#c4122f', width: 3, fill: null, fillOpacity: 0.25, opacity: 1, fontSize: Math.round(h * 0.45) },
  };
}

export function fitBox(w, h, maxW, maxH) {
  const k = Math.min(maxW / w, maxH / h, 1e9);
  return [w * k, h * k];
}

export function placeRect(c, w, h, rot = 0) {
  const [dx, dy] = rot % 180 ? [h, w] : [w, h];
  return [c[0] - dx / 2, c[1] - dy / 2, c[0] + dx / 2, c[1] + dy / 2];
}

const box = [Infinity, Infinity, -Infinity, -Infinity];
for (const it of items) { box[0] = Math.min(box[0], it.box[0]); box[1] = Math.min(box[1], it.box[1]); box[2] = Math.max(box[2], it.box[2]); box[3] = Math.max(box[3], it.box[3]); }
const pad = Math.max(...items.map((it) => (it.lw || 0) / 2 + 0.5));   // a stroke's half width sits outside its path's box
box[0] -= pad; box[1] -= pad; box[2] += pad; box[3] += pad;
if (!(box[2] > box[0] && box[3] > box[1])) return { refused: 'empty' };

/**
 * The `add` item that pastes a clip. `delta` moves it from where it was copied (paste in place = [0, 0]); `center` puts
 * the middle of the copied box there. `rotate` = the target page's /Rotate: the content is turned by the difference, so
 * it reads the same way on screen as where it was copied.
 */
export function pasteContent(clip, { rotate = null, delta = null, center = null } = {}, id = 'p' + Date.now().toString(36)) {
  const [x0, y0, x1, y1] = clip.box;
  const cx = (x0 + x1) / 2, cy = (y0 + y1) / 2;
  const turn = rotate === null ? 0 : (norm(rotate) - clip.rotate + 360) % 360;   // degrees, counter-clockwise in page space
  const R = { 0: [1, 0, 0, 1], 90: [0, 1, -1, 0], 180: [-1, 0, 0, -1], 270: [0, -1, 1, 0] }[turn];
  const to = center || [cx + (delta?.[0] || 0), cy + (delta?.[1] || 0)];
  const T = mul(mul(translate(-cx, -cy), [...R, 0, 0]), translate(to[0], to[1]));
  return { id, kind: 'pdf', pdf: clip.pdf, box: clip.box.slice(), T };
}