// @ts-check
/**
 * The page: a stack of layers, one per participant, each holding that
 * participant's strokes.  Coordinates are in page units of 0.1 mm.
 *
 * This module holds data only.  It does not draw and does not talk to the
 * network.
 */

/** A blank page is A4. */
// An A4 sheet in landscape (Andy, 2026-10-08; portrait until then).
export const BLANK_PAGE_WIDTH = 2970;
export const BLANK_PAGE_HEIGHT = 2100;

/**
 * The page grows to keep this much room around everything written on it,
 * in steps of the same amount so that it does not shift with every pen
 * point; "Shrink" leaves the same room.  5 mm, Andy's choice (2026-10-08;
 * 8 mm from 2026-10-03, 15 mm before that).
 */
export const WRITING_MARGIN = 50;

/**
 * An image is placed this far inside the sheet's edge, and below the
 * image above.  5 mm, Andy's choice (2026-10-08; 8 mm before); it is
 * deliberately a separate setting from WRITING_MARGIN.
 */
export const IMAGE_MARGIN = 50;

/**
 * @typedef {object} Stroke
 * @property {string} id
 * @property {string} color     CSS color.
 * @property {number} width     Nominal width in page units.
 * @property {number[]} points  x, y, pressure for each point, in sequence.
 *                              Pressure is 0 to 1.
 * @property {boolean} done     False while the stroke is being drawn.
 */

/** Numbers per point in Stroke.points. */
export const POINT_SIZE = 3;

/**
 * Typed text on a layer.  Its top-left corner is (x, y); with a width it
 * wraps there, without one it breaks lines only at the writer's Enter.
 * @typedef {object} TextBlock
 * @property {string} id
 * @property {number} x
 * @property {number} y
 * @property {number | null} width  Page units, or null for no wrapping.
 * @property {number | null} height  With a width: the block is a *text
 *     rectangle* (Andy's teacher, 2026-10-08), drawn with a red frame on
 *     a white ground that hides the image beneath, wrapping inside and
 *     growing downward by lines when the text needs more.  Null for free
 *     text, which is only as large as its lines.
 * @property {string} text          As typed, with the writer's line breaks.
 * @property {string[]} lines       As shown, laid out by the writer's client.
 * @property {number} size          Font size in page units.
 * @property {TextFont} font        One of the families every computer has.
 * @property {string} color
 * @property {number} boxWidth      The rectangle the lines take up.
 * @property {number} boxHeight
 */

/**
 * The font families a block may use: the generic ones, so that the page
 * file looks right on any computer.
 * @typedef {'sans-serif' | 'serif' | 'monospace'} TextFont
 */
export const TEXT_FONTS = /** @type {const} */ (['sans-serif', 'serif', 'monospace']);

/** Page units (0.1 mm) in a typographic point. */
export const UNITS_PER_POINT = 254 / 72;
/** Text sizes in points that may be chosen. */
export const LEAST_TEXT_POINTS = 6;
export const MOST_TEXT_POINTS = 100;
/** The size to begin with: 14 points (Andy, 2026-10-03). */
export const TEXT_SIZE = Math.round(14 * UNITS_PER_POINT * 10) / 10;
const MAX_TEXT_CHARACTERS = 20000;
const MAX_TEXT_LINES = 2000;

/**
 * @param {Stroke} stroke
 * @returns {number}
 */
export function pointCount(stroke) {
  return stroke.points.length / POINT_SIZE;
}

/**
 * Add points to a stroke.  `at` is the number of points that preceded these
 * when they were sent, so that points received twice are added only once.
 * @param {Stroke} stroke
 * @param {number} at
 * @param {number[]} points
 */
export function appendPoints(stroke, at, points) {
  const overlap = Math.max(0, pointCount(stroke) - at);
  for (let i = overlap * POINT_SIZE; i < points.length; i++) stroke.points.push(points[i]);
}

/**
 * Round a coordinate or a pressure for storage and sending.
 * @param {number} value
 * @param {number} scale  10 for coordinates (0.01 mm), 1000 for pressure.
 */
export function rounded(value, scale) {
  return Math.round(value * scale) / scale;
}

// Checking data that comes from outside: other participants and page files.

export const MAX_NAME_LENGTH = 40;
const MAX_ID_LENGTH = 40;
const MAX_STROKE_WIDTH = 200;
const COLOR_PATTERN = /^#[0-9a-fA-F]{6}$/;

/** A longer stroke is split, so that one stroke always fits in a message. */
export const MAX_STROKE_POINTS = 20000;

/**
 * @param {unknown} name
 * @returns {string}
 */
export function cleanName(name) {
  return typeof name === 'string' ? name.trim().slice(0, MAX_NAME_LENGTH) : '';
}

/**
 * @param {unknown} id
 * @returns {id is string}
 */
export function validId(id) {
  return typeof id === 'string' && id.length > 0 && id.length <= MAX_ID_LENGTH;
}

/**
 * @param {unknown} points
 * @returns {points is number[]}
 */
export function validPoints(points) {
  return Array.isArray(points) && points.length % POINT_SIZE === 0 &&
    points.length <= MAX_STROKE_POINTS * POINT_SIZE && points.every(Number.isFinite);
}

/**
 * Check a stroke that came from outside.
 * @param {any} received
 * @returns {Stroke | null}  A stroke that is safe to keep, or null.
 */
export function cleanStroke(received) {
  if (!received || !validId(received.id) || !COLOR_PATTERN.test(received.color) ||
      !(received.width > 0 && received.width <= MAX_STROKE_WIDTH)) return null;
  const points = received.points ?? [];
  if (!validPoints(points)) return null;
  return {
    id: received.id, color: received.color, width: received.width,
    points: points.slice(), done: received.done !== false,
  };
}

/**
 * Check a text block that came from outside.
 * @param {any} received
 * @returns {TextBlock | null}
 */
export function cleanText(received) {
  if (!received || !validId(received.id) || !COLOR_PATTERN.test(received.color) ||
      typeof received.text !== 'string' || received.text.length > MAX_TEXT_CHARACTERS ||
      !Array.isArray(received.lines) || received.lines.length > MAX_TEXT_LINES ||
      !received.lines.every((/** @type {unknown} */ line) => typeof line === 'string') ||
      ![received.x, received.y].every((v) => Number.isFinite(v) && Math.abs(v) <= 10 * MAX_PAGE_SIZE) ||
      (received.width !== null && !(received.width >= 10 && received.width <= MAX_PAGE_SIZE)) ||
      (received.height != null && !(received.height >= 10 && received.height <= 10 * MAX_PAGE_SIZE)) ||
      !(received.size >= 10 && received.size <= 400) ||
      !TEXT_FONTS.includes(received.font) ||
      !(received.boxWidth >= 0 && received.boxWidth <= MAX_PAGE_SIZE) ||
      !(received.boxHeight >= 0 && received.boxHeight <= 10 * MAX_PAGE_SIZE)) return null;
  return {
    id: received.id, x: received.x, y: received.y, width: received.width,
    height: received.height == null || received.width === null ? null : received.height,
    text: received.text, lines: received.lines.slice(), size: received.size, font: received.font,
    color: received.color, boxWidth: received.boxWidth, boxHeight: received.boxHeight,
  };
}

/**
 * The rectangle a text block takes up: its own, grown to its lines, for a
 * text rectangle; the lines' box for free text.
 * @param {TextBlock} block
 * @returns {Rectangle}
 */
export function textBounds(block) {
  if (block.width !== null && block.height !== null) {
    return { left: block.x, top: block.y, width: block.width, height: Math.max(block.height, block.boxHeight) };
  }
  return { left: block.x, top: block.y, width: block.boxWidth, height: block.boxHeight };
}

/**
 * A *Hide* rectangle: white, drawn above all writing, hiding what lies
 * beneath (Andy's teacher, 2026-10-08).  A page object like an image,
 * made, moved and removed by those who may make pages, unaffected by
 * anyone hiding a layer on their own screen.
 * @typedef {object} HideRect
 * @property {string} id
 * @property {number} x
 * @property {number} y
 * @property {number} width
 * @property {number} height
 */

/**
 * @param {any} received
 * @returns {HideRect | null}
 */
export function cleanHide(received) {
  if (!received || !validId(received.id) ||
      ![received.x, received.y].every((v) => Number.isFinite(v) && Math.abs(v) <= MAX_PAGE_SIZE) ||
      ![received.width, received.height].every((v) => v >= 1 && v <= MAX_PAGE_SIZE)) return null;
  return {
    id: received.id, x: Math.round(received.x), y: Math.round(received.y),
    width: Math.round(received.width), height: Math.round(received.height),
  };
}

/** A page holds at most this many Hide rectangles. */
export const MAX_PAGE_HIDES = 50;

export class Layer {
  /**
   * @param {string} id    The participant's id.
   * @param {string} name  The participant's display name.
   */
  constructor(id, name) {
    this.id = id;
    this.name = name;
    /** @type {Map<string, Stroke>}  In drawing sequence. */
    this.strokes = new Map();
    /** @type {Map<string, TextBlock>}  In the sequence of making. */
    this.texts = new Map();
  }

  /** @returns {boolean} */
  isEmpty() {
    return this.strokes.size === 0 && this.texts.size === 0;
  }
}

/**
 * An image on a page, usually a scanned exercise, and where it lies on the
 * page.  A page may hold several, one below the other.
 * @typedef {object} PageImage
 * @property {'image/png' | 'image/jpeg'} type
 * @property {number} size   Bytes.
 * @property {string} hash   SHA-256 of the bytes, base64url.
 * @property {number} x      Its rectangle on the page, in page units.
 * @property {number} y
 * @property {number} width
 * @property {number} height
 * @property {string} by     The participant who added it ('' if unknown):
 *     they may remove it even without the right to make pages (Andy,
 *     2026-10-08).
 * @property {Uint8Array<ArrayBuffer> | null} data  Null until the bytes
 *     have arrived from another participant.
 */

/**
 * What a descriptor says about an image: everything but the bytes.
 * @param {PageImage} image
 * @returns {Omit<PageImage, 'data'>}
 */
function withoutData(image) {
  const { data, ...rest } = image;
  return rest;
}

/**
 * What identifies a page and gives its size.  The host sends it to the
 * others when the page changes.
 * @typedef {object} PageDescriptor
 * @property {string} id
 * @property {number} number  Counts the pages of a session from 1.
 * @property {number} left    The sheet's left edge: 0 to begin with; less
 *     once "Widen" has grown the sheet, which grows it equally on both
 *     sides so that nothing on it moves; anything once "Shrink" has made
 *     the sheet the contents' bounding box (Andy, 2026-10-08).
 * @property {number} top     The sheet's top edge: 0 until "Shrink".
 * @property {number} width
 * @property {number} height
 * @property {Omit<PageImage, 'data'>[]} images  In stacking order, the last in front.
 * @property {HideRect[]} hides  The Hide rectangles, in stacking order.
 * @property {number} revision  Counts the changes made to `images`, `hides`
 *     and the sheet, so that of two lists the later one can be told.
 */

/**
 * A rectangle in page units.
 * @typedef {{left: number, top: number, width: number, height: number}} Rectangle
 */

const MAX_PAGE_SIZE = 20000;

/** An image larger than this is made smaller before it is shared. */
export const MAX_IMAGE_BYTES = 4 << 20;

/**
 * A page holds at most this many images, and this many bytes of them,
 * because the page file holds them all and is rewritten at every save.
 */
export const MAX_PAGE_IMAGES = 12;
export const MAX_PAGE_IMAGE_BYTES = 24 << 20;

/**
 * Check the description of a page's image that came from outside.
 * @param {any} received
 * @returns {PageImage | null}
 */
export function cleanImage(received) {
  if (!received || (received.type !== 'image/png' && received.type !== 'image/jpeg') ||
      !Number.isInteger(received.size) || received.size < 1 || received.size > MAX_IMAGE_BYTES ||
      typeof received.hash !== 'string' || !/^[A-Za-z0-9_-]{43}$/.test(received.hash) ||
      ![received.x, received.y].every((v) => Number.isFinite(v) && Math.abs(v) <= MAX_PAGE_SIZE) ||
      ![received.width, received.height].every((v) => v >= 1 && v <= MAX_PAGE_SIZE)) return null;
  return {
    type: received.type, size: received.size, hash: received.hash,
    x: received.x, y: received.y, width: received.width, height: received.height,
    by: validId(received.by) ? received.by : '', data: null,
  };
}

/**
 * Where an image goes on the page, and the sheet that then holds it.
 *
 * Below the lowest image on the page, or at the page's top if there is
 * none, the margin apart, centred across the page's width, at its
 * natural size: one way for every image (Andy, 2026-10-08, dropping the
 * shrink-to-fit choice and composition mode, since an image can be moved
 * and scaled by hand).  An image wider than the page widens the sheet
 * equally on both sides; one wider than a page can be is scaled to that.
 * @param {Page} page
 * @param {number} naturalWidth   In page units.
 * @param {number} naturalHeight
 * @returns {{x: number, y: number, width: number, height: number, sheet: Rectangle}}
 *     The image's rectangle, and the sheet that holds it and everything
 *     the sheet held before.
 */
export function placeImage(page, naturalWidth, naturalHeight) {
  const scale = Math.min(1, (MAX_PAGE_SIZE - 2 * IMAGE_MARGIN) / naturalWidth);
  const width = Math.round(naturalWidth * scale);
  const height = Math.round(naturalHeight * scale);
  const x = page.left + Math.round((page.width - width) / 2);
  const below = page.images.length ? page.imagesBottom() : page.top;
  const y = Math.round(below) + IMAGE_MARGIN;
  return { x, y, width, height, sheet: sheetHolding(page, { left: x, top: y, width, height }) };
}

/**
 * Which of some rectangles lies under a point, the last (frontmost) first,
 * and whether the point is within `reach` of one of its corners, which
 * counts before lying inside.
 * @param {Rectangle[]} rects
 * @param {number} x
 * @param {number} y
 * @param {number} reach
 * @returns {{index: number, corner: [number, number] | null} | null}
 *     The corner as (0 or 1, 0 or 1): left or right, top or bottom.
 */
export function rectAt(rects, x, y, reach) {
  for (let index = rects.length - 1; index >= 0; index -= 1) {
    const r = rects[index];
    for (const cx of [0, 1]) {
      for (const cy of [0, 1]) {
        if (Math.hypot(x - (r.left + cx * r.width), y - (r.top + cy * r.height)) <= reach) {
          return { index, corner: [cx, cy] };
        }
      }
    }
    if (x >= r.left && x <= r.left + r.width && y >= r.top && y <= r.top + r.height) {
      return { index, corner: null };
    }
  }
  return null;
}

/**
 * The sheet that holds what it holds now and the given rectangle with
 * the image margin around it.
 * @param {Page} page
 * @param {Rectangle} rect
 * @returns {Rectangle}
 */
export function sheetHolding(page, rect) {
  const left = Math.min(page.baseLeft, rect.left - IMAGE_MARGIN);
  const top = Math.min(page.baseTop, rect.top - IMAGE_MARGIN);
  const right = Math.max(page.baseLeft + page.baseWidth, rect.left + rect.width + IMAGE_MARGIN);
  const bottom = Math.max(page.baseTop + page.baseHeight, rect.top + rect.height + IMAGE_MARGIN);
  return { left, top, width: right - left, height: bottom - top };
}

/** An image is never scaled below this, in page units (1 cm). */
export const LEAST_IMAGE_SIDE = 100;

/**
 * Check a page descriptor that came from outside.
 * @param {any} received
 * @returns {PageDescriptor | null}
 */
export function cleanPageDescriptor(received) {
  if (!received || !validId(received.id) || !Number.isInteger(received.number) ||
      received.number < 1 ||
      !(received.width >= 100 && received.width <= MAX_PAGE_SIZE) ||
      !(received.height >= 100 && received.height <= MAX_PAGE_SIZE)) return null;
  const listed = received.images ?? [];
  if (!Array.isArray(listed) || listed.length > MAX_PAGE_IMAGES) return null;
  const images = [];
  for (const one of listed) {
    const image = cleanImage(one);
    if (!image) return null;
    images.push(withoutData(image));
  }
  const listedHides = received.hides ?? [];
  if (!Array.isArray(listedHides) || listedHides.length > MAX_PAGE_HIDES) return null;
  const hides = [];
  for (const one of listedHides) {
    const hide = cleanHide(one);
    if (!hide) return null;
    hides.push(hide);
  }
  /** @param {any} value */
  const edge = (value) => (Number.isFinite(value) && Math.abs(value) <= MAX_PAGE_SIZE ? Math.round(value) : 0);
  return {
    id: received.id, number: received.number, left: edge(received.left), top: edge(received.top),
    width: received.width, height: received.height,
    images, hides,
    revision: Number.isInteger(received.revision) && received.revision >= 0 ? received.revision : 0,
  };
}

export class Page {
  /**
   * @param {number} [width]
   * @param {number} [height]
   * @param {string} [id]      Empty for the placeholder a guest shows
   *                           before the host's page arrives.
   * @param {number} [number]  0 for the placeholder.
   */
  constructor(width = BLANK_PAGE_WIDTH, height = BLANK_PAGE_HEIGHT, id = '', number = 0) {
    /**
     * The size of the sheet before anything is written on it: A4, or taller
     * if its images need the room.
     */
    this.baseLeft = 0;
    this.baseTop = 0;
    this.baseWidth = width;
    this.baseHeight = height;
    this.id = id;
    this.number = number;
    /** @type {PageImage[]}  From the top of the page down. */
    this.images = [];
    /** @type {HideRect[]}  In stacking order. */
    this.hides = [];
    /** Counts the changes made to `images`. */
    this.imagesRevision = 0;
    /** The page's present rectangle.  See updateExtent(). */
    this.left = 0;
    this.top = 0;
    this.width = width;
    this.height = height;
    /** @type {Rectangle | null}  Around every stroke, or null if none. */
    this.strokeBounds = null;
    /** @type {Map<string, Layer>} */
    this.layers = new Map();
  }

  /** @returns {PageDescriptor} */
  descriptor() {
    return {
      id: this.id, number: this.number, left: this.baseLeft, top: this.baseTop,
      width: this.baseWidth, height: this.baseHeight,
      images: this.images.map(withoutData),
      hides: this.hides.map((hide) => ({ ...hide })),
      revision: this.imagesRevision,
    };
  }

  /**
   * The Hide rectangle under a point, and whether the point is near one of
   * its corners, the frontmost first; as imageAt.
   * @param {number} x
   * @param {number} y
   * @param {number} reach
   * @returns {{index: number, corner: [number, number] | null} | null}
   */
  hideAt(x, y, reach) {
    return rectAt(this.hides.map((hide) => ({ left: hide.x, top: hide.y, width: hide.width, height: hide.height })),
                  x, y, reach);
  }

  /**
   * The image under a point, and whether the point is near one of its
   * corners: the frontmost (last) image whose rectangle holds the point
   * or has a corner within `reach` of it.
   * @param {number} x
   * @param {number} y
   * @param {number} reach  Page units.
   * @returns {{index: number, corner: [number, number] | null} | null}
   *     The corner as (0 or 1, 0 or 1): left or right, top or bottom.
   */
  imageAt(x, y, reach) {
    return rectAt(this.images.map((image) => ({ left: image.x, top: image.y, width: image.width, height: image.height })),
                  x, y, reach);
  }

  /** @returns {number}  The bottom edge of the lowest image; 0 if there is none. */
  imagesBottom() {
    return Math.max(0, ...this.images.map((image) => image.y + image.height));
  }

  /** @returns {boolean}  Whether its images have made the sheet larger than A4. */
  isLargerThanSheet() {
    return this.baseWidth > BLANK_PAGE_WIDTH || this.baseHeight > BLANK_PAGE_HEIGHT;
  }

  /**
   * Whether one more image may be added, given what the page holds.
   * @param {number} size    Bytes of the image.
   * @param {number} bottom  Where its bottom edge would lie.
   * @returns {boolean}
   */
  hasRoomForImage(size, bottom) {
    const bytes = this.images.reduce((sum, image) => sum + image.size, 0);
    return this.images.length < MAX_PAGE_IMAGES && bytes + size <= MAX_PAGE_IMAGE_BYTES &&
      bottom + IMAGE_MARGIN <= MAX_PAGE_SIZE;
  }

  /**
   * The rectangle the page has before anything is written on it: the
   * sheet, which holds the images if there are any.
   * @returns {Rectangle}
   */
  baseExtent() {
    return { left: this.baseLeft, top: this.baseTop, width: this.baseWidth, height: this.baseHeight };
  }

  /**
   * The smallest sheet that holds everything on the page with the margin
   * around it: what "Shrink" makes the sheet (Andy, 2026-10-08).
   * @returns {Rectangle | null}  Null if the page is blank.
   */
  contentSheet() {
    /** @type {Rectangle | null} */
    let box = this.strokeBounds ? { ...this.strokeBounds } : null;
    for (const item of [...this.images, ...this.hides]) {
      if (!box) {
        box = { left: item.x, top: item.y, width: item.width, height: item.height };
        continue;
      }
      const right = Math.max(box.left + box.width, item.x + item.width);
      const bottom = Math.max(box.top + box.height, item.y + item.height);
      box.left = Math.min(box.left, item.x);
      box.top = Math.min(box.top, item.y);
      box.width = right - box.left;
      box.height = bottom - box.top;
    }
    if (!box) return null;
    // The greater of the two margins (Andy, 2026-10-08), exactly, the same
    // on all four sides (a grid made them uneven, Andy, 2026-10-08).
    const margin = Math.max(WRITING_MARGIN, IMAGE_MARGIN);
    return {
      left: Math.floor(box.left - margin), top: Math.floor(box.top - margin),
      width: Math.ceil(box.left + box.width + margin) - Math.floor(box.left - margin),
      height: Math.ceil(box.top + box.height + margin) - Math.floor(box.top - margin),
    };
  }

  /**
   * Widen the record of where strokes lie to include these points.
   * @param {Stroke} stroke
   * @param {number} [from]  Index of the first point not yet included.
   */
  includeStroke(stroke, from = 0) {
    const p = stroke.points;
    const reach = stroke.width * 2;    // The drawn width at full pressure, and a little more.
    let b = this.strokeBounds;
    for (let i = from * POINT_SIZE; i < p.length; i += POINT_SIZE) {
      const x = p[i];
      const y = p[i + 1];
      if (!b) {
        b = this.strokeBounds = { left: x - reach, top: y - reach, width: 2 * reach, height: 2 * reach };
        continue;
      }
      const right = Math.max(b.left + b.width, x + reach);
      const bottom = Math.max(b.top + b.height, y + reach);
      b.left = Math.min(b.left, x - reach);
      b.top = Math.min(b.top, y - reach);
      b.width = right - b.left;
      b.height = bottom - b.top;
    }
  }

  /**
   * Widen the record of where things lie to include a text block.
   * @param {TextBlock} block
   */
  includeText(block) {
    const bounds = textBounds(block);
    const corners = [bounds.left, bounds.top, 0, bounds.left + bounds.width, bounds.top + bounds.height, 0];
    this.includeStroke({ id: '', color: '', width: 0, points: corners, done: true });
  }

  /** Find where strokes and text lie again, after some were removed or replaced. */
  recomputeStrokeBounds() {
    this.strokeBounds = null;
    for (const layer of this.layers.values()) {
      for (const stroke of layer.strokes.values()) this.includeStroke(stroke);
      for (const block of layer.texts.values()) this.includeText(block);
    }
  }

  /**
   * Whether a point of a stroke of the given nominal width lies where the
   * page would not grow to hold it: inside the edges by the margin and
   * the stroke's reach.  With "Extend" off, writing stops there (Andy,
   * 2026-10-08), so that the page keeps its size on everyone's screen.
   * @param {number} x
   * @param {number} y
   * @param {number} width
   * @returns {boolean}
   */
  holdsWriting(x, y, width) {
    const inset = WRITING_MARGIN + width * 2;    // The reach of includeStroke.
    return x >= this.left + inset && x <= this.left + this.width - inset &&
      y >= this.top + inset && y <= this.top + this.height - inset;
  }

  /**
   * Set the page's rectangle from what is on it: the base rectangle,
   * widened to hold every stroke with the margin around it, in steps of
   * the margin.  The same contents give the same rectangle on every
   * participant's computer.
   * @returns {boolean}  Whether the rectangle changed.
   */
  updateExtent() {
    const base = this.baseExtent();
    let { left, top } = base;
    let right = base.left + base.width;
    let bottom = base.top + base.height;
    const b = this.strokeBounds;
    if (b) {
      // Writing that comes within the margin of a sheet's edge moves that
      // edge out in steps of the margin, counted from the sheet's edge
      // (not from a fixed grid, since 2026-10-08: a sheet that "Shrink"
      // made exact stays exact until writing reaches its margin).
      const step = WRITING_MARGIN;
      /** @param {number} short  How far the writing's margin reaches past an edge. */
      const steps = (short) => (short > 0 ? Math.ceil(short / step) * step : 0);
      left -= steps(left - (b.left - WRITING_MARGIN));
      top -= steps(top - (b.top - WRITING_MARGIN));
      right += steps(b.left + b.width + WRITING_MARGIN - right);
      bottom += steps(b.top + b.height + WRITING_MARGIN - bottom);
    }
    const changed = left !== this.left || top !== this.top ||
      right - left !== this.width || bottom - top !== this.height;
    this.left = left;
    this.top = top;
    this.width = right - left;
    this.height = bottom - top;
    return changed;
  }

  /**
   * An empty page from its descriptor.
   * @param {PageDescriptor} descriptor
   * @returns {Page}
   */
  static from(descriptor) {
    const page = new Page(descriptor.width, descriptor.height, descriptor.id, descriptor.number);
    page.baseLeft = descriptor.left;
    page.baseTop = descriptor.top;
    page.images = descriptor.images.map((image) => ({ ...image, data: null }));
    page.hides = descriptor.hides.map((hide) => ({ ...hide }));
    page.imagesRevision = descriptor.revision;
    page.updateExtent();
    return page;
  }

  /** @returns {boolean}  Nothing is written on the page. */
  isBlank() {
    for (const layer of this.layers.values()) {
      if (!layer.isEmpty()) return false;
    }
    return true;
  }

  /**
   * Layer ids from bottom to top.  The host's layer is on top so that
   * corrections lie over the writing they correct.
   * @param {string} hostId
   * @returns {string[]}
   */
  layerOrder(hostId) {
    return [...this.layers.keys()].sort((a, b) =>
      Number(a === hostId) - Number(b === hostId) || a.localeCompare(b));
  }

  /**
   * The layer of a participant, created if it does not exist.
   * @param {string} id
   * @param {string} [name]
   * @returns {Layer}
   */
  layer(id, name) {
    let layer = this.layers.get(id);
    if (!layer) {
      layer = new Layer(id, name ?? '');
      this.layers.set(id, layer);
    } else if (name) {
      layer.name = name;
    }
    return layer;
  }
}

/**
 * Squared distance from point (px, py) to the segment (ax, ay)-(bx, by).
 * @param {number} px
 * @param {number} py
 * @param {number} ax
 * @param {number} ay
 * @param {number} bx
 * @param {number} by
 */
function distanceSquaredToSegment(px, py, ax, ay, bx, by) {
  const dx = bx - ax;
  const dy = by - ay;
  const lengthSquared = dx * dx + dy * dy;
  let t = lengthSquared === 0 ? 0 : ((px - ax) * dx + (py - ay) * dy) / lengthSquared;
  t = Math.max(0, Math.min(1, t));
  const cx = ax + t * dx - px;
  const cy = ay + t * dy - py;
  return cx * cx + cy * cy;
}

/**
 * The text blocks of a layer whose rectangle the segment from (x0, y0) to
 * (x1, y1) passes through, widened by `radius`.
 * @param {Layer} layer
 * @param {number} x0
 * @param {number} y0
 * @param {number} x1
 * @param {number} y1
 * @param {number} radius
 * @returns {string[]}  Text block ids.
 */
export function textsTouched(layer, x0, y0, x1, y1, radius) {
  const touched = [];
  const steps = Math.max(1, Math.ceil(Math.hypot(x1 - x0, y1 - y0) / radius));
  for (const block of layer.texts.values()) {
    const b = textBounds(block);
    for (let s = 0; s <= steps; s++) {
      const x = x0 + (x1 - x0) * s / steps;
      const y = y0 + (y1 - y0) * s / steps;
      if (x >= b.left - radius && x <= b.left + b.width + radius &&
          y >= b.top - radius && y <= b.top + b.height + radius) {
        touched.push(block.id);
        break;
      }
    }
  }
  return touched;
}

/**
 * @param {Layer} layer
 * @param {number} x
 * @param {number} y
 * @returns {TextBlock | null}  The block of the layer at the point, if any.
 */
export function textAt(layer, x, y) {
  for (const block of [...layer.texts.values()].reverse()) {
    const b = textBounds(block);     // A text rectangle counts whole, empty part included.
    if (x >= b.left && x <= b.left + b.width && y >= b.top && y <= b.top + b.height) return block;
  }
  return null;
}

/**
 * The strokes of a layer that pass within `radius` of the segment from
 * (x0, y0) to (x1, y1): what an eraser moved along that segment touches.
 * @param {Layer} layer
 * @param {number} x0
 * @param {number} y0
 * @param {number} x1
 * @param {number} y1
 * @param {number} radius
 * @returns {string[]}  Stroke ids.
 */
export function strokesTouched(layer, x0, y0, x1, y1, radius) {
  const touched = [];
  const steps = Math.max(1, Math.ceil(Math.hypot(x1 - x0, y1 - y0) / radius));
  for (const stroke of layer.strokes.values()) {
    const points = stroke.points;
    const reach = radius + stroke.width;
    const reachSquared = reach * reach;
    let hit = false;
    for (let s = 0; s <= steps && !hit; s++) {
      const ex = x0 + (x1 - x0) * s / steps;
      const ey = y0 + (y1 - y0) * s / steps;
      for (let i = 0; i < points.length && !hit; i += POINT_SIZE) {
        const j = Math.min(i + POINT_SIZE, points.length - POINT_SIZE);
        hit = distanceSquaredToSegment(
          ex, ey, points[i], points[i + 1], points[j], points[j + 1]) <= reachSquared;
      }
    }
    if (hit) touched.push(stroke.id);
  }
  return touched;
}