/**
 * Geometry of a transition: the straight arrow drawn between two states. It runs border to border
 * rather than pin to pin, because a diagonal line into a port would pass under the target node and
 * take its arrowhead with it – the usual curve never does, since it swings in horizontally.
 */

export interface Point {
  x: number;
  y: number;
}

export interface Rect {
  x: number;
  y: number;
  w: number;
  h: number;
}

/** Length of an arrowhead along the line, and half its width across. */
export const ARROW = 10;
export const ARROW_HALF_WIDTH = 4.5;
/** Air between a node's border and the end of the arrow touching it. */
export const BORDER_GAP = 7;
/** How far apart two transitions between the same pair of states are pushed. */
export const PARALLEL_SEP = 14;

export function centreOf(box: Rect): Point {
  return { x: box.x + box.w / 2, y: box.y + box.h / 2 };
}

/** Null when the two points coincide: there is no direction to draw along. */
export function direction(a: Point, b: Point): Point | null {
  const length = Math.hypot(b.x - a.x, b.y - a.y);
  return length === 0 ? null : { x: (b.x - a.x) / length, y: (b.y - a.y) / length };
}

/** Where a ray leaving the box's centre crosses its border. */
export function boxExit(box: Rect, dir: Point): Point {
  const centre = centreOf(box);
  const tx = dir.x === 0 ? Infinity : box.w / 2 / Math.abs(dir.x);
  const ty = dir.y === 0 ? Infinity : box.h / 2 / Math.abs(dir.y);
  const t = Math.min(tx, ty);
  return { x: centre.x + dir.x * t, y: centre.y + dir.y * t };
}

/** The normal of a direction, pointing to its right. */
function normal(dir: Point): Point {
  return { x: -dir.y, y: dir.x };
}

function shift(point: Point, out: Point, along: number, n: Point, across: number): Point {
  return { x: point.x + out.x * along + n.x * across, y: point.y + out.y * along + n.y * across };
}

/**
 * The two points a transition between these nodes runs between: each a border crossing, pushed
 * `BORDER_GAP` clear of the node and `offset` sideways. Null when the boxes share a centre.
 */
export function transitionEnds(from: Rect, to: Rect, offset = 0): { start: Point; end: Point } | null {
  const dir = direction(centreOf(from), centreOf(to));
  if (!dir) return null;
  const back = { x: -dir.x, y: -dir.y };
  const n = normal(dir);
  return {
    start: shift(boxExit(from, dir), dir, BORDER_GAP, n, offset),
    end: shift(boxExit(to, back), back, BORDER_GAP, n, offset),
  };
}

/** How far apart a self-loop's two ends sit on the node's top edge, and how high it rises. */
const LOOP_SPREAD = 14;
const LOOP_RISE = 44;
/** What each further loop on the same state adds, so they nest with room for a name between them. */
const LOOP_SPREAD_STEP = 6;
const LOOP_RISE_STEP = 24;

/** A transition from a state back into itself: one cubic curve over the node's top edge. */
export interface Loop {
  start: Point;
  c1: Point;
  c2: Point;
  end: Point;
}

/**
 * The loop over the middle of the box, left end out and right end in, both `BORDER_GAP` clear of
 * the border like every other transition. The control points lean outwards, so the curve bulges
 * wider than its feet and reads as a loop rather than a hump. `ring` counts the loops already on the
 * state: each further one sits outside the last.
 */
export function selfLoop(box: Rect, ring = 0): Loop {
  const x = box.x + box.w / 2;
  const y = box.y - BORDER_GAP;
  const spread = LOOP_SPREAD + ring * LOOP_SPREAD_STEP;
  const rise = LOOP_RISE + ring * LOOP_RISE_STEP;
  return {
    start: { x: x - spread, y },
    c1: { x: x - spread * 2.5, y: y - rise },
    c2: { x: x + spread * 2.5, y: y - rise },
    end: { x: x + spread, y },
  };
}

/** Which ring each loop takes: the loops on one state count up from 0 in edge order. */
export function loopRings(links: readonly TransitionLink[]): Map<string, number> {
  const count = new Map<string, number>();
  const rings = new Map<string, number>();
  for (const link of links) {
    if (link.from !== link.to) continue;
    const ring = count.get(link.from) ?? 0;
    rings.set(link.id, ring);
    count.set(link.from, ring + 1);
  }
  return rings;
}

/** The point at `t` along the loop, 0 at its start and 1 at the arrow's tip. */
export function loopPoint(loop: Loop, t: number): Point {
  const u = 1 - t;
  const [a, b, c, d] = [u * u * u, 3 * u * u * t, 3 * u * t * t, t * t * t];
  return {
    x: a * loop.start.x + b * loop.c1.x + c * loop.c2.x + d * loop.end.x,
    y: a * loop.start.y + b * loop.c1.y + c * loop.c2.y + d * loop.end.y,
  };
}

/** How far a name may slide along its arrow looking for room, and in which steps. */
const LABEL_REACH = 120;
const LABEL_STEP = 2;

function overlaps(a: Rect, b: Rect): boolean {
  return a.x < b.x + b.w && b.x < a.x + a.w && a.y < b.y + b.h && b.y < a.y + a.h;
}

/**
 * Where a transition's name goes, as the centre of a `w` by `h` plate: at `centre` where that plate
 * overlaps none already placed, else at the nearest free spot along `dir`, its own arrow – arrows
 * side by side are closer than a name is wide, and a name slid sideways would read as the
 * neighbour's. Stays at `centre` when nothing within reach is free.
 */
export function freeLabelSpot(
  centre: Point,
  w: number,
  h: number,
  dir: Point,
  placed: readonly Rect[],
): Point {
  for (let s = 0; s <= LABEL_REACH; s += LABEL_STEP) {
    for (const sign of s === 0 ? [1] : [1, -1]) {
      const spot = { x: centre.x + dir.x * s * sign, y: centre.y + dir.y * s * sign };
      if (!placed.some((p) => overlaps(p, { x: spot.x - w / 2, y: spot.y - h / 2, w, h }))) return spot;
    }
  }
  return centre;
}

/** One transition as the offsets care about it: which states it joins, under which edge id. */
export interface TransitionLink {
  id: string;
  from: string;
  to: string;
}

/**
 * How far each transition is pushed sideways, so several between the same two states lie next to
 * each other instead of on top. The fan is computed in the canonical direction of the pair, and a
 * transition running the other way takes the opposite sign – which is what puts a there-and-back
 * pair on either side of the line rather than both on the same one.
 */
export function transitionOffsets(links: readonly TransitionLink[]): Map<string, number> {
  const groups = new Map<string, TransitionLink[]>();
  for (const link of links) {
    const [a, b] = link.from < link.to ? [link.from, link.to] : [link.to, link.from];
    const key = `${a}\u0000${b}`;
    const group = groups.get(key);
    if (group) group.push(link);
    else groups.set(key, [link]);
  }
  const offsets = new Map<string, number>();
  for (const group of groups.values()) {
    for (const [i, link] of group.entries()) {
      const canonical = (i - (group.length - 1) / 2) * PARALLEL_SEP;
      offsets.set(link.id, link.from <= link.to ? canonical : -canonical);
    }
  }
  return offsets;
}

/**
 * The line drawn while a transition is being dragged: out of the source's border towards the
 * pointer, or border to border once the drag has found another state.
 */
export function transitionPreview(
  source: Rect,
  target: Rect | null,
  pointer: Point,
): {
  start: Point;
  end: Point;
} {
  if (target) return transitionEnds(source, target) ?? { start: centreOf(source), end: pointer };
  const dir = direction(centreOf(source), pointer);
  if (!dir) return { start: centreOf(source), end: pointer };
  return { start: shift(boxExit(source, dir), dir, BORDER_GAP, normal(dir), 0), end: pointer };
}

/** Where the line stops: at the head's base, so the stroke does not blunt its tip. */
export function arrowShaft(start: Point, end: Point): Point {
  const u = direction(start, end);
  return u ? { x: end.x - u.x * ARROW, y: end.y - u.y * ARROW } : end;
}

/** The three corners of the arrowhead at the target end, tip first. */
export function arrowCorners(start: Point, end: Point): [Point, Point, Point] | null {
  const u = direction(start, end);
  if (!u) return null;
  const base = arrowShaft(start, end);
  const nx = -u.y * ARROW_HALF_WIDTH;
  const ny = u.x * ARROW_HALF_WIDTH;
  return [end, { x: base.x + nx, y: base.y + ny }, { x: base.x - nx, y: base.y - ny }];
}