import type { Vec2 } from './geometry';

/**
 * Coping axis as a polyline IP1 → (IP4) → IP3 (spec §4.1). Each stretch is straight and has its own frame.
 * Coordinates: k = stretch index, s = arc length from IP1 (the same s for both stretches), n = offset to the right of u.
 * The lateral offset uses the same convention as the straight model: nrm = (u.n, −u.e).
 */
export interface AxisSegment {
  start: Vec2;
  u: Vec2;
  nrm: Vec2;
  /** Arc length at the start of this stretch. */
  s0: number;
}

export interface Axis {
  segments: AxisSegment[];
  /** Total arc length L_IP. */
  length: number;
  /** Bend point IP4, or null for a straight axis. */
  kink: Vec2 | null;
  /** Mitre normal u1 + u2 (unit) at the kink; null for a straight axis. A point is on stretch 0 when (p − kink)·mitre ≤ 0. */
  mitre: Vec2 | null;
}

export interface AxisPoint {
  k: number;
  s: number;
  n: number;
}

const dist = (a: Vec2, b: Vec2) => Math.hypot(b.e - a.e, b.n - a.n);
const sub = (a: Vec2, b: Vec2): Vec2 => ({ e: a.e - b.e, n: a.n - b.n });
const dot = (a: Vec2, b: Vec2) => a.e * b.e + a.n * b.n;
const unit = (v: Vec2): Vec2 => {
  const len = Math.hypot(v.e, v.n);
  if (len === 0) throw new Error('축 길이가 0입니다.');
  return { e: v.e / len, n: v.n / len };
};

function frame(start: Vec2, end: Vec2): { u: Vec2; nrm: Vec2 } {
  const u = unit(sub(end, start));
  return { u, nrm: { e: u.n, n: -u.e } };
}

export function buildAxis(ip1: Vec2, ip3: Vec2, kink: Vec2 | null): Axis {
  if (!kink) {
    const f = frame(ip1, ip3);
    return { segments: [{ start: ip1, ...f, s0: 0 }], length: dist(ip1, ip3), kink: null, mitre: null };
  }
  const a = dist(ip1, kink);
  const f1 = frame(ip1, kink);
  const f2 = frame(kink, ip3);
  return {
    segments: [
      { start: ip1, ...f1, s0: 0 },
      { start: kink, ...f2, s0: a },
    ],
    length: a + dist(kink, ip3),
    kink,
    mitre: unit({ e: f1.u.e + f2.u.e, n: f1.u.n + f2.u.n }),
  };
}

/** Stretch and local coordinates of a world point. Points on the stretch-0 side of the mitre plane belong to stretch 0. */
export function toAxis(axis: Axis, p: Vec2): AxisPoint {
  const k = axis.mitre && axis.kink && dot(sub(p, axis.kink), axis.mitre) > 0 ? 1 : 0;
  const seg = axis.segments[k];
  const d = sub(p, seg.start);
  return { k, s: seg.s0 + dot(d, seg.u), n: dot(d, seg.nrm) };
}

/** World point of local coordinates (inverse of toAxis for the same k). */
export function fromAxis(axis: Axis, q: AxisPoint): Vec2 {
  const seg = axis.segments[q.k];
  const ds = q.s - seg.s0;
  return {
    e: seg.start.e + ds * seg.u.e + q.n * seg.nrm.e,
    n: seg.start.n + ds * seg.u.n + q.n * seg.nrm.n,
  };
}

/** Arc-length span of the coping of length L, centred on the axis (spec §4.2: centre at L_IP / 2). */
export function copingSpan(axis: Axis, L: number): { sStart: number; sEnd: number } {
  return { sStart: axis.length / 2 - L / 2, sEnd: axis.length / 2 + L / 2 };
}

/** Arc length of the kink, or null for a straight axis. */
export function kinkArc(axis: Axis): number | null {
  return axis.kink ? axis.segments[1].s0 : null;
}

/** Positions (arc length) closer than minDistance to the kink. Used to refuse columns at the bend. */
export function nearKink(axis: Axis, sPositions: number[], minDistance: number): number[] {
  const a = kinkArc(axis);
  if (a === null) return [];
  return sPositions.filter((s) => Math.abs(s - a) < minDistance);
}