Aislo/B05_Profile/logic/B05_Profile_PlanFootprint.ts

/* =============================================================================
 * B05_Profile/logic/B05_Profile_PlanFootprint.ts
 * 평면 발자국 — 측점 횡단 설계 결과를 평면 선으로(도로 끝 좌 · 우 · 비탈 끝 깎기 · 쌓기 · 눈금) (346-2)
 *
 * ⚠⚠ 짝: `B07_DesignDetail/B07_DesignDetail_Engine_Cad_PlanSlope.py`
 *     (`route_frame` · `route_normal` · `side_is_cut` · `slope_end` · `slope_pieces` 와 그 아래
 *     단조 3차 보간 · 촘촘히 · 접힘 버림 · 353-1 · 모서리 둥글림 · 364-3) — 한쪽만 고치면
 *     종단 · 횡단 편집 중 평면과 B07 계획평면도가 갈린다.
 *     `footprintRecord` = `B07_DesignDetail_Router_Support_Plan.slope_records` 의 측점 한 줄.
 *     거울 시험: `resources/tester/test_346_2_plan_footprint_mirror.py`
 *
 * 순수 계산 — 화면 · three · fetch · sessionStorage 없음 · 좌표 = 사업지 m · 오프셋 좌(+) · 우(-).
 * ========================================================================== */

import type { PlanFootprint, Vertex } from "../../A00_Common/design/logic/design_pipeline_types";

/** 횡단 설계선 · 지반 표본 한 점(`CrossDesignEdge` · `CrossGroundSample` 꼴). */
export interface FootprintPoint {
  offset_m?: number | null;
  elevation_m?: number | null;
  valid?: boolean;
}

/** 측점 한 자리 — 중심 · 진행 방향 · 그 측점 횡단 설계 결과 · 지반 표본. */
export interface FootprintStation {
  chainage_m: number;
  x: number;
  y: number;
  /** 진행 방향(크기 무관) — 좌측 법선 = (−ty, tx). */
  tx: number;
  ty: number;
  design: {
    road_edges?: {
      left?: FootprintPoint | null;
      right?: FootprintPoint | null;
    } | null;
    design_line?: FootprintPoint[] | null;
  } | null;
  samples: FootprintPoint[];
}

/** `slope_pieces` 의 측점 줄. */
export interface FootprintRecord {
  /** 측점 열쇠(footprint 단계가 붙임 · 범위 밖 재사용) — 셈에는 안 씀. */
  key?: string;
  chainage_m: number;
  left_edge_m: number;
  left_end_m: number;
  right_edge_m: number;
  right_end_m: number;
  left_cut?: boolean;
  right_cut?: boolean;
  x?: number;
  y?: number;
  nx?: number;
  ny?: number;
}

type Line = number[][];

/** B07 `slope_pieces` 꼴(거울 시험 · 도면). */
export interface SlopePieces {
  /** 도로 끝 [좌, 우]. */
  edge: Line[];
  /** 비탈 끝 — 쌓기(성토) 구간 · 깎기(절토) 구간. */
  fill: Line[];
  cut: Line[];
  /** 비탈 눈금 — 도로 끝에서 비탈 끝으로(긴 · 짧은 번갈아). */
  ticks: Line[];
}

/** 비탈 눈금 간격(1/1,200 실거리 m). 짝: `TICK_STEP_M`. */
export const TICK_STEP_M = 2.0;

type Side = "left" | "right";
const SIDES: Side[] = ["left", "right"];
const KEYS = ["left_edge_m", "left_end_m", "right_edge_m", "right_end_m"] as const;

/** 파이썬 `round(v, n)` 대용 — 반올림 경계(…5)만 다를 수 있음(1e-n 안). */
const roundTo = (value: number, digits: number): number => {
  const scale = 10 ** digits;
  return Math.round(value * scale) / scale;
};

function bisectLeft(values: number[], target: number): number {
  let low = 0;
  let high = values.length;
  while (low < high) {
    const middle = (low + high) >> 1;
    if (values[middle] < target) low = middle + 1;
    else high = middle;
  }
  return low;
}

/** 노선 [누가거리, x, y] 위 그 자리와 좌측 법선 [x, y, nx, ny]. 짝: `route_frame`. */
export function routeFrame(route: Array<[number, number, number]>, chainage: number): number[] {
  const chainages = route.map((item) => item[0]);
  const index = Math.min(Math.max(bisectLeft(chainages, chainage), 1), route.length - 1);
  const [c0, x0, y0] = route[index - 1];
  const [c1, x1, y1] = route[index];
  const dx = x1 - x0;
  const dy = y1 - y0;
  const length = Math.hypot(dx, dy) || 1.0;
  const ratio = c1 > c0 ? (chainage - c0) / (c1 - c0) : 0.0;
  return [x0 + dx * ratio, y0 + dy * ratio, -dy / length, dx / length];
}

function groundOf(samples: FootprintPoint[]): Array<[number, number]> {
  return samples
    .filter(
      (item) =>
        ("valid" in item ? Boolean(item.valid) : true) && typeof item.elevation_m === "number",
    )
    .map((item): [number, number] => [Number(item.offset_m), Number(item.elevation_m)])
    .sort((a, b) => a[0] - b[0] || a[1] - b[1]);
}

function groundAt(ground: Array<[number, number]>, offset: number): number {
  const offsets = ground.map(([x]) => x);
  const index = Math.min(Math.max(bisectLeft(offsets, offset), 1), ground.length - 1);
  const [x0, z0] = ground[index - 1] ?? ground[ground.length - 1];
  const [x1, z1] = ground[index];
  return z0 + (z1 - z0) * (x1 > x0 ? (offset - x0) / (x1 - x0) : 0.0);
}

/** 도로 끝에서 지반이 노면보다 높으면 그 쪽 비탈은 깎기. 짝: `side_is_cut`. */
export function sideIsCut(samples: FootprintPoint[], edge: number, elevation: number): boolean {
  const ground = groundOf(samples);
  return ground.length >= 2 && groundAt(ground, edge) > elevation;
}

/** 도로 끝에서 바깥으로 — 설계선이 원지반에 닿는 오프셋(비탈 끝). 짝: `slope_end`. */
export function slopeEnd(
  designLine: FootprintPoint[],
  samples: FootprintPoint[],
  edge: number,
  side: Side,
): number {
  const ground = groundOf(samples);
  const points = designLine
    .map((p): [number, number] => [Number(p.offset_m), Number(p.elevation_m)])
    .sort((a, b) => a[0] - b[0] || a[1] - b[1]);
  const outward =
    side === "left"
      ? points.filter((p) => p[0] > edge)
      : [...points].reverse().filter((p) => p[0] < edge);
  if (!ground.length) return outward.length ? outward[outward.length - 1][0] : edge;
  let end = edge;
  let differs = false;
  for (const [offset, elevation] of outward) {
    if (Math.abs(elevation - groundAt(ground, offset)) <= 1e-3) return differs ? offset : end;
    differs = true;
    end = offset;
  }
  return end;
}

/** 측점 한 자리 → `slope_pieces` 줄 · 도로 끝이 없으면 null. 짝: `slope_records` 한 줄. */
export function footprintRecord(station: FootprintStation): FootprintRecord | null {
  const edges = station.design?.road_edges;
  const left = Number(edges?.left?.offset_m);
  const right = Number(edges?.right?.offset_m);
  if (edges?.left?.offset_m == null || edges?.right?.offset_m == null) return null;
  if (!Number.isFinite(left) || !Number.isFinite(right)) return null;
  const line = station.design?.design_line ?? [];
  const samples = station.samples ?? [];
  const record: FootprintRecord = {
    chainage_m: station.chainage_m,
    left_edge_m: left,
    left_end_m: slopeEnd(line, samples, left, "left"),
    right_edge_m: right,
    right_end_m: slopeEnd(line, samples, right, "right"),
  };
  for (const side of SIDES) {
    const elevation = edges[side]?.elevation_m;
    if (typeof elevation === "number") {
      record[`${side}_cut`] = sideIsCut(samples, record[`${side}_edge_m`], elevation);
    }
  }
  const length = Math.hypot(station.tx, station.ty) || 1.0;
  record.x = station.x;
  record.y = station.y;
  record.nx = -station.ty / length;
  record.ny = station.tx / length;
  return record;
}

/** 한 선을 참 · 거짓 구간으로 끊음 — 바뀌는 자리 점은 앞뒤가 나눠 가져 이어짐. */
function splitRuns(points: Line, flags: boolean[]): [Line[], Line[]] {
  const runs: { true: Line[]; false: Line[] } = { true: [], false: [] };
  let current: Line = [];
  let previous: boolean | null = null;
  points.forEach((point, index) => {
    const flag = flags[index];
    if (flag !== previous) {
      if (current.length) current.push(point);
      current = [point];
      runs[`${flag}`].push(current);
      previous = flag;
    } else {
      current.push(point);
    }
  });
  return [runs.true.filter((run) => run.length >= 2), runs.false.filter((run) => run.length >= 2)];
}

/** 절/성토선 매끄럽게(353-1) — 네 선 중 하나라도 사이 가운데 점에서 이보다 꺾이면 반으로 나눔(°). 짝 같은 이름. */
export const SPLIT_TURN_DEG = 2.0;
/** 나눔 깊이 상한(2 m → 12.5 cm). */
export const SPLIT_DEPTH = 4;
/** 사이 점 법선을 재는 앞뒤 거리(m) — 측점 횡단 틀(`stationFrameAt`)과 같은 값. */
export const NORMAL_PROBE_M = 1.0;

type Frame = [number, number, number, number];

/** 노선 위 그 자리와 좌측 법선 — 법선은 앞뒤 ±1 m 두 점을 잇는 방향. 짝: `route_normal`. */
export function routeNormal(route: Array<[number, number, number]>, chainage: number): Frame {
  const [x, y, nx, ny] = routeFrame(route, chainage);
  const first = route[0][0];
  const last = route[route.length - 1][0];
  let before = Math.max(first, chainage - NORMAL_PROBE_M);
  let after = Math.min(last, chainage + NORMAL_PROBE_M);
  if (after - before <= 1e-9) {
    before = Math.max(first, chainage - 1e-3);
    after = Math.min(last, chainage + 1e-3);
  }
  const [x0, y0] = routeFrame(route, before);
  const [x1, y1] = routeFrame(route, after);
  const length = Math.hypot(x1 - x0, y1 - y0);
  if (length <= 1e-9) return [x, y, nx, ny];
  return [x, y, -(y1 - y0) / length, (x1 - x0) / length];
}

function bisectRight(values: number[], target: number): number {
  let low = 0;
  let high = values.length;
  while (low < high) {
    const middle = (low + high) >> 1;
    if (target < values[middle]) high = middle;
    else low = middle + 1;
  }
  return low;
}

type Knots = [number[], number[], number[]];

/** 단조 3차(Fritsch–Carlson) 꺾임점 기울기 — 이웃 값 사이를 넘지 않음. 짝: `_pchip_slopes`. */
function pchipSlopes(xs: number[], ys: number[]): number[] {
  const n = xs.length;
  if (n < 2) return xs.map(() => 0);
  const h = xs.slice(1).map((x, i) => x - xs[i]);
  const delta = h.map((span, i) => (ys[i + 1] - ys[i]) / span);
  const slopes = [delta[0], ...new Array<number>(n - 2).fill(0), delta[n - 2]];
  for (let k = 1; k < n - 1; k += 1) {
    if (delta[k - 1] * delta[k] > 0) {
      const w1 = 2 * h[k] + h[k - 1];
      const w2 = h[k] + 2 * h[k - 1];
      slopes[k] = (w1 + w2) / (w1 / delta[k - 1] + w2 / delta[k]);
    }
  }
  return slopes;
}

/** 꺾임점 값을 그대로 지나는 단조 3차 보간 — 범위 밖은 끝값. 짝: `_pchip`. */
function pchip([xs, ys, slopes]: Knots, x: number): number {
  if (x <= xs[0]) return ys[0];
  if (x >= xs[xs.length - 1]) return ys[ys.length - 1];
  const i = bisectRight(xs, x) - 1;
  const h = xs[i + 1] - xs[i];
  const t = (x - xs[i]) / h;
  return (
    (1 + 2 * t) * (1 - t) ** 2 * ys[i] +
    t * (1 - t) ** 2 * h * slopes[i] +
    t * t * (3 - 2 * t) * ys[i + 1] +
    t * t * (t - 1) * h * slopes[i + 1]
  );
}

const knots = (xs: number[], ys: number[]): Knots => [xs, ys, pchipSlopes(xs, ys)];

interface SideCurves {
  chainages: number[];
  flags: boolean[];
  switches: number[];
  edge: Knots;
  width: Knots;
}

/** 한 쪽 도로 끝 · 비탈 폭 보간 + 깎기↔쌓기 바뀜 자리(폭 0 = 비탈 끝이 도로 끝으로 모임). 짝: `_side_curves`. */
function sideCurves(records: FootprintRecord[], side: Side): SideCurves {
  const chainages = records.map((record) => record.chainage_m);
  const edges = records.map((record) => record[`${side}_edge_m`]);
  const widths = records.map((record) => record[`${side}_end_m`] - record[`${side}_edge_m`]);
  const flags = records.map((record) => Boolean(record[`${side}_cut`]));
  const switches: number[] = [];
  const widthX = [chainages[0]];
  const widthY = [widths[0]];
  for (let i = 1; i < records.length; i += 1) {
    const c0 = chainages[i - 1];
    const c1 = chainages[i];
    const w0 = Math.abs(widths[i - 1]);
    const w1 = Math.abs(widths[i]);
    const at = c0 + (c1 - c0) * (w0 + w1 > 1e-9 ? w0 / (w0 + w1) : 0.5);
    switches.push(at);
    if (flags[i - 1] !== flags[i] && c0 + 1e-9 < at && at < c1 - 1e-9) {
      widthX.push(at);
      widthY.push(0.0);
    }
    widthX.push(c1);
    widthY.push(widths[i]);
  }
  return {
    chainages,
    flags,
    switches,
    edge: knots(chainages, edges),
    width: knots(widthX, widthY),
  };
}

/** 그 자리 깎기 여부 — 바뀜 자리부터 뒤 측점 것(바뀌는 점은 앞뒤 조각이 나눠 가짐). 짝: `_cut_at`. */
function cutAt(curves: SideCurves, chainage: number): boolean {
  const { flags } = curves;
  const i = bisectRight(curves.chainages, chainage);
  if (i === 0) return flags[0];
  if (i === flags.length) return flags[flags.length - 1];
  if (flags[i - 1] === flags[i]) return flags[i];
  return chainage < curves.switches[i - 1] ? flags[i - 1] : flags[i];
}

/** 진행을 거스르는 점(안쪽 비탈 끝이 곡선 중심을 넘어 접힘)을 버린 남는 점 번호. 짝: `_forward_only`. */
function forwardOnly(points: Line, frames: Frame[]): number[] {
  const kept = points.length ? [0] : [];
  for (let i = 1; i < points.length; i += 1) {
    const last = points[kept[kept.length - 1]];
    const [, , nx, ny] = frames[i];
    if ((points[i][0] - last[0]) * ny - (points[i][1] - last[1]) * nx > 1e-6) kept.push(i);
  }
  return kept;
}

function turnDeg(a: number[], m: number[], b: number[]): number {
  const u = [m[0] - a[0], m[1] - a[1]];
  const v = [b[0] - m[0], b[1] - m[1]];
  return Math.abs(
    (Math.atan2(u[0] * v[1] - u[1] * v[0], u[0] * v[0] + u[1] * v[1]) * 180) / Math.PI,
  );
}

/** 비탈 끝 모서리 둥글게(364-3) — 접힘 버린 자리 · 잔 갈지자가 이보다 꺾이면 둥글림(°). 짝 같은 이름. */
export const ROUND_TURN_DEG = 15.0;
/** 둥글리는 앞뒤 길이(선 따라 m) — 측점 · 깎기↔쌓기 바뀜 점은 넘지 않음 · 그 틈이 ROUND_MIN_M 보다 좁으면 그대로. */
export const ROUND_M = 3.0;
export const ROUND_MIN_M = 0.5;
/** 둥근 곡선 한 마디 꺾임(°) · 되풀이 상한. */
export const ROUND_STEP_DEG = 5.0;
export const ROUND_PASSES = 200;

const dist = (a: number[], b: number[]): number =>
  Math.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2);

/** 가장 많이 꺾인 점부터 앞뒤 같은 길이를 2차 베지어로 바꿈 — 측점(pins) · 바뀜 점 · 양 끝은 그대로.
 *  돌려줌 = 새 점 · 점마다 깎기 여부 · 점마다 원래 번호(새로 만든 점 -1). 짝: `_round_corners`. */
function roundCorners(
  points: Line,
  flags: boolean[],
  pins: boolean[],
): [Line, boolean[], number[]] {
  const pts = points.map((p) => [...p]);
  const fl = [...flags];
  const src = points.map((_p, i) => i);
  const pinned = (i: number): boolean => src[i] >= 0 && pins[src[i]];
  const fixed = (i: number): boolean =>
    i === 0 || i === pts.length - 1 || fl[i] !== fl[i - 1] || pinned(i);
  /** i 에서 step 쪽으로 length(그 전에 붙박인 점이면 거기까지) — [남길 점 번호, 그 자리, 간 길이, 그 자리 선 방향(i 쪽)]. */
  const walk = (i: number, step: number, length: number): [number, number[], number, number[]] => {
    let gone = 0.0;
    let j = i;
    for (;;) {
      const k = j + step;
      const seg = dist(pts[j], pts[k]);
      const toward = [pts[j][0] - pts[k][0], pts[j][1] - pts[k][1]];
      if (gone + seg >= length) {
        const ratio = (length - gone) / seg;
        return [k, [pts[j][0] - toward[0] * ratio, pts[j][1] - toward[1] * ratio], length, toward];
      }
      // 측점은 반만 다가감 — 끝까지 가면 꺾임이 측점에 몰림
      if (fixed(k)) return [k, pts[k], pinned(k) ? (gone + seg) / 2.0 : gone + seg, toward];
      gone += seg;
      j = k;
    }
  };
  /** 두 끝 접선이 만나는 점(곡선이 앞뒤 선에 매끄럽게 붙음) — 못 쓰면 null. */
  const control = (a: number[], ta: number[], b: number[], tb: number[], reach: number) => {
    const den = ta[0] * tb[1] - ta[1] * tb[0];
    if (Math.abs(den) < 1e-12) return null;
    const s = ((b[0] - a[0]) * tb[1] - (b[1] - a[1]) * tb[0]) / den;
    const u = ((b[0] - a[0]) * ta[1] - (b[1] - a[1]) * ta[0]) / den;
    const c = [a[0] + ta[0] * s, a[1] + ta[1] * s];
    if (s <= 0 || u <= 0 || dist(a, c) > 2 * reach || dist(b, c) > 2 * reach) return null;
    return c;
  };
  for (let pass = 0; pass < ROUND_PASSES; pass += 1) {
    let worst = ROUND_TURN_DEG;
    let at = -1;
    let reach = 0.0;
    for (let i = 1; i < pts.length - 1; i += 1) {
      if (fixed(i)) continue;
      const turn = turnDeg(pts[i - 1], pts[i], pts[i + 1]);
      if (turn > worst) {
        const room = Math.min(walk(i, -1, ROUND_M)[2], walk(i, 1, ROUND_M)[2]);
        if (room >= ROUND_MIN_M) [worst, at, reach] = [turn, i, room];
      }
    }
    if (at < 0) break;
    const [before, a, , ta] = walk(at, -1, reach);
    const [after, b, , tb] = walk(at, 1, reach);
    const p = control(a, ta, b, tb, reach) ?? pts[at];
    const count = Math.max(2, Math.ceil(worst / ROUND_STEP_DEG));
    const curve: Line = [];
    for (let n = 0; n <= count; n += 1) {
      const t = n / count;
      const point = [0, 1].map((k) =>
        roundTo((1 - t) ** 2 * a[k] + 2 * t * (1 - t) * p[k] + t * t * b[k], 4),
      );
      if (dist(point, pts[before]) > 1e-6 && dist(point, pts[after]) > 1e-6) curve.push(point);
    }
    pts.splice(before + 1, after - before - 1, ...curve);
    fl.splice(before + 1, after - before - 1, ...curve.map(() => fl[at]));
    src.splice(before + 1, after - before - 1, ...curve.map(() => -1));
  }
  return [pts, fl, src];
}

/** 곡선 · 폭이 가파르게 바뀌는 자리 — 가운데 점에서 많이 꺾이는 사이를 반씩 나눔. 짝: `_densify`. */
function densify(
  chainages: number[],
  frameOf: (chainage: number) => Frame,
  place: (chainage: number, frame: Frame) => Line,
): [number[], Frame[]] {
  const split = (c0: number, p0: Line, c1: number, p1: Line, depth: number): number[] => {
    if (depth >= SPLIT_DEPTH) return [];
    const middle = (c0 + c1) / 2.0;
    const pm = place(middle, frameOf(middle));
    // 4분 점도 봄 — S 자(가운데가 현 위)는 가운데 점만으론 안 꺾여 보임(364-3)
    const q1 = place((c0 + middle) / 2.0, frameOf((c0 + middle) / 2.0));
    const q3 = place((middle + c1) / 2.0, frameOf((middle + c1) / 2.0));
    const triples = [
      ...pm.map((m, k) => [p0[k], m, p1[k]]),
      ...q1.map((q, k) => [p0[k], q, pm[k]]),
      ...q3.map((q, k) => [pm[k], q, p1[k]]),
    ];
    // 되돌아가는 꺾임(90° 넘음)은 접힘 — 버릴 점이라 나누지 않음
    const bends = triples.some(([a, m, b]) => {
      const turn = turnDeg(a, m, b);
      return SPLIT_TURN_DEG < turn && turn < 90.0;
    });
    if (!bends) return [];
    return [
      ...split(c0, p0, middle, pm, depth + 1),
      middle,
      ...split(middle, pm, c1, p1, depth + 1),
    ];
  };
  const points = chainages.map((chainage) => place(chainage, frameOf(chainage)));
  const out = chainages.slice(0, 1);
  for (let i = 1; i < chainages.length; i += 1) {
    out.push(...split(chainages[i - 1], points[i - 1], chainages[i], points[i], 0));
    out.push(chainages[i]);
  }
  return [out, out.map(frameOf)];
}

interface Sampled {
  lines: Record<(typeof KEYS)[number], Line>;
  cut: Record<Side, boolean[]>;
  ticks: Line[];
}

/** 측점 줄 → 네 선 · 쪽마다 깎기 여부 · 눈금. `slope_pieces` 의 몸통. */
function sampleLines(
  route: Array<[number, number, number]>,
  input: FootprintRecord[],
  startM: number,
  endM: number,
  stepM: number,
): Sampled | null {
  const sorted = input
    .map((record) => ({
      ...record,
      left_cut: Boolean(record.left_cut),
      right_cut: Boolean(record.right_cut),
    }))
    .sort((a, b) => a.chainage_m - b.chainage_m);
  if (route.length < 2 || !sorted.length) return null;
  // 같은 누가거리 측점은 뒤 것 하나만
  const records: FootprintRecord[] = [];
  for (const record of sorted) {
    const last = records[records.length - 1];
    if (last && record.chainage_m - last.chainage_m <= 1e-9) records[records.length - 1] = record;
    else records.push(record);
  }
  const curves = { left: sideCurves(records, "left"), right: sideCurves(records, "right") };
  const byChainage = new Map<number, FootprintRecord>();
  for (const record of records) byChainage.set(roundTo(record.chainage_m, 3), record);
  const base = new Set<number>();
  for (const record of records) {
    if (startM <= record.chainage_m && record.chainage_m <= endM)
      base.add(roundTo(record.chainage_m, 3));
  }
  for (let step = startM; step <= endM; step += stepM) base.add(roundTo(step, 3));
  const all = new Set(base);
  for (const side of SIDES) {
    const { flags, switches } = curves[side];
    switches.forEach((at, i) => {
      if (flags[i] !== flags[i + 1] && startM <= at && at <= endM) all.add(at);
    });
  }
  const frameOf = (chainage: number): Frame => {
    const record = byChainage.get(roundTo(chainage, 3));
    const { x, y, nx, ny } = record ?? {};
    if (x !== undefined && y !== undefined && nx !== undefined && ny !== undefined)
      return [x, y, nx, ny];
    return routeNormal(route, chainage);
  };
  const valuesAt = (chainage: number): Record<string, number> => {
    const values: Record<string, number> = {};
    for (const side of SIDES) {
      const edge = pchip(curves[side].edge, chainage);
      values[`${side}_edge_m`] = edge;
      values[`${side}_end_m`] = edge + pchip(curves[side].width, chainage);
    }
    return values;
  };
  const place = (chainage: number, [x, y, nx, ny]: Frame): Line => {
    const values = valuesAt(chainage);
    return KEYS.map((key) => [x + nx * values[key], y + ny * values[key]]);
  };
  const [chainages, frames] = densify(
    [...all].sort((a, b) => a - b),
    frameOf,
    place,
  );
  const offsets = chainages.map(valuesAt);
  const raw = Object.fromEntries(KEYS.map((key) => [key, []])) as unknown as Sampled["lines"];
  frames.forEach(([x, y, nx, ny], i) => {
    for (const key of KEYS)
      raw[key].push([roundTo(x + nx * offsets[i][key], 4), roundTo(y + ny * offsets[i][key], 4)]);
  });
  const kept = Object.fromEntries(
    KEYS.map((key) => [key, forwardOnly(raw[key], frames)]),
  ) as unknown as Record<(typeof KEYS)[number], number[]>;
  const lines = Object.fromEntries(
    KEYS.map((key) => [key, kept[key].map((i) => raw[key][i])]),
  ) as unknown as Sampled["lines"];
  const cut: Record<Side, boolean[]> = {
    left: kept.left_end_m.map((i) => cutAt(curves.left, chainages[i])),
    right: kept.right_end_m.map((i) => cutAt(curves.right, chainages[i])),
  };
  const keptSets = { left: new Set(kept.left_end_m), right: new Set(kept.right_end_m) };
  for (const side of SIDES) {
    const key = `${side}_end_m` as const;
    const pins = kept[key].map((i) => byChainage.has(roundTo(chainages[i], 3)));
    const [line, flags, src] = roundCorners(lines[key], cut[side], pins);
    lines[key] = line;
    cut[side] = flags;
    keptSets[side] = new Set(src.filter((j) => j >= 0).map((j) => kept[key][j]));
  }
  // 눈금은 도로 끝에서 비탈 끝으로 — 측점 · 눈금 간격 자리만 · 긴 것 · 짧은 것이 번갈아(납품
  // 도면 관례) · 접혀 버리거나 둥글린 자리는 뺌.
  const ticks: Line[] = [];
  const position = new Map(chainages.map((chainage, i) => [chainage, i]));
  [...base]
    .sort((a, b) => a - b)
    .forEach((chainage, index) => {
      const i = position.get(chainage) ?? 0;
      const [x, y, nx, ny] = frames[i];
      for (const side of SIDES) {
        const edge = offsets[i][`${side}_edge_m`];
        const end = offsets[i][`${side}_end_m`];
        if (Math.abs(end - edge) < 0.05 || !keptSets[side].has(i)) continue;
        const reach = index % 2 === 0 ? end : edge + (end - edge) / 2.0;
        ticks.push([raw[`${side}_edge_m`][i], [x + nx * reach, y + ny * reach]]);
      }
    });
  return { lines, cut, ticks };
}

/** 측점 줄 → 도로 끝선 · 쌓기 · 깎기 비탈 끝선 · 눈금. 짝: `slope_pieces`. */
export function slopePieces(
  route: Array<[number, number, number]>,
  input: FootprintRecord[],
  startM: number,
  endM: number,
  stepM: number = TICK_STEP_M,
): SlopePieces {
  const sampled = sampleLines(route, input, startM, endM, stepM);
  if (!sampled) return { edge: [], fill: [], cut: [], ticks: [] };
  const { lines, cut, ticks } = sampled;
  const cutLines: Line[] = [];
  const fillLines: Line[] = [];
  for (const side of SIDES) {
    const [cutRuns, fillRuns] = splitRuns(lines[`${side}_end_m`], cut[side]);
    cutLines.push(...cutRuns);
    fillLines.push(...fillRuns);
  }
  return { edge: [lines.left_edge_m, lines.right_edge_m], fill: fillLines, cut: cutLines, ticks };
}

/** 측점들 → 평면 발자국(도로 끝이 없는 측점은 뺌). */
export function planFootprint(
  route: Array<[number, number, number]>,
  stations: FootprintStation[],
  startM: number,
  endM: number,
  stepM: number = TICK_STEP_M,
): SlopePieces {
  const records = stations
    .map(footprintRecord)
    .filter((record): record is FootprintRecord => record !== null);
  return slopePieces(route, records, startM, endM, stepM);
}

/** 계약 `PlanFootprint` + 비탈 끝 점마다 깎기 여부 · 눈금 · 측점 줄(다음 계산이 범위 밖을 재사용). */
export interface FootprintLines extends PlanFootprint {
  slopeLeftCut: boolean[];
  slopeRightCut: boolean[];
  ticks: Line[];
  records: FootprintRecord[];
}

/** 측점 줄 → 계약 꼴 평면 발자국(시점 → 종점 · 선은 `slopePieces` 와 같은 점). */
export function footprintLines(
  route: Array<[number, number, number]>,
  records: FootprintRecord[],
  startM: number,
  endM: number,
  stepM: number = TICK_STEP_M,
): FootprintLines {
  const sampled = sampleLines(route, records, startM, endM, stepM);
  if (!sampled) {
    const empty = { roadLeft: [], roadRight: [], slopeLeft: [], slopeRight: [] };
    return { ...empty, slopeLeftCut: [], slopeRightCut: [], ticks: [], records };
  }
  const { lines, cut, ticks } = sampled;
  return {
    roadLeft: lines.left_edge_m as Vertex[],
    roadRight: lines.right_edge_m as Vertex[],
    slopeLeft: lines.left_end_m as Vertex[],
    slopeRight: lines.right_end_m as Vertex[],
    slopeLeftCut: cut.left,
    slopeRightCut: cut.right,
    ticks,
    records,
  };
}