Merge remote-tracking branch 'origin/sub_laptop_2' into main_laptop_1 — 586-0 겹 맞춤 · UI_Page 충돌(points + epsg) 양쪽 살림 · test_582 겹 수 낡은 단언(12 → 모두 바탕)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

D03_PlanAnalysis/D03_PlanAnalysis_UI_LayerDefs.ts

@@ -236,10 +236,21 @@ export function drawRaster(
   map: ScreenMap,
   raster: { raster: PlanRaster; image: HTMLImageElement },
 ): void {
+  // 세 귀퉁이로 놓음 — TM 격자는 경위도 바탕에 대해 수렴각만큼 돌아 있음(586-0)
   const [x0, y0, x1, y1] = raster.raster.box_m;
   const [left, top] = map.toScreen([x0, y1]);
-  const [right, bottom] = map.toScreen([x1, y0]);
-  context.drawImage(raster.image, left, top, right - left, bottom - top);
+  const [right, rightY] = map.toScreen([x1, y1]);
+  const [bottomX, bottom] = map.toScreen([x0, y0]);
+  const { naturalWidth: w, naturalHeight: h } = raster.image;
+  context.transform(
+    (right - left) / w,
+    (rightY - top) / w,
+    (bottomX - left) / h,
+    (bottom - top) / h,
+    left,
+    top,
+  );
+  context.drawImage(raster.image, 0, 0);
 }
 
 /** 켬끔 취향(`key`) — 없거나 깨지면 처음 값. */

D03_PlanAnalysis/D03_PlanAnalysis_UI_Map.ts

@@ -10,6 +10,7 @@
  * 겹은 돌리기 전 그림 좌표로 그리고 받음 — 누른 자리는 `unrotate` 로 되돌려 넘김.
  * 캔버스 두 장(582) — 아래 = 위성 · 바탕 겹(`base`) · 위 = 그은 선 · 재기 · 누름 받음.
  *   마우스 움직임 = 위만 다시 그림 · 화면이 바뀌면(옮김 · 확대 · 돌림 · 겹) 둘 다 · 한 화면 한 번(rAF).
+ * TM 겹(그은 선 · 재기 · 그림 겹)은 경위도로 바꿔 바탕과 같은 자리(586-0 · `localTmFrame`) — 좌표계를 모르면 옛 꼴.
  * ========================================================================== */
 
 import { createMapTools, mapToolButton } from "@ui/ui_template_map_tools";
@@ -19,6 +20,8 @@ import {
   computeMapRect,
   computeRouteView,
   createMetricProjector,
+  createNormalizer,
+  lonLatToScreen,
   normalizedToScreen,
   routeLineColor,
   type ViewState,
@@ -27,6 +30,7 @@ import { bindRouteEditNavigation } from "../B05_Profile/B05_Profile_UI_RouteEdit
 import { createMapRotation } from "../B05_Profile/B05_Profile_UI_RouteEdit_Rotate";
 import { fitCanvas, screenToMetric } from "../B05_Profile/B05_Profile_UI_RouteEdit_View";
 import type { Vertex } from "./logic/D03_PlanAnalysis_Plan";
+import { localTmFrame, tmParams } from "./logic/D03_PlanAnalysis_Tm";
 
 /** 측점 간격(m) — B 규칙 측점과 같음. */
 export const PLAN_STATION_INTERVAL_M = 20;
@@ -48,6 +52,8 @@ export interface PlanMapScene {
   image: HTMLImageElement | null;
   /** 처음 맞출 점(시점 · 종점 · 그은 선). */
   fit: Vertex[];
+  /** 작업 좌표계 — TM 겹을 경위도 바탕에 맞춤(586-0). */
+  epsg?: number | null;
 }
 
 /** 겹이 쓰는 좌표 — 그림 px(돌리기 전) ↔ 작업 좌표계 m · 글자 세우기. */
@@ -105,6 +111,8 @@ export interface PlanMap {
   fit: () => void;
   /** 검증 창구 — 작업 좌표계 점 → 화면에 보이는 px(돌린 뒤 · 그리기 전이면 null). */
   screenOf: (point: Vertex) => [number, number] | null;
+  /** 검증 창구 — 경위도 → 화면 px(바탕 겹 꼴 · 586-0 맞춤 대조). */
+  screenOfLonLat: (lon: number, lat: number) => [number, number] | null;
   /** 검증 창구 — 지금 돌린 각(도). */
   rotationDeg: () => number;
   dispose: () => void;
@@ -204,12 +212,40 @@ export function createPlanMap(events: PlanMapEvents): PlanMap {
     onChange: () => draw(),
   });
 
-  const screenMap = (): ScreenMap => {
-    const projector = createMetricProjector(meta!, view);
+  /** TM ↔ 그림 px — 경위도 바탕에 맞춤(586-0) · 가짜 도엽 · 모르는 좌표계 = 옛 「같은 직사각형」 꼴. */
+  const metricFrame = (): Pick<ScreenMap, "toScreen" | "toMetric" | "pxPerMeter"> => {
+    const params = tmParams(scene.epsg);
+    if (!params || !scene.meta || meta !== scene.meta) {
+      const projector = createMetricProjector(meta!, view);
+      return {
+        toScreen: (point) => projector.toScreen(point[0], point[1]),
+        toMetric: (px, py) => screenToMetric(meta!, view, px, py),
+        pxPerMeter: projector.pxPerMeter,
+      };
+    }
+    const normalizer = createNormalizer(scene.meta);
+    const [x0, y0] = normalizedToScreen(view, 0, 0);
+    const [x1, y1] = normalizedToScreen(view, 1, 1);
+    const frame = localTmFrame(
+      params,
+      (lon, lat) => lonLatToScreen(normalizer, view, lon, lat),
+      (px, py) => [
+        normalizer.lonMin + ((px - x0) / (x1 - x0)) * normalizer.lonRange,
+        normalizer.latMin + (1 - (py - y0) / (y1 - y0)) * normalizer.latRange,
+      ],
+      view.width / 2,
+      view.height / 2,
+    );
     return {
-      toScreen: (point) => projector.toScreen(point[0], point[1]),
-      toMetric: (px, py) => screenToMetric(meta!, view, px, py),
-      pxPerMeter: projector.pxPerMeter,
+      toScreen: (point) => frame.toScreen(point[0], point[1]),
+      toMetric: (px, py) => frame.toMetric(px, py),
+      pxPerMeter: frame.pxPerMeter,
+    };
+  };
+
+  const screenMap = (): ScreenMap => {
+    return {
+      ...metricFrame(),
       view,
       ...marks,
       uprightRad: rotation.uprightRad(),
@@ -380,6 +416,10 @@ export function createPlanMap(events: PlanMapEvents): PlanMap {
       const [x, y] = screenMap().toScreen(point);
       return rotation.rerotate(x, y);
     },
+    screenOfLonLat: (lon, lat) => {
+      if (!scene.meta) return null;
+      return rotation.rerotate(...lonLatToScreen(createNormalizer(scene.meta), view, lon, lat));
+    },
     rotationDeg: () => (rotation.radians() * 180) / Math.PI,
     dispose: () => {
       observer.disconnect();

D03_PlanAnalysis/D03_PlanAnalysis_UI_Page.ts

@@ -577,6 +577,7 @@ export async function renderD03PlanAnalysis(root: HTMLElement): Promise<void> {
     base: () => points,
     lineNames: () => lineNames(network.lines),
     screenOf: map.screenOf,
+    screenOfLonLat: map.screenOfLonLat,
     preview: draw.preview,
     stroke: draw.stroke,
     selected: edit.selected,
@@ -632,7 +633,7 @@ export async function renderD03PlanAnalysis(root: HTMLElement): Promise<void> {
     drawYearPick.setOptions(yearOptions(), String(drawYear));
     const draft = readState<Draft>("d03-plan", projectId);
     if (draft?.version === DRAFT_VERSION && draft.network?.lines?.length) network = draft.network;
-    map.update({ fit: [...points, ...allVertices()] });
+    map.update({ fit: [...points, ...allVertices()], epsg });
     refresh();
     await loadSurface();
     refresh();

D03_PlanAnalysis/logic/D03_PlanAnalysis_Tm.ts

@@ -0,0 +1,138 @@
+/* =============================================================================
+ * D03_PlanAnalysis_Tm.ts
+ * 작업 좌표계(TM m) ↔ 경위도 — 한국 GRS80 TM(EPSG:5185~5188 · 5179) · 화면 한 장 TM 틀(PLAN 586-0).
+ *   짝 = pyproj(`common_util_crs.tm_to_lonlat`) · 거울 시험 `test_586_tm_frame.py`.
+ *   바탕(위성 · 도엽 겹)은 경위도로 펴고 그은 선 · 급경사 그림은 TM 이라, 두 상자를 같은 직사각형으로 보면
+ *   자오선 수렴각만큼 어긋남(D 프로젝트 귀퉁이 63 m) → TM 점을 경위도로 바꿔 바탕과 같은 자리에 놓음.
+ *   DOM · fetch · sessionStorage 없음.
+ * ========================================================================== */
+
+export interface TmParams {
+  lon0: number;
+  lat0: number;
+  k0: number;
+  fe: number;
+  fn: number;
+}
+
+const KOREA_TM: Record<number, TmParams> = {
+  5185: { lon0: 125, lat0: 38, k0: 1, fe: 200000, fn: 600000 },
+  5186: { lon0: 127, lat0: 38, k0: 1, fe: 200000, fn: 600000 },
+  5187: { lon0: 129, lat0: 38, k0: 1, fe: 200000, fn: 600000 },
+  5188: { lon0: 131, lat0: 38, k0: 1, fe: 200000, fn: 600000 },
+  5179: { lon0: 127.5, lat0: 38, k0: 0.9996, fe: 1000000, fn: 2000000 },
+};
+
+/** 아는 좌표계만(GRS80 TM) — 그 밖(옛 Bessel 등) = null. */
+export const tmParams = (epsg: number | null | undefined): TmParams | null =>
+  (epsg && KOREA_TM[epsg]) || null;
+
+// GRS80 · Krüger 6차(Karney 2011) — 수 km 안 mm 아래
+const F = 1 / 298.257222101;
+const N = F / (2 - F);
+const E = Math.sqrt(F * (2 - F));
+const A = (6378137 / (1 + N)) * (1 + N ** 2 / 4 + N ** 4 / 64 + N ** 6 / 256);
+const ALPHA = [
+  N / 2 - (2 * N ** 2) / 3 + (5 * N ** 3) / 16 + (41 * N ** 4) / 180 - (127 * N ** 5) / 288,
+  (13 * N ** 2) / 48 - (3 * N ** 3) / 5 + (557 * N ** 4) / 1440 + (281 * N ** 5) / 630,
+  (61 * N ** 3) / 240 - (103 * N ** 4) / 140 + (15061 * N ** 5) / 26880,
+  (49561 * N ** 4) / 161280 - (179 * N ** 5) / 168,
+  (34729 * N ** 5) / 80640,
+];
+const BETA = [
+  N / 2 - (2 * N ** 2) / 3 + (37 * N ** 3) / 96 - N ** 4 / 360 - (81 * N ** 5) / 512,
+  N ** 2 / 48 + N ** 3 / 15 - (437 * N ** 4) / 1440 + (46 * N ** 5) / 105,
+  (17 * N ** 3) / 480 - (37 * N ** 4) / 840 - (209 * N ** 5) / 4480,
+  (4397 * N ** 4) / 161280 - (11 * N ** 5) / 504,
+  (4583 * N ** 5) / 161280,
+];
+const DELTA = [
+  2 * N - (2 * N ** 2) / 3 - 2 * N ** 3 + (116 * N ** 4) / 45,
+  (7 * N ** 2) / 3 - (8 * N ** 3) / 5 - (227 * N ** 4) / 45,
+  (56 * N ** 3) / 15 - (136 * N ** 4) / 35,
+  (4279 * N ** 4) / 630,
+];
+const RAD = Math.PI / 180;
+
+/** 경위도 → 등각 (ξ, η). */
+function conformal(lonRad: number, latRad: number): [number, number] {
+  const s = Math.sin(latRad);
+  const t = Math.sinh(Math.atanh(s) - E * Math.atanh(E * s));
+  const xi1 = Math.atan2(t, Math.cos(lonRad));
+  const eta1 = Math.atanh(Math.sin(lonRad) / Math.sqrt(1 + t * t));
+  let xi = xi1;
+  let eta = eta1;
+  ALPHA.forEach((a, i) => {
+    const j = 2 * (i + 1);
+    xi += a * Math.sin(j * xi1) * Math.cosh(j * eta1);
+    eta += a * Math.cos(j * xi1) * Math.sinh(j * eta1);
+  });
+  return [xi, eta];
+}
+
+const xi0Of = (p: TmParams): number => conformal(0, p.lat0 * RAD)[0];
+
+export function lonLatToTm(p: TmParams, lon: number, lat: number): [number, number] {
+  const [xi, eta] = conformal((lon - p.lon0) * RAD, lat * RAD);
+  return [p.fe + p.k0 * A * eta, p.fn + p.k0 * A * (xi - xi0Of(p))];
+}
+
+export function tmToLonLat(p: TmParams, x: number, y: number): [number, number] {
+  const xi = (y - p.fn) / (p.k0 * A) + xi0Of(p);
+  const eta = (x - p.fe) / (p.k0 * A);
+  let xi1 = xi;
+  let eta1 = eta;
+  BETA.forEach((b, i) => {
+    const j = 2 * (i + 1);
+    xi1 -= b * Math.sin(j * xi) * Math.cosh(j * eta);
+    eta1 -= b * Math.cos(j * xi) * Math.sinh(j * eta);
+  });
+  const chi = Math.asin(Math.sin(xi1) / Math.cosh(eta1));
+  let lat = chi;
+  DELTA.forEach((d, i) => (lat += d * Math.sin(2 * (i + 1) * chi)));
+  return [p.lon0 + Math.atan2(Math.sinh(eta1), Math.cos(xi1)) / RAD, lat / RAD];
+}
+
+/** 화면 한 장 TM 틀 — 화면 가운데 둘레 1차 맞춤(그 화면 안 1 px 아래 · 그림 겹은 세 귀퉁이로 놓음). */
+export interface TmFrame {
+  toScreen: (x: number, y: number) => [number, number];
+  toMetric: (px: number, py: number) => [number, number];
+  pxPerMeter: number;
+}
+
+/** 미분 걸음(m) — 가운데 차분. */
+const STEP_M = 25;
+
+/**
+ * 바탕이 경위도를 화면에 펴는 길(`project` · `unproject`)을 받아, 화면 가운데(`cx`, `cy`) 둘레에서
+ * TM → 화면을 1차식으로 맞춤. 바탕이 어떤 꼴(캔버스 직사각형 · MapLibre 메르카토르)이든 같은 식.
+ */
+export function localTmFrame(
+  p: TmParams,
+  project: (lon: number, lat: number) => [number, number],
+  unproject: (px: number, py: number) => [number, number],
+  cx: number,
+  cy: number,
+): TmFrame {
+  const [mx, my] = lonLatToTm(p, ...unproject(cx, cy));
+  const at = (x: number, y: number): [number, number] => project(...tmToLonLat(p, x, y));
+  const [ox, oy] = at(mx, my);
+  const [x1, y1] = at(mx + STEP_M, my);
+  const [x0, y0] = at(mx - STEP_M, my);
+  const [x3, y3] = at(mx, my + STEP_M);
+  const [x2, y2] = at(mx, my - STEP_M);
+  const a = (x1 - x0) / (2 * STEP_M);
+  const b = (y1 - y0) / (2 * STEP_M);
+  const c = (x3 - x2) / (2 * STEP_M);
+  const d = (y3 - y2) / (2 * STEP_M);
+  const det = a * d - b * c || 1;
+  return {
+    toScreen: (x, y) => [ox + a * (x - mx) + c * (y - my), oy + b * (x - mx) + d * (y - my)],
+    toMetric: (px, py) => {
+      const dx = px - ox;
+      const dy = py - oy;
+      return [mx + (d * dx - c * dy) / det, my + (a * dy - b * dx) / det];
+    },
+    pxPerMeter: Math.sqrt(Math.abs(det)),
+  };
+}

resources/tester/helper_586_tm_frame.cjs

@@ -0,0 +1,41 @@
+/* 586 TM ↔ 경위도 · 화면 TM 틀 헬퍼 — `D03_PlanAnalysis_Tm.ts` 를 stdin 점 목록으로 돌려 JSON 으로 냄.
+ *   입력 { points: [[epsg, x, y]], lonlat: [[epsg, lon, lat]], frames: [{ epsg, box, view, probes }] }
+ */
+const path = require("path");
+const { makeLoader } = require("./helper_ts_stub_loader.cjs");
+
+const ROOT = path.join(__dirname, "..", "..");
+const { load } = makeLoader({ root: ROOT });
+const tm = load("D03_PlanAnalysis", "logic", "D03_PlanAnalysis_Tm.ts");
+
+const input = JSON.parse(require("fs").readFileSync(0, "utf-8"));
+const out = {
+  unknown: tm.tmParams(5174),
+  toLonLat: input.points.map(([epsg, x, y]) => tm.tmToLonLat(tm.tmParams(epsg), x, y)),
+  toTm: input.lonlat.map(([epsg, lon, lat]) => tm.lonLatToTm(tm.tmParams(epsg), lon, lat)),
+  frames: input.frames.map(({ epsg, box, view, probes }) => {
+    // 경위도 상자를 화면 직사각형에 펴는 바탕(캔버스 지금 꼴) · 가운데 = (cx, cy)
+    const [lonMin, latMin, lonMax, latMax] = box;
+    const [w, h, x0, y0, sx, sy] = view;
+    const project = (lon, lat) => [
+      x0 + ((lon - lonMin) / (lonMax - lonMin)) * sx,
+      y0 + ((latMax - lat) / (latMax - latMin)) * sy,
+    ];
+    const unproject = (px, py) => [
+      lonMin + ((px - x0) / sx) * (lonMax - lonMin),
+      latMax - ((py - y0) / sy) * (latMax - latMin),
+    ];
+    const p = tm.tmParams(epsg);
+    const frame = tm.localTmFrame(p, project, unproject, w / 2, h / 2);
+    return {
+      pxPerMeter: frame.pxPerMeter,
+      probes: probes.map(([x, y]) => {
+        const exact = project(...tm.tmToLonLat(p, x, y));
+        const got = frame.toScreen(x, y);
+        const back = frame.toMetric(...got);
+        return { exact, got, back };
+      }),
+    };
+  }),
+};
+process.stdout.write(JSON.stringify(out));

resources/tester/test_582_contour_lod.py

@@ -75,7 +75,7 @@ def test_D03_만_켬():
     layers = _read("D03_PlanAnalysis/D03_PlanAnalysis_UI_Layers.ts")
     assert "indexLayerLod(prepare(collection" in layers
     # 581-1 합침 — 겹 모두 바탕 캔버스
-    assert layers.count("base: true") == layers.count("draw: (context, map)") == 12
+    assert layers.count("base: true") == layers.count("draw: (context, map)") >= 12  # 겹 모두 바탕(581 · 584 로 늘어남)
     plan_map = _read("D03_PlanAnalysis/D03_PlanAnalysis_UI_Map.ts")
     assert "requestAnimationFrame(flush)" in plan_map
     assert "drawTop();" in plan_map

resources/tester/test_586_tm_frame.py

@@ -0,0 +1,120 @@
+# -*- coding: utf-8 -*-
+"""586-0 TM ↔ 경위도 거울 · 화면 TM 틀 — 그은 선 · 급경사 그림을 위성 · 도엽 겹과 같은 자리에.
+
+- `D03_PlanAnalysis_Tm.ts` 의 TM ↔ 경위도 = pyproj(`common_util_crs`) 와 1 mm 안(5185~5188 · 5179)
+- 모르는 좌표계(5174 Bessel) = null(지금 꼴로 그림)
+- 화면 TM 틀(가운데 1차 맞춤) = 정식 변환 자리와 화면 안 0.5 px 안 · 되돌림 = 1 mm 안
+- 옛 「같은 직사각형」 꼴은 D 프로젝트 귀퉁이에서 수십 m 어긋남(고친 까닭)
+
+Node 헬퍼(`helper_586_tm_frame.cjs`)가 진짜 TS 를 돌린다.
+"""
+
+import json
+import math
+import os
+import subprocess
+
+import pytest
+
+from common_util.common_util_crs import lonlat_to_tm, tm_to_lonlat
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+
+# 검증_sub2_D 위성 상자(EPSG:5186 · vworld-meta)
+META = {
+    "x_min": 282572.566652281,
+    "x_max": 288034.8885857916,
+    "y_min": 408543.914277056,
+    "y_max": 411930.1592677671,
+    "lon_min": 127.9193115234375,
+    "lon_max": 127.979736328125,
+    "lat_min": 36.270850207239036,
+    "lat_max": 36.30184530368433,
+}
+POINTS = [
+    (5186, 285303.7, 410237.0),
+    (5186, 282572.6, 411930.2),
+    (5186, 288034.9, 408543.9),
+    (5185, 180000.0, 450000.0),
+    (5187, 210000.0, 350000.0),
+    (5188, 190000.0, 520000.0),
+    (5179, 960000.0, 1800000.0),
+]
+LONLAT = [(5186, 127.95, 36.28), (5187, 129.1, 35.5), (5179, 127.0, 37.5), (5185, 126.3, 34.8)]
+
+
+def _view(w, h, scale, ox, oy):
+    """지금 캔버스 꼴 — 상자 비율 그대로 화면에 맞추고 배율 · 옮김."""
+    ratio = (META["x_max"] - META["x_min"]) / (META["y_max"] - META["y_min"])
+    mw, mh = (w, w / ratio) if ratio > w / h else (h * ratio, h)
+    x0 = (w - mw) / 2 * scale + w / 2 * (1 - scale) + ox
+    y0 = (h - mh) / 2 * scale + h / 2 * (1 - scale) + oy
+    return [w, h, x0, y0, mw * scale, mh * scale]
+
+
+@pytest.fixture(scope="module")
+def r():
+    box = [META["lon_min"], META["lat_min"], META["lon_max"], META["lat_max"]]
+    corners = [
+        (META["x_min"], META["y_max"]),
+        (META["x_max"], META["y_max"]),
+        (META["x_min"], META["y_min"]),
+        (META["x_max"], META["y_min"]),
+        (285303.7, 410237.0),
+    ]
+    frames = [
+        {"epsg": 5186, "box": box, "view": _view(1400, 900, 1, 0, 0), "probes": corners},
+        {
+            "epsg": 5186,
+            "box": box,
+            "view": _view(1400, 900, 40, -3000, 2000),
+            "probes": [(285303.7 + dx, 410237.0 + dy) for dx in (-40, 0, 40) for dy in (-25, 25)],
+        },
+    ]
+    payload = {"points": POINTS, "lonlat": LONLAT, "frames": frames}
+    proc = subprocess.run(
+        ["node", os.path.join(HERE, "helper_586_tm_frame.cjs")],
+        input=json.dumps(payload),
+        capture_output=True,
+        text=True,
+        encoding="utf-8",
+        timeout=60,
+    )
+    assert proc.returncode == 0, proc.stderr
+    return json.loads(proc.stdout)
+
+
+def test_TM_경위도_pyproj_와_같음(r):
+    for (epsg, x, y), (lon, lat) in zip(POINTS, r["toLonLat"]):
+        want_lon, want_lat = tm_to_lonlat(x, y, epsg)
+        assert abs(lon - want_lon) < 1e-8 and abs(lat - want_lat) < 1e-8, (epsg, x, y)
+    for (epsg, lon, lat), (x, y) in zip(LONLAT, r["toTm"]):
+        want_x, want_y = lonlat_to_tm(lon, lat, epsg)
+        assert math.hypot(x - want_x, y - want_y) < 1e-3, (epsg, lon, lat)
+
+
+def test_모르는_좌표계는_null(r):
+    assert r["unknown"] is None
+
+
+def test_화면_TM_틀이_정식_자리와_같음(r):
+    for frame in r["frames"]:
+        for probe in frame["probes"]:
+            (ex, ey), (gx, gy) = probe["exact"], probe["got"]
+            assert math.hypot(ex - gx, ey - gy) < 0.5, probe
+    # 되돌림(화면 → TM)
+    probes = [(285303.7 + dx, 410237.0 + dy) for dx in (-40, 0, 40) for dy in (-25, 25)]
+    for (x, y), probe in zip(probes, r["frames"][1]["probes"]):
+        bx, by = probe["back"]
+        assert math.hypot(bx - x, by - y) < 1e-3
+
+
+def test_옛_같은_직사각형_꼴은_귀퉁이에서_어긋남():
+    """고친 까닭 — TM 상자 · 경위도 상자를 같은 직사각형으로 보면 위 오른쪽 귀퉁이 수십 m."""
+    x, y = META["x_max"], META["y_max"]
+    lon, lat = tm_to_lonlat(x, y, 5186)
+    w = META["x_max"] - META["x_min"]
+    h = META["y_max"] - META["y_min"]
+    dx = ((lon - META["lon_min"]) / (META["lon_max"] - META["lon_min"]) - 1) * w
+    dy = ((META["lat_max"] - lat) / (META["lat_max"] - META["lat_min"])) * h
+    assert math.hypot(dx, dy) > 50