From 158c5ff37fb7b1be1d7a326baa8f6ab3eb2fc949 Mon Sep 17 00:00:00 2001
From: umsangdon <umsangdon@gmail.com>
Date: Thu, 8 Oct 2026 12:20:08 +0900
Subject: [PATCH 1/3] =?UTF-8?q?feat(B06):=20=EC=9C=A0=EC=B6=9C=EC=B8=A1=20?=
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Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013rJwJMVL4EE31y77TB11AP
---
 ...5_Profile_UI_Corridor_Station_Structure.ts |   6 +-
 B06_Section/B06_Section_UI_Cross_Box.ts       |   2 +-
 B06_Section/B06_Section_UI_Cross_Box_Geom.ts  |  12 +-
 B06_Section/B06_Section_UI_Cross_Culvert.ts   |  11 +-
 .../B06_Section_UI_Cross_Culvert_Basin.ts     |  30 ++---
 .../B06_Section_UI_Cross_Culvert_Extra.ts     |  39 +++----
 .../B06_Section_UI_Cross_Culvert_Geom.ts      |   5 +-
 .../B06_Section_UI_Cross_Culvert_Tiers.ts     |   3 +-
 .../B06_Section_UI_Cross_Culvert_Types.ts     |   4 +-
 B06_Section/B06_Section_UI_Cross_Ford.ts      |   2 +-
 B06_Section/B06_Section_UI_Cross_Ford_Geom.ts |   4 +-
 .../B06_Section_UI_Cross_Structure_Cut.ts     | 107 ++++++++++++++++++
 resources/tester/helper_91_ground_free.cjs    |  61 ++++++++++
 resources/tester/test_79_guard_shape.py       |   3 +-
 resources/tester/test_91_ground_free.py       |  31 +++++
 15 files changed, 251 insertions(+), 69 deletions(-)
 create mode 100644 B06_Section/B06_Section_UI_Cross_Structure_Cut.ts

diff --git a/B05_Profile/B05_Profile_UI_Corridor_Station_Structure.ts b/B05_Profile/B05_Profile_UI_Corridor_Station_Structure.ts
index e0c6913f4..13b7a6c7e 100644
--- a/B05_Profile/B05_Profile_UI_Corridor_Station_Structure.ts
+++ b/B05_Profile/B05_Profile_UI_Corridor_Station_Structure.ts
@@ -211,7 +211,7 @@ export function fordSilhouettes(section: CrossSection): StructureSilhouette[] {
       points.push(floorOuter);
       patchPoints.push(floorOuter);
       const run: OffsetPoint[] = [floorOuter];
-      for (const cutPoint of [side.cutLine.from, side.cutLine.to]) {
+      for (const cutPoint of side.cutLine) {
         const at = { offset_m: cutPoint.offset, elevation_m: cutPoint.elevation };
         points.push(at);
         patchPoints.push(at);
@@ -347,8 +347,8 @@ export function culvertSilhouettes(section: CrossSection): StructureSilhouette[]
     }
     // 집수정이 원지반에 박히면 절토선까지 — 그만큼 원지반을 걷어낸다.
     if (layout.basin.cutLine) {
-      push(inletSide, [layout.basin.cutLine.from, layout.basin.cutLine.to]);
-      addRun(inletSide, [layout.basin.cutLine.from, layout.basin.cutLine.to]);
+      push(inletSide, layout.basin.cutLine);
+      addRun(inletSide, layout.basin.cutLine);
       basinCut = true;
     }
     spans[inletSide] = basinSpanOf(section);
diff --git a/B06_Section/B06_Section_UI_Cross_Box.ts b/B06_Section/B06_Section_UI_Cross_Box.ts
index c83a1a607..ab2422824 100644
--- a/B06_Section/B06_Section_UI_Cross_Box.ts
+++ b/B06_Section/B06_Section_UI_Cross_Box.ts
@@ -136,7 +136,7 @@ export function appendBoxOverlay(
     }));
     if (side.cutLine)
       lines.push({
-        points: [side.cutLine.from, side.cutLine.to],
+        points: side.cutLine,
         text: `${mark}측 끝 절토선(계획선)`,
       });
     for (const line of lines) {
diff --git a/B06_Section/B06_Section_UI_Cross_Box_Geom.ts b/B06_Section/B06_Section_UI_Cross_Box_Geom.ts
index a9ae4f1b3..247e0dae7 100644
--- a/B06_Section/B06_Section_UI_Cross_Box_Geom.ts
+++ b/B06_Section/B06_Section_UI_Cross_Box_Geom.ts
@@ -26,6 +26,7 @@ import type {
 import { buildExtrasAt } from "./B06_Section_UI_Cross_Culvert_Extra";
 import { FILL_SLOPE_RATIO_MIN } from "./B06_Section_UI_Cross_Culvert_Const";
 import { designInterpolator, groundInterpolator } from "./B06_Section_UI_Cross_Culvert_Solve";
+import { structureCutPoints, structureCutSpec } from "./B06_Section_UI_Cross_Structure_Cut";
 
 /** 구체 한쪽 끝의 조작값 — 좌·우를 따로 잡는다(2026-08-25 사용자). */
 export interface BoxSideAdjust {
@@ -135,7 +136,8 @@ export function computeBoxLayout(
   // 본체는 늘 수평(79-7) — 좌 · 우 표고 조정이 달라도(옛 저장) 평균 하나로 섬.
   const riseM = (adjust.left.riseM + adjust.right.riseM) / 2;
   const sampleOffsets = groundSamples.map((sample) => sample.offset_m ?? 0);
-  const cutSlopeRatio = section.design?.cut_slope_ratio ?? 1.0;
+  // 끝 절토 = 본선 절토 사면과 같은 복합경사(91-4)
+  const cutSpec = structureCutSpec(section.design);
 
   const sideOf = (role: BoxSideRole): BoxSideLayout => {
     const outward = role === "left" ? 1 : -1;
@@ -172,13 +174,7 @@ export function computeBoxLayout(
     let cutLine: BasinLayout["cutLine"] = null;
     let fillSegments: OutletFillSegment[] = [];
     if (groundAt(end.offset) > end.elevation + 0.05) {
-      for (let h = 0.05; h <= 20; h += 0.05) {
-        const probe = end.offset + outward * cutSlopeRatio * h;
-        if (groundAt(probe) <= end.elevation + h) {
-          cutLine = { from: end, to: { offset: probe, elevation: end.elevation + h } };
-          break;
-        }
-      }
+      cutLine = structureCutPoints(end, outward, cutSpec, groundAt);
     } else if (groundAt(end.offset) < end.elevation - 0.05) {
       fillSegments = buildExtrasAt(end, {
         startBottomElevation: bottomElevation,
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert.ts b/B06_Section/B06_Section_UI_Cross_Culvert.ts
index 245e18dd4..c05df849a 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert.ts
@@ -225,11 +225,12 @@ export function appendCulvertOverlay(
       layer.append(shape);
     }
     if (basin.cutLine) {
-      const cut = document.createElementNS(SVG_NS, "line");
-      cut.setAttribute("x1", String(x(basin.cutLine.from.offset)));
-      cut.setAttribute("y1", String(toDisplayY(basin.cutLine.from.elevation)));
-      cut.setAttribute("x2", String(x(basin.cutLine.to.offset)));
-      cut.setAttribute("y2", String(toDisplayY(basin.cutLine.to.elevation)));
+      // 점열(암 무릎 · 소단 · 91-4)
+      const cut = document.createElementNS(SVG_NS, "polyline");
+      cut.setAttribute(
+        "points",
+        basin.cutLine.map((point) => `${x(point.offset)},${toDisplayY(point.elevation)}`).join(" "),
+      );
       // 절토선은 **공사 계획선**이다 — 설계선과 같은 보라 실선으로 그린다
       // (2026-08-20 사용자 ②).
       cut.setAttribute("class", "b06-chart__design-cross");
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert_Basin.ts b/B06_Section/B06_Section_UI_Cross_Culvert_Basin.ts
index 3ef18d3fc..3d362750a 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert_Basin.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert_Basin.ts
@@ -20,7 +20,7 @@ import {
   REVET_FREEBOARD_M,
   REVET_LEAN_RATIO,
 } from "./B06_Section_UI_Cross_Culvert_Const";
-import type { CulvertSideSpec } from "./B06_Section_Api_Fetch";
+import type { CrossDesign, CulvertSideSpec } from "./B06_Section_Api_Fetch";
 import {
   minShoulderWallOffset,
   slopeLengthAlong,
@@ -34,6 +34,7 @@ import type {
   OffsetPoint,
   InletStructureChoice,
 } from "./B06_Section_UI_Cross_Culvert_Types";
+import { structureCutPoints, structureCutSpec } from "./B06_Section_UI_Cross_Structure_Cut";
 
 /** 자동(기본) 집수정 모양(54-36) — 좌측 폼 「(기본)」 표시도 이 값. */
 export const DEFAULT_BASIN_SHAPE: BasinShape = "L";
@@ -140,8 +141,10 @@ export interface BasinBuildInput {
   /** 이 측의 노견 끝 점 — 벽 상단 접점·I형 높이 성장 기준. */
   edge: { offset_m: number; elevation_m: number };
   groundAt: (offset: number) => number;
-  /** 표준단면 절토 경사(1:n) — 절토 계획선용. */
-  cutSlopeRatio: number;
+  /** 표준단면 절토 경사(1:n) — 절토 계획선용(`cutDesign` 이 없을 때 경사 하나). */
+  cutSlopeRatio?: number;
+  /** 측점 설계값 — 있으면 절토선이 본선과 같은 복합경사(암 무릎 · 소단 · 91-4). */
+  cutDesign?: Partial<CrossDesign> | null;
   adjust: BasinAdjust;
   /** 벽 두께(m). 기본 = 집수정 부재 두께. 세월교 측벽이 다른 두께를 쓸 때 넘긴다. */
   memberThicknessM?: number;
@@ -183,17 +186,8 @@ export const BASIN_INNER_WIDTH_M = 1.0;
 
 /** 집수정 단면을 만든다. 형태별 규칙은 파일 머리말 참조. */
 export function buildBasin(input: BasinBuildInput): BasinBuildResult {
-  const {
-    anchor: baseAnchor,
-    outward,
-    shape,
-    reason,
-    diameterM,
-    edge,
-    groundAt,
-    cutSlopeRatio,
-    adjust,
-  } = input;
+  const { anchor: baseAnchor, outward, shape, reason, diameterM, edge, groundAt, adjust } = input;
+  const cutSpec = structureCutSpec(input.cutDesign ?? { cut_slope_ratio: input.cutSlopeRatio });
   /** 이 부재의 기움 — 집수정 0.3, 세월교 0(수직). */
   const lean = input.leanRatio ?? REVET_LEAN_RATIO;
   const movedAnchor = {
@@ -339,13 +333,7 @@ export function buildBasin(input: BasinBuildInput): BasinBuildResult {
         : { offset: floorOuter, elevation: anchor.elevation };
     const groundHere = groundAt(refTop.offset);
     if (groundHere > refTop.elevation + 0.05) {
-      for (let h = 0.05; h <= 20; h += 0.05) {
-        const probe = refTop.offset + outward * cutSlopeRatio * h;
-        if (groundAt(probe) <= refTop.elevation + h) {
-          basinCut = { from: refTop, to: { offset: probe, elevation: refTop.elevation + h } };
-          break;
-        }
-      }
+      basinCut = structureCutPoints(refTop, outward, cutSpec, groundAt);
     } else if (groundHere < refTop.elevation - 0.05) {
       // 원지반 밖으로 나왔다 — 성토부선은 유출측과 같은 체계(1:1.2 + 5m 다단)로
       // 본체가 그린다(2026-08-22 사용자 확정). 여기서는 시작점만 넘긴다.
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert_Extra.ts b/B06_Section/B06_Section_UI_Cross_Culvert_Extra.ts
index 720b9452e..fb01894dd 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert_Extra.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert_Extra.ts
@@ -29,6 +29,8 @@ import type {
   WallAdjust,
   WallLayout,
 } from "./B06_Section_UI_Cross_Culvert_Types";
+import { structureCutPoints } from "./B06_Section_UI_Cross_Structure_Cut";
+import type { StructureCutSpec } from "./B06_Section_UI_Cross_Structure_Cut";
 import { buildRevetWallGeometry } from "./B06_Section_UI_Cross_Wall";
 
 export interface OutletExtrasInput {
@@ -48,20 +50,19 @@ export interface OutletExtrasInput {
   equalize?: boolean;
   /** 단 벽의 전면 기울기 — 형태·순수 높이로 표준경사를 고름(없으면 종전 1:0.3). */
   leanFor?: (form: string, pureHeightM: number) => number;
-  /** 끝이 원지반에 묻힐 때 수평공간 뒤 절토 경사(1:n)로 지반까지(세월교 · 박스 흙막이 · 79-7).
-   *  없으면 종전 3도 선. */
-  cutBerm?: { lengthM: number; slopeRatio: number };
+  /** 끝이 원지반에 묻힐 때 수평공간 뒤 절토(본선과 같은 복합경사 · 91-4)로 지반까지(세월교 · 박스
+   *  흙막이 · 79-7). 없으면 종전 3도 선. */
+  cutBerm?: { lengthM: number; cut: StructureCutSpec };
 }
 
-/** 수평공간(berm) 뒤 절토 경사로 원지반까지 — 공간 안에서 지반을 만나면 거기서 끝(79-7). */
+/** 수평공간(berm) 뒤 절토(복합경사 · 91-4)로 원지반까지 — 공간 안에서 지반을 만나면 거기서 끝(79-7). */
 function bermCut(
   src: OffsetPoint,
   outward: number,
-  berm: { lengthM: number; slopeRatio: number },
+  berm: { lengthM: number; cut: StructureCutSpec },
   groundAt: (offset: number) => number,
   limitOffset: number,
 ): OutletFillSegment {
-  const ratio = Math.max(berm.slopeRatio, 0.1);
   const flat = slopedCrossing(src, outward, 0, groundAt, limitOffset);
   const segment = (points: OffsetPoint[]): OutletFillSegment => ({
     points,
@@ -78,22 +79,16 @@ function bermCut(
   if (flat !== null && (flat - src.offset) * outward <= berm.lengthM + 1e-9)
     return segment([src, { offset: flat, elevation: src.elevation }]);
   const bend = { offset: src.offset + outward * berm.lengthM, elevation: src.elevation };
-  const span = (limitOffset - bend.offset) * outward;
-  let previousGap = groundAt(bend.offset) - bend.elevation;
-  for (let t = 0.25; t <= span + 1e-9; t += 0.25) {
-    const gap = groundAt(bend.offset + outward * t) - (bend.elevation + t / ratio);
-    if (gap <= 0) {
-      const fraction = previousGap > 1e-12 ? previousGap / (previousGap - gap) : 1;
-      const cross = t - 0.25 * (1 - fraction);
-      return segment([
-        src,
-        bend,
-        { offset: bend.offset + outward * cross, elevation: bend.elevation + cross / ratio },
-      ]);
-    }
-    previousGap = gap;
-  }
-  return segment([src, bend]);
+  // 소단 셈은 수평공간 끝에서 새로(91-4)
+  const cut = structureCutPoints(
+    bend,
+    outward,
+    berm.cut,
+    groundAt,
+    (limitOffset - bend.offset) * outward,
+  );
+  const head = berm.lengthM > 1e-9 ? [src, bend] : [src];
+  return segment(cut ? [...head, ...cut.slice(1)] : head.length > 1 ? head : [src, bend]);
 }
 
 export interface OutletExtrasResult {
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert_Geom.ts b/B06_Section/B06_Section_UI_Cross_Culvert_Geom.ts
index 7c3b5bbd9..ebb01bf9c 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert_Geom.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert_Geom.ts
@@ -56,6 +56,7 @@ import {
   inletChoiceAvailability,
 } from "./B06_Section_UI_Cross_Culvert_Basin";
 import { inletGroundConnector } from "./B06_Section_UI_Cross_Culvert_Extra";
+import { withBackCut } from "./B06_Section_UI_Cross_Structure_Cut";
 import {
   buildCulvertTiers,
   drawnFillPoints,
@@ -335,7 +336,7 @@ export function computeCulvertLayout(
         diameterM: diameter,
         edge: spec.role === "inlet" ? inletInfo.edge : outletInfo.edge,
         groundAt,
-        cutSlopeRatio: section.design?.cut_slope_ratio ?? 1.0,
+        cutDesign: section.design,
         adjust: basinAdjust,
         heightM: basinHeightM,
       });
@@ -615,7 +616,7 @@ export function computeCulvertLayout(
   const slopeOf = (wall: WallLayout): FillSlopeSegment =>
     fillSlopeOf(wall, wall.role === "inlet" ? inletInfo.edge : outletInfo.edge);
   for (const wall of walls) {
-    const slope = slopeOf(wall);
+    const slope = withBackCut(slopeOf(wall), wall, section.design, groundAt, !culvert.hidden_pipe);
     // 사면선은 노견부터 우리가 그린다 — 트림 경계를 노견까지 당겨 백엔드 설계선의
     // 성토 구간을 통째로 덮는다(설계선은 1:1.2 고정이라 그대로 두면 다시 어긋난다).
     if (wall.outward > 0) {
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert_Tiers.ts b/B06_Section/B06_Section_UI_Cross_Culvert_Tiers.ts
index 6396cc06f..37815717a 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert_Tiers.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert_Tiers.ts
@@ -16,6 +16,7 @@ import { buildExtrasAt } from "./B06_Section_UI_Cross_Culvert_Extra";
 import { fillWallBaseWidth } from "./B06_Section_UI_Cross_Culvert_Solve";
 import type { OffsetPoint, WallAdjust, WallLayout } from "./B06_Section_UI_Cross_Culvert_Types";
 import { outlineLeanOf } from "./B06_Section_UI_Cross_Lean";
+import { structureCutSpec } from "./B06_Section_UI_Cross_Structure_Cut";
 
 // d의 0점 = **성토선 길이 0 지점**(벽 상단 = 노견 — 2026-08-23 사용자 확정).
 // 그 자리(하단선 중점)는 이음선 상단점이 노견 끝에 오는 offset이고, 기본 자리는
@@ -89,7 +90,7 @@ export function buildCulvertTiers(input: {
     culvert?.body
       ? {
           lengthM: Math.max(spec?.revet_berm_m ?? GUARD_CUT_BERM_M, 0),
-          slopeRatio: section.design?.cut_slope_ratio ?? 1.0,
+          cut: structureCutSpec(section.design),
         }
       : undefined;
   // 성토부선 + 다단 기슭막이(2026-08-22 — 보호공 삭제, 윗면 선만 성토부선으로).
diff --git a/B06_Section/B06_Section_UI_Cross_Culvert_Types.ts b/B06_Section/B06_Section_UI_Cross_Culvert_Types.ts
index 322748453..98bd07199 100644
--- a/B06_Section/B06_Section_UI_Cross_Culvert_Types.ts
+++ b/B06_Section/B06_Section_UI_Cross_Culvert_Types.ts
@@ -112,8 +112,8 @@ export interface BasinLayout {
    *  "cut" = 절토측 유입(성토사면 없음), "short" = 성토사면 3m 이하,
    *  "manual" = 규칙상 기슭막이 자리지만 사용자가 집수정을 선택. */
   reason: "cut" | "short" | "manual";
-  /** 집수정이 원지반 안으로 들어갈 때의 절토선(구조물 바깥 끝 → 지반 교차점). */
-  cutLine: { from: OffsetPoint; to: OffsetPoint } | null;
+  /** 집수정이 원지반 안으로 들어갈 때의 절토선 점열(구조물 바깥 끝 → 복합경사 → 지반 교차점 · 91-4). */
+  cutLine: OffsetPoint[] | null;
   /** 구조물이 원지반 밖으로 나올 때의 성토(되메움)선 — 경사 5도(임시), 지반 교차점까지. */
   fillLine: { from: OffsetPoint; to: OffsetPoint } | null;
 }
diff --git a/B06_Section/B06_Section_UI_Cross_Ford.ts b/B06_Section/B06_Section_UI_Cross_Ford.ts
index f21cc38ca..6ea9ed38d 100644
--- a/B06_Section/B06_Section_UI_Cross_Ford.ts
+++ b/B06_Section/B06_Section_UI_Cross_Ford.ts
@@ -138,7 +138,7 @@ export function appendFordOverlay(
       );
     }
     if (side.cutLine) {
-      planLine([side.cutLine.from, side.cutLine.to], `${role} 측벽 절토선(계획선)`);
+      planLine(side.cutLine, `${role} 측벽 절토선(계획선)`);
     }
   }
 
diff --git a/B06_Section/B06_Section_UI_Cross_Ford_Geom.ts b/B06_Section/B06_Section_UI_Cross_Ford_Geom.ts
index d40326c05..c33ac5554 100644
--- a/B06_Section/B06_Section_UI_Cross_Ford_Geom.ts
+++ b/B06_Section/B06_Section_UI_Cross_Ford_Geom.ts
@@ -148,7 +148,6 @@ export function computeFordLayout(
   const uphill = section.uphill_side ?? "left";
   const inletOnLeft = uphill === "left";
   const roadTopAt = roadTopFactory(section, edges.left, edges.right);
-  const cutSlopeRatio = section.design?.cut_slope_ratio ?? 1.0;
 
   // 바닥판이 놓일 계류 하상 — 두 노견 사이 원지반 최저점.
   const bedElevation = (() => {
@@ -182,7 +181,8 @@ export function computeFordLayout(
       diameterM: ford.diameter_m,
       edge: { offset_m: edge.offset_m, elevation_m: roadTopAt(edge.offset_m) },
       groundAt,
-      cutSlopeRatio,
+      // 측벽 끝 절토 = 본선 절토 사면과 같은 복합경사(91-4)
+      cutDesign: section.design,
       // 내공 폭 자리에 날개벽 투영 연장을 넣는다 — 바닥판이 그만큼 계류측으로 뻗는다.
       adjust: {
         innerWidthM: Math.max(wing.slab_extend_m, 0),
diff --git a/B06_Section/B06_Section_UI_Cross_Structure_Cut.ts b/B06_Section/B06_Section_UI_Cross_Structure_Cut.ts
new file mode 100644
index 000000000..d24ec6819
--- /dev/null
+++ b/B06_Section/B06_Section_UI_Cross_Structure_Cut.ts
@@ -0,0 +1,107 @@
+/* =============================================================================
+ * B06_Section_UI_Cross_Structure_Cut.ts
+ * 구조물 끝 → 원지반 **절토선 점열**(91-4) — 본선 절토 사면과 같은 복합경사.
+ *
+ * 꼭짓점은 `common_util_cross_berm.cutProfilePoints` 그대로(암 → 토사 무릎 · 소단) · 경계 = 원지반 +
+ * `rock_boundary_offset_m` · 켬 = 암 프리셋 + `two_stage_slope` · 소단 = `design.berm` · 소단 셈은
+ * 구조물 끝에서 새로 · 원지반 교점에서 자름.
+ * 쓰는 곳 = 흙막이 수평공간 뒤 · 박스 끝 · 세월교 측벽 끝 · ㄴ·ㄷ 집수정 끝 · 절토 쪽 배관 유출 벽 뒤.
+ * ========================================================================== */
+
+import { bermSpec, cutProfilePoints } from "../common_util/common_util_cross_berm";
+import type { BermSpec } from "../common_util/common_util_cross_berm";
+import type { CrossDesign } from "./B06_Section_Api_Fetch";
+import type { OffsetPoint } from "./B06_Section_UI_Cross_Culvert_Types";
+
+/** 절토 제원 — 암(또는 단일) 경사 · 토사 경사 · 암 경계 오프셋(없으면 경사 하나) · 소단. */
+export interface StructureCutSpec {
+  cutRatio: number;
+  soilRatio: number;
+  rockOffsetM: number | null;
+  berm: BermSpec | null;
+}
+
+/** 측점 설계값에서 절토 제원 — 본선 `computeCrossDesign` 과 같은 켬 조건. */
+export function structureCutSpec(design?: Partial<CrossDesign> | null): StructureCutSpec {
+  const cutRatio = Math.max(design?.cut_slope_ratio ?? 1.0, 0.1);
+  const offset = design?.rock_boundary_offset_m;
+  const twoStage =
+    design?.geometry_preset === "rock" && design.two_stage_slope === true && offset != null;
+  const berm = design?.berm;
+  return {
+    cutRatio,
+    soilRatio: Math.max(design?.soil_cut_slope_ratio ?? cutRatio, 0.1),
+    rockOffsetM: twoStage ? offset : null,
+    berm: berm ? bermSpec(berm.width_m, berm.interval_m, berm.slope_deg) : null,
+  };
+}
+
+/** 원지반 교점 찾는 걸음(m). */
+const STEP_M = 0.05;
+
+/**
+ * `from`(원지반 아래) → 바깥(`outward`)으로 절토 꼭짓점 · 마지막 점 = 원지반 교점.
+ * `reachM` 안에서 못 만나면 null.
+ */
+export function structureCutPoints(
+  from: OffsetPoint,
+  outward: number,
+  spec: StructureCutSpec,
+  groundAt: (offset: number) => number,
+  reachM = 50,
+): OffsetPoint[] | null {
+  const at = (dist: number): number => from.offset + outward * dist;
+  const rockOffsetM = spec.rockOffsetM;
+  const boundary = rockOffsetM === null ? null : (dist: number) => groundAt(at(dist)) + rockOffsetM;
+  const profile = cutProfilePoints(
+    0,
+    from.elevation,
+    spec.cutRatio,
+    spec.soilRatio,
+    boundary,
+    spec.berm,
+    Math.max(reachM, STEP_M),
+    // 소단이 있으면 경계를 오갈 때마다 꺾음 — 본선 `cutPoints` 와 같음.
+    spec.berm !== null,
+  );
+  const points: OffsetPoint[] = [from];
+  for (let i = 1; i < profile.length; i += 1) {
+    const [d0, z0] = profile[i - 1];
+    const [d1, z1] = profile[i];
+    const steps = Math.max(1, Math.ceil((d1 - d0) / STEP_M));
+    let previousGap = groundAt(at(d0)) - z0;
+    for (let k = 1; k <= steps; k += 1) {
+      const t = k / steps;
+      const gap = groundAt(at(d0 + (d1 - d0) * t)) - (z0 + (z1 - z0) * t);
+      if (gap <= 0) {
+        // 걸음 사이 교점 보간 — 선이 지반을 넘지 않게
+        const share = previousGap > 1e-12 ? previousGap / (previousGap - gap) : 1;
+        const tc = (k - 1 + share) / steps;
+        points.push({ offset: at(d0 + (d1 - d0) * tc), elevation: z0 + (z1 - z0) * tc });
+        return points;
+      }
+      previousGap = gap;
+    }
+    points.push({ offset: at(d1), elevation: z1 });
+  }
+  return null;
+}
+
+/**
+ * 배관 유출 벽이 절토 쪽(벽 바깥 윗모서리가 원지반 아래)이면 그 모서리부터 절토선을 사면 점열 뒤에
+ * 이음 — 트림이 노견부터 설계선을 지워 절토사면이 사라지던 자리(91-4). 관 숨김(세월교 · 박스 흙막이 ·
+ * 독립 기슭막이)은 `enabled` 거짓.
+ */
+export function withBackCut<T extends { points: OffsetPoint[] }>(
+  slope: T,
+  wall: { role: string; outward: number; points: OffsetPoint[] },
+  design: Partial<CrossDesign> | null | undefined,
+  groundAt: (offset: number) => number,
+  enabled: boolean,
+): T {
+  const corner = wall.points[2];
+  if (!enabled || wall.role !== "outlet" || !corner) return slope;
+  if (groundAt(corner.offset) <= corner.elevation + 0.05) return slope;
+  const cut = structureCutPoints(corner, wall.outward, structureCutSpec(design), groundAt);
+  return cut ? { ...slope, points: [...slope.points, ...cut] } : slope;
+}
diff --git a/resources/tester/helper_91_ground_free.cjs b/resources/tester/helper_91_ground_free.cjs
index 5aed020f1..47eb605a6 100644
--- a/resources/tester/helper_91_ground_free.cjs
+++ b/resources/tester/helper_91_ground_free.cjs
@@ -127,4 +127,65 @@ out.lean = ["left_cut", "right_cut", "both_fill", "both_cut"].map((mode) => [
   leanOf({ form: "돌쌓기(찰)", height_m: 1.5, section_mode: mode, side: "좌" }),
   leanOf({ form: "돌쌓기(찰)", height_m: 1.5, section_mode: mode, side: "좌", face_role: "절토" }),
 ]);
+// ③ 91-4 유출측 절토 복합경사 — 꼭짓점 사이 경사(수평/수직) · 사면 길이 · 끝 = 원지반 교점
+const { groundInterpolator } = loadTs(B06("B06_Section_UI_Cross_Culvert_Solve.ts"));
+function profile(points, samples) {
+  const groundAt = groundInterpolator(samples);
+  const legs = points.slice(1).map((p, i) => {
+    const dx = Math.abs(p.offset - points[i].offset);
+    const dz = p.elevation - points[i].elevation;
+    return { ratio: dz > 1e-9 ? r3(dx / dz) : null, slant: r3(Math.hypot(dx, dz)), run: r3(dx) };
+  });
+  const end = points[points.length - 1];
+  return { legs, endGap: r3(Math.abs(groundAt(end.offset) - end.elevation)) };
+}
+const withBerm = (s) => {
+  s.design.berm = { width_m: 0.5, interval_m: 3, slope_deg: 0 };
+};
+// 흙막이 수평공간 뒤(박스 352.14 · 세월교 173.09)
+function guardTails(base, edit = () => undefined) {
+  const s = clone(base);
+  edit(s);
+  const { culvert } = layoutsOf(s, base);
+  return [...culvert.outletFill.segments, ...culvert.basinFill.segments]
+    .filter((g) => g.kind === "cut")
+    .map((g) => profile(g.points, s.samples));
+}
+out.guardTails = [...guardTails(at(352.14)), ...guardTails(FORD)];
+// 박스 끝 · 세월교 측벽 끝(흙막이 없음)
+const { computeBoxLayout } = loadTs(B06("B06_Section_UI_Cross_Box_Geom.ts"));
+const { computeFordLayout } = loadTs(B06("B06_Section_UI_Cross_Ford_Geom.ts"));
+function endCuts(base, compute) {
+  const s = clone(base);
+  delete s.culvert;
+  s.uphill_side = "left"; // 절토 쪽(우측)을 유출로
+  return compute(s, s.samples)
+    .sides.filter((side) => side.cutLine)
+    .map((side) => profile(side.cutLine, s.samples));
+}
+out.boxEnd = endCuts(at(352.14), computeBoxLayout);
+out.fordEnd = endCuts(FORD, computeFordLayout);
+// 절토 쪽 배관 유출 벽 뒤(관 340 · 유출 = 우측 절토) · 소단 있음/없음
+function cutOutlet(edit = () => undefined) {
+  const s = clone(at(340));
+  s.uphill_side = "left";
+  s.culvert = {
+    type: "pipe",
+    chainage_m: 340,
+    pipe_kind: "흄관",
+    diameter_m: 1.0,
+    min_cover_m: 0.5,
+    inlet: { role: "inlet", structure: "기슭막이", revet_form: "돌쌓기(찰)" },
+    outlet: { role: "outlet", structure: "기슭막이", revet_form: "돌쌓기(찰)" },
+  };
+  s.design.inlet_structure = "revet";
+  edit(s);
+  const layout = computeCulvertLayout(s, s.samples, undefined, "revet");
+  const wall = layout.walls.find((w) => w.role === "outlet");
+  const pts = layout.designTrim.minSlope.points;
+  const from = pts.findIndex((p) => Math.abs(p.offset - wall.points[2].offset) < 1e-9);
+  return profile(pts.slice(from), s.samples);
+}
+out.cutOutlet = cutOutlet();
+out.cutOutletBerm = cutOutlet(withBerm);
 process.stdout.write(JSON.stringify(out));
diff --git a/resources/tester/test_79_guard_shape.py b/resources/tester/test_79_guard_shape.py
index f33cbcafe..22607986f 100644
--- a/resources/tester/test_79_guard_shape.py
+++ b/resources/tester/test_79_guard_shape.py
@@ -80,7 +80,8 @@ def test_흙막이_끝_절토는_수평공간_뒤(shape: dict) -> None:
     tails = [tail for group in shape["cutDefault"] for tail in group]
     assert tails, "절토 끝선이 없음"
     for tail in tails:
-        assert tail["points"] == 3
+        # 시작 · 수평공간 끝 · (암 무릎 · 소단) · 원지반 교점 — 본선 절토와 같은 복합경사(91-4)
+        assert tail["points"] >= 3
         assert tail["flat"] == pytest.approx(0, abs=1e-6)
         assert tail["berm"] == pytest.approx(1.0, abs=1e-3)
     for tail in shape["cutBerm2"]:
diff --git a/resources/tester/test_91_ground_free.py b/resources/tester/test_91_ground_free.py
index 7fc4cdf36..09e1c5de4 100644
--- a/resources/tester/test_91_ground_free.py
+++ b/resources/tester/test_91_ground_free.py
@@ -83,3 +83,34 @@ def test_지형에_막힘_잔재_없음() -> None:
         source = (ROOT / "B06_Section" / name).read_text(encoding="utf-8")
         assert "shiftBlockedM" not in source and "지형에 막힘" not in source, name
         assert "noticeExtraLimit" not in source and "noticeShortfall" not in source, name
+
+
+def _knee(cut: dict) -> bool:
+    """암(1:0.4) 뒤 토사(1:1.0) 무릎이 있음 — 픽스처 = 리핑암 · 2단계 · 경계 −0.5 m."""
+    ratios = [leg["ratio"] for leg in cut["legs"] if leg["ratio"] is not None]
+    return any(a == 0.4 and b == 1.0 for a, b in zip(ratios, ratios[1:]))
+
+
+def test_흙막이_수평공간_뒤_절토_복합경사(fit: dict) -> None:
+    tails = fit["guardTails"]
+    assert tails and all(cut["endGap"] < 0.01 for cut in tails)
+    assert all(cut["legs"][0]["ratio"] is None for cut in tails)  # 수평공간 먼저
+    assert sum(_knee(cut) for cut in tails) >= 2
+
+
+def test_박스_끝_세월교_측벽_끝_절토_복합경사(fit: dict) -> None:
+    for cuts in (fit["boxEnd"], fit["fordEnd"]):
+        assert cuts and all(_knee(cut) and cut["endGap"] < 0.01 for cut in cuts)
+
+
+def test_절토_쪽_배관_유출_벽_뒤_절토사면_살아남(fit: dict) -> None:
+    cut = fit["cutOutlet"]
+    assert _knee(cut) and cut["endGap"] < 0.01
+
+
+def test_소단은_구조물_끝에서_새로_셈(fit: dict) -> None:
+    legs = fit["cutOutletBerm"]["legs"]
+    flat = next(i for i, leg in enumerate(legs) if leg["ratio"] is None)
+    assert sum(leg["slant"] for leg in legs[:flat]) == pytest.approx(3.0, abs=1e-3)
+    assert legs[flat]["run"] == pytest.approx(0.5, abs=1e-3)
+    assert fit["cutOutletBerm"]["endGap"] < 0.01

From ea8495792756df33e95669cfeb34a844a010ffc3 Mon Sep 17 00:00:00 2001
From: umsangdon <umsangdon@gmail.com>
Date: Thu, 8 Oct 2026 12:34:54 +0900
Subject: [PATCH 2/3] =?UTF-8?q?feat(spreadsheet):=20=EC=9A=B0=ED=81=B4?=
 =?UTF-8?q?=EB=A6=AD=20=EB=A9=94=EB=89=B4=EC=97=90=20=EB=B6=99=EC=97=AC?=
 =?UTF-8?q?=EB=84=A3=EA=B8=B0=20=C2=B7=20=EC=82=BD=EC=9E=85/=EC=82=AD?=
 =?UTF-8?q?=EC=A0=9C=20=E2=96=B8=20=C2=B7=20=ED=81=AC=EA=B8=B0=20=C2=B7=20?=
 =?UTF-8?q?=EC=A0=95=EB=A0=AC=20=C2=B7=20=ED=95=84=ED=84=B0=20=C2=B7=20?=
 =?UTF-8?q?=EA=B3=A0=EC=A0=95=20=C2=B7=20=EA=B7=B8=EB=A3=B9=20=C2=B7=20?=
 =?UTF-8?q?=EB=8D=94=EB=B3=B4=EA=B8=B0=20=EB=B6=99=EC=9E=84=20=C2=B7=20?=
 =?UTF-8?q?=EC=9D=BD=EA=B8=B0=20=EC=A0=84=EC=9A=A9=20=EB=B3=B5=EC=82=AC(81?=
 =?UTF-8?q?-3)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

- spreadsheet_menu.ts — 칸 · 행 머리 · 열 머리 메뉴에 spreadsheet_menu_items 펼침 · 구분선
- 잘라내기 · 복사 — 초점을 격자로 되돌린 뒤 execCommand(메뉴가 닫히며 초점이 빠져 빈 복사되던 흠)
- 읽기 전용 · 미리보기 시트 우클릭 = 「복사」 한 줄(spreadsheet.ts 메뉴 늘 붙임)
- 시험 test_stage4_menu_items.ts 34 · 크기 화면 16.3 KB(예산 72)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UoSr2sqvYtBf1dtQdus88s
---
 A00_Common/spreadsheet/spreadsheet.ts         |   4 +-
 A00_Common/spreadsheet/spreadsheet_menu.ts    |  54 +++-
 .../spreadsheet/test_stage4_menu_items.ts     | 304 ++++++++++++++++++
 3 files changed, 343 insertions(+), 19 deletions(-)
 create mode 100644 resources/tester/spreadsheet/test_stage4_menu_items.ts

diff --git a/A00_Common/spreadsheet/spreadsheet.ts b/A00_Common/spreadsheet/spreadsheet.ts
index 5596915d8..4c7e91766 100644
--- a/A00_Common/spreadsheet/spreadsheet.ts
+++ b/A00_Common/spreadsheet/spreadsheet.ts
@@ -110,7 +110,7 @@ export function createSpreadsheet(
 ): SpreadsheetHandle {
   const readOnly = !!opts.readOnly;
   const noTabs = opts.tabs === false;
-  const bare = readOnly || !!opts.preview; // 도구 모음 · 메뉴 없음
+  const bare = readOnly || !!opts.preview; // 도구 모음 없음 · 우클릭은 「복사」 한 줄
   const root = el("div", {
     className: `ss${readOnly ? " ss--readonly" : ""}${noTabs ? " ss--notabs" : ""}${opts.preview ? " ss--preview" : ""}`,
   });
@@ -142,7 +142,7 @@ export function createSpreadsheet(
   ctx.editor = ed;
   const toolbar: PartHandle | null = bare ? null : mountToolbar(ctx);
   const tabs: PartHandle | null = noTabs ? null : mountTabs(ctx);
-  const menu: PartHandle | null = bare ? null : attachMenu(ctx);
+  const menu: PartHandle = attachMenu(ctx); // 읽기 전용 · 미리보기는 「복사」 한 줄(81-3)
   const clip = attachClipboard(ctx);
   const status = createStatusBar(ctx);
   const others = [toolbar, tabs, menu, clip, status].filter((p): p is PartHandle => !!p);
diff --git a/A00_Common/spreadsheet/spreadsheet_menu.ts b/A00_Common/spreadsheet/spreadsheet_menu.ts
index 603fa99e7..a2af5138f 100644
--- a/A00_Common/spreadsheet/spreadsheet_menu.ts
+++ b/A00_Common/spreadsheet/spreadsheet_menu.ts
@@ -12,10 +12,21 @@
  * ========================================================================== */
 
 import { createMapContextMenu, type MapContextMenuItem } from "@ui/ui_template_context_menu";
-import { createButton, el, showToast } from "@ui/ui_template_elements";
+import { createButton, el } from "@ui/ui_template_elements";
 import { rangeToA1 } from "./spreadsheet_address";
 import { confirmMerge, dialogKeys } from "./spreadsheet_actions";
 import { deleteComment, getComment, setComment } from "./spreadsheet_comments";
+import {
+  cellInsertItems,
+  cellMoreItems,
+  colInsertItems,
+  colMoreItems,
+  copyCut,
+  copyOnlyItems,
+  pasteItems,
+  rowInsertItems,
+  rowMoreItems,
+} from "./spreadsheet_menu_items";
 import { st } from "./spreadsheet_text";
 import { MAX_COLS, MAX_ROWS, type CellRange } from "./spreadsheet_types";
 import type { PartHandle, SpreadsheetContext } from "./spreadsheet_view_types";
@@ -28,7 +39,8 @@ function within(range: CellRange, r: number, c: number): boolean {
 
 /** `ctx.root` 의 contextmenu 를 받음(root null) */
 export function attachMenu(ctx: SpreadsheetContext): PartHandle {
-  if (ctx.readOnly) return { root: null, refresh() {}, destroy() {} };
+  // 읽기 전용 · 미리보기 = 「복사」 한 줄(81-3)
+  const bare = ctx.readOnly || ctx.root.classList.contains("ss--preview");
 
   const menu = createMapContextMenu("ss");
   ctx.root.append(menu.element);
@@ -39,7 +51,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
   }
 
   function cutCopy(kind: "cut" | "copy"): void {
-    document.execCommand(kind);
+    copyCut(ctx, kind);
   }
 
   /** 메모 글 입력 — 작은 오버레이(native prompt 안 씀, 자동화 창이 native 창을 자동 취소하는
@@ -79,7 +91,10 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
     return [
       [st("MenuCut"), () => cutCopy("cut")],
       [st("MenuCopy"), () => cutCopy("copy")],
-      [st("MenuPasteHint"), () => showToast(st("MenuPasteHint"), "info")],
+      ...pasteItems(ctx),
+      "-",
+      ...cellInsertItems(ctx, range),
+      "-",
       [
         st("MenuClearContent"),
         () => ctx.dispatch({ 종류: "내용지움", 시트: ctx.selection.시트, 범위: [range] }),
@@ -107,6 +122,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
       ...(note
         ? ([[st("MenuCommentDelete"), () => deleteComment(ctx, r, c)]] as MapContextMenuItem[])
         : []),
+      ...cellMoreItems(ctx, range),
       ...(ctx.cellMenuExtra?.(r, c) ?? []),
     ];
   }
@@ -117,11 +133,9 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
     return [
       [st("MenuCut"), () => cutCopy("cut")],
       [st("MenuCopy"), () => cutCopy("copy")],
-      [st("MenuPasteHint"), () => showToast(st("MenuPasteHint"), "info")],
-      [
-        st("MenuInsertRow"),
-        () => ctx.dispatch({ 종류: "행넣기", 시트: ctx.selection.시트, at, 수 }),
-      ],
+      ...pasteItems(ctx),
+      "-",
+      ...rowInsertItems(ctx, at, 수),
       [
         st("MenuDeleteRow"),
         () => ctx.dispatch({ 종류: "행지우기", 시트: ctx.selection.시트, at, 수 }),
@@ -148,6 +162,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
             숨김: false,
           }),
       ],
+      ...rowMoreItems(ctx, rows),
     ];
   }
 
@@ -157,11 +172,9 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
     return [
       [st("MenuCut"), () => cutCopy("cut")],
       [st("MenuCopy"), () => cutCopy("copy")],
-      [st("MenuPasteHint"), () => showToast(st("MenuPasteHint"), "info")],
-      [
-        st("MenuInsertCol"),
-        () => ctx.dispatch({ 종류: "열넣기", 시트: ctx.selection.시트, at, 수 }),
-      ],
+      ...pasteItems(ctx),
+      "-",
+      ...colInsertItems(ctx, at, 수),
       [
         st("MenuDeleteCol"),
         () => ctx.dispatch({ 종류: "열지우기", 시트: ctx.selection.시트, at, 수 }),
@@ -188,6 +201,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
             숨김: false,
           }),
       ],
+      ...colMoreItems(ctx, cols),
     ];
   }
 
@@ -217,7 +231,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
           활성: { r: hit.r, c: 0 },
           기준: { r: hit.r, c: 0 },
         });
-      menu.open(x, y, rowMenuItems(rows));
+      menu.open(x, y, bare ? copyOnlyItems(ctx) : rowMenuItems(rows));
       return;
     }
 
@@ -235,7 +249,7 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
           활성: { r: 0, c: hit.c },
           기준: { r: 0, c: hit.c },
         });
-      menu.open(x, y, colMenuItems(cols));
+      menu.open(x, y, bare ? copyOnlyItems(ctx) : colMenuItems(cols));
       return;
     }
 
@@ -250,7 +264,13 @@ export function attachMenu(ctx: SpreadsheetContext): PartHandle {
         });
       }
       const active = ctx.selection.범위[0] ?? range(hit.r, hit.c, hit.r, hit.c);
-      menu.open(x, y, cellMenuItems(active, hit.r, hit.c));
+      menu.open(
+        x,
+        y,
+        bare
+          ? [...copyOnlyItems(ctx), ...(ctx.cellMenuExtra?.(hit.r, hit.c) ?? [])]
+          : cellMenuItems(active, hit.r, hit.c),
+      );
     }
   }
 
diff --git a/resources/tester/spreadsheet/test_stage4_menu_items.ts b/resources/tester/spreadsheet/test_stage4_menu_items.ts
new file mode 100644
index 000000000..3c7fe1aec
--- /dev/null
+++ b/resources/tester/spreadsheet/test_stage4_menu_items.ts
@@ -0,0 +1,304 @@
+/* =============================================================================
+ * test_stage4_menu_items.ts — 우클릭 메뉴 덧붙인 항목(81-3) 시험.
+ * 행 위/아래 · 열 좌우 삽입 · 셀 삽입/삭제 · 행열 삭제 · 크기 · 시트 정렬 · 필터 · 고정 · 그룹 ·
+ * 범위 이름 · 붙여넣기 보안 문맥 갈래 · 구분선 · 읽기 전용 복사.
+ * 돌리기: npx tsx resources/tester/spreadsheet/test_stage4_menu_items.ts
+ * ========================================================================== */
+
+import { register } from "node:module";
+import type { MapContextMenuItem } from "../../../ui_template/ui_template_context_menu.ts";
+import { applyCommand } from "../../../A00_Common/spreadsheet/spreadsheet_commands.ts";
+import { createCalcEngine } from "../../../A00_Common/spreadsheet/spreadsheet_graph.ts";
+import {
+  canMenuPaste,
+  cellInsertItems,
+  cellMoreItems,
+  colInsertItems,
+  colMoreItems,
+  copyOnlyItems,
+  menuPaste,
+  nameRange,
+  pasteItems,
+  resizeLines,
+  rowInsertItems,
+  rowMoreItems,
+  sortByColumn,
+  usedRange,
+} from "../../../A00_Common/spreadsheet/spreadsheet_menu_items.ts";
+import type { Cell, Command, Workbook } from "../../../A00_Common/spreadsheet/spreadsheet_types.ts";
+import type {
+  Selection,
+  SpreadsheetContext,
+} from "../../../A00_Common/spreadsheet/spreadsheet_view_types.ts";
+import { a1, assertEqual, makeBook, makeCtx, makeSheet, v } from "./test_stage2_helpers.ts";
+
+// 늦게 부르는 창 모듈의 css 는 node 에서 빈 모듈로
+register(
+  "data:text/javascript,export async function load(u,c,n){return u.endsWith('.css')?{format:'module',source:'',shortCircuit:true}:n(u,c)}",
+);
+const tick = () => new Promise((r) => setTimeout(r, 30));
+
+/** 진짜 명령 · 엔진 · 고름을 쓰는 문맥 */
+function realCtx(cells: Record<string, Cell>): SpreadsheetContext & { sent: Command[] } {
+  const book: Workbook = makeBook([makeSheet("s1", cells)]);
+  const base = makeCtx(book, "s1");
+  const sent: Command[] = [];
+  const ctx = base as unknown as SpreadsheetContext & { sent: Command[] };
+  ctx.engine = createCalcEngine(book);
+  ctx.sent = sent;
+  ctx.dispatch = (cmd: Command) => {
+    sent.push(cmd);
+    applyCommand(book, cmd);
+    ctx.engine.rebuild(book);
+  };
+  ctx.select = (sel: Selection) => void (ctx.selection = sel);
+  return ctx;
+}
+const col = (n: number) =>
+  Object.fromEntries(Array.from({ length: n }, (_, i) => [a1(i, 0), v(i + 1)]));
+const row = (n: number) =>
+  Object.fromEntries(Array.from({ length: n }, (_, i) => [a1(0, i), v(i + 1)]));
+const val = (ctx: SpreadsheetContext, r: number, c: number) => ctx.sheet().칸[a1(r, c)]?.값;
+const leaf = (items: MapContextMenuItem[], label: string): (() => void) => {
+  for (const it of items) {
+    if (it === "-") continue;
+    if (Array.isArray(it)) {
+      if (it[0] === label) return it[1];
+    } else {
+      const hit = it.children.find(([l]) => l === label);
+      if (hit) return hit[1];
+    }
+  }
+  throw new Error(`항목 없음: ${label}`);
+};
+const labels = (items: MapContextMenuItem[]) =>
+  items.map((it) => (it === "-" ? "-" : Array.isArray(it) ? it[0] : `${it.label} ▸`));
+
+// ── 행 위 · 아래 삽입(고른 2행 B2:B3 → at 1 · 수 2) ─────────────────────────
+{
+  const ctx = realCtx(col(5));
+  leaf(rowInsertItems(ctx, 1, 2), "위에 2행 삽입")();
+  assertEqual(
+    [val(ctx, 0, 0), val(ctx, 1, 0), val(ctx, 2, 0), val(ctx, 3, 0)],
+    [1, undefined, undefined, 2],
+    "위에 2행 — 2행부터 밀림",
+  );
+}
+{
+  const ctx = realCtx(col(5));
+  leaf(rowInsertItems(ctx, 1, 2), "아래에 2행 삽입")();
+  assertEqual(
+    [val(ctx, 2, 0), val(ctx, 3, 0), val(ctx, 4, 0), val(ctx, 5, 0)],
+    [3, undefined, undefined, 4],
+    "아래에 2행 — 고른 줄 뒤에 끼움",
+  );
+}
+// ── 열 왼 · 오른쪽 삽입 ──────────────────────────────────────────────────
+{
+  const ctx = realCtx(row(4));
+  leaf(colInsertItems(ctx, 1, 1), "왼쪽에 1열 삽입")();
+  assertEqual([val(ctx, 0, 0), val(ctx, 0, 1), val(ctx, 0, 2)], [1, undefined, 2], "왼쪽에 1열");
+}
+{
+  const ctx = realCtx(row(4));
+  leaf(colInsertItems(ctx, 1, 1), "오른쪽에 1열 삽입")();
+  assertEqual([val(ctx, 0, 1), val(ctx, 0, 2), val(ctx, 0, 3)], [2, undefined, 3], "오른쪽에 1열");
+}
+// ── 칸 메뉴 — 셀 삽입/삭제 ▸ · 행열 삭제 ▸ ──────────────────────────────
+{
+  const g = { r0: 0, c0: 1, r1: 0, c1: 1 };
+  const ctx = realCtx(row(3));
+  const items = cellInsertItems(ctx, g);
+  assertEqual(
+    labels(items),
+    ["행 · 열 삽입 ▸", "셀 삽입 ▸", "행 · 열 삭제 ▸", "셀 삭제 ▸"],
+    "칸 메뉴 하위 넷",
+  );
+  leaf(items, "셀 삽입 후 오른쪽으로 밀기")();
+  await tick();
+  assertEqual(
+    [val(ctx, 0, 1), val(ctx, 0, 2), val(ctx, 0, 3)],
+    [undefined, 2, 3],
+    "셀 삽입 · 오른쪽으로",
+  );
+  leaf(cellInsertItems(ctx, g), "셀 삭제 후 왼쪽으로 당기기")();
+  await tick();
+  assertEqual([val(ctx, 0, 1), val(ctx, 0, 2)], [2, 3], "셀 삭제 · 왼쪽으로");
+}
+{
+  const ctx = realCtx(col(3));
+  leaf(cellInsertItems(ctx, { r0: 1, c0: 0, r1: 1, c1: 0 }), "셀 삽입 후 아래로 밀기")();
+  await tick();
+  assertEqual([val(ctx, 1, 0), val(ctx, 2, 0)], [undefined, 2], "셀 삽입 · 아래로");
+  leaf(cellInsertItems(ctx, { r0: 1, c0: 0, r1: 1, c1: 0 }), "셀 삭제 후 위로 당기기")();
+  await tick();
+  assertEqual([val(ctx, 1, 0), val(ctx, 2, 0)], [2, 3], "셀 삭제 · 위로");
+  leaf(cellInsertItems(ctx, { r0: 0, c0: 0, r1: 1, c1: 0 }), "2행 삭제")();
+  assertEqual(val(ctx, 0, 0), 3, "칸 메뉴 행 삭제 · 고른 2행");
+}
+// ── 크기 — px → 열폭(글자) · 행높이(pt) · 잘못된 값 ─────────────────────────
+{
+  const ctx = realCtx(row(2));
+  assertEqual(
+    resizeLines(ctx, false, [0, 1], "abc"),
+    "1 이상 숫자를 넣을 것",
+    "크기 · 글이면 거름",
+  );
+  assertEqual(resizeLines(ctx, false, [0, 1], "0"), "1 이상 숫자를 넣을 것", "크기 · 0 거름");
+  assertEqual(resizeLines(ctx, false, [0, 1], "100"), null, "열 너비 100px");
+  const w = ctx.sheet().열!;
+  assertEqual(w.A?.폭 === w.B?.폭 && (w.A?.폭 ?? 0) > 10, true, "열 둘 같은 폭(한 명령)");
+  resizeLines(ctx, true, [2], "40");
+  assertEqual(
+    Math.round((ctx.sheet().행?.["3"]?.높이 ?? 0) * 100) / 100,
+    30,
+    "행 높이 40px = 30pt",
+  );
+}
+// ── 시트 정렬(열 머리) — 쓴 범위 통째 · 고름 되돌림 · 빈 열은 안 함 ───────────────
+{
+  const ctx = realCtx({
+    A1: v("이름"),
+    B1: v("값"),
+    A2: v("다"),
+    B2: v(3),
+    A3: v("가"),
+    B3: v(1),
+    A4: v("나"),
+    B4: v(2),
+  });
+  const keep = ctx.selection;
+  await sortByColumn(ctx, 1, false);
+  assertEqual(
+    [val(ctx, 1, 0), val(ctx, 2, 0), val(ctx, 3, 0)],
+    ["가", "나", "다"],
+    "B 열 기준 오름 — A 열도 같이",
+  );
+  assertEqual(val(ctx, 0, 0), "이름", "머리 행 그대로");
+  assertEqual(ctx.selection, keep, "정렬 뒤 고름 되돌림");
+  await sortByColumn(ctx, 1, true);
+  assertEqual([val(ctx, 1, 1), val(ctx, 3, 1)], [3, 1], "내림");
+  const before = ctx.sent.length;
+  await sortByColumn(ctx, 5, false);
+  assertEqual(ctx.sent.length, before, "빈 열 정렬은 명령 없음");
+  assertEqual(usedRange(ctx.sheet()), { r0: 0, c0: 0, r1: 3, c1: 1 }, "쓴 범위");
+}
+// ── 필터 · 고정 · 그룹 · 더보기 ─────────────────────────────────────────────
+{
+  const ctx = realCtx({ A1: v("머리"), A2: v(1), B2: v(2) });
+  const calls: [string, unknown][] = [];
+  ctx.dataMenu = (kind) => calls.push([kind, structuredClone(ctx.selection.범위)]);
+  const more = colMoreItems(ctx, [0]);
+  assertEqual(
+    labels(more),
+    [
+      "-",
+      "열 크기 조절…",
+      "데이터에 맞추기",
+      "-",
+      "시트 정렬 A → Z",
+      "시트 정렬 Z → A",
+      "필터 만들기",
+      "-",
+      "고정 ▸",
+      "그룹 ▸",
+    ],
+    "열 머리 덧붙임 순서",
+  );
+  leaf(more, "필터 만들기")();
+  await tick();
+  assertEqual(calls[0], ["filter", [{ r0: 0, c0: 0, r1: 1, c1: 1 }]], "열 머리 필터 = 쓴 범위로");
+  leaf(cellMoreItems(ctx, { r0: 0, c0: 0, r1: 0, c1: 0 }), "드롭다운…")();
+  leaf(cellMoreItems(ctx, { r0: 0, c0: 0, r1: 0, c1: 0 }), "조건부 서식…")();
+  assertEqual(
+    calls.slice(1).map((c) => c[0]),
+    ["validation", "condfmt"],
+    "더보기 → 데이터 창",
+  );
+  leaf(rowMoreItems(ctx, [0]), "첫 행 고정")();
+  await tick();
+  assertEqual(ctx.sent.at(-1)?.종류, "틀고정", "고정 ▸ 첫 행");
+  ctx.selection = {
+    시트: "s1",
+    범위: [{ r0: 1, c0: 0, r1: 1, c1: 16383 }],
+    활성: { r: 1, c: 0 },
+    기준: { r: 1, c: 0 },
+  };
+  leaf(rowMoreItems(ctx, [1]), "그룹으로 묶기")();
+  await tick();
+  assertEqual(ctx.sheet().행?.["2"]?.묶음, { 층: 1 }, "그룹 ▸ 묶기");
+  assertEqual(
+    await nameRange(ctx, "", { r0: 0, c0: 0, r1: 0, c1: 0 }),
+    "이름을 넣을 것",
+    "범위 이름 · 빈 값",
+  );
+  assertEqual(
+    await nameRange(ctx, "합계칸", { r0: 1, c0: 0, r1: 1, c1: 1 }),
+    null,
+    "범위 이름 지정",
+  );
+  assertEqual(
+    typeof (await nameRange(ctx, "합계칸", { r0: 0, c0: 0, r1: 0, c1: 0 })),
+    "string",
+    "같은 이름은 거름",
+  );
+}
+// ── 붙여넣기 — 보안 문맥 갈래 ───────────────────────────────────────────────
+{
+  const g = globalThis as Record<string, unknown>;
+  g.isSecureContext = false;
+  assertEqual(canMenuPaste(), false, "http(보안 문맥 아님) — 메뉴로 못 읽음 → Ctrl+V 안내");
+  g.isSecureContext = true;
+  assertEqual(canMenuPaste(), false, "클립보드 API 없음 — 안내");
+  const clip = { html: "", text: "7\t8" };
+  Object.defineProperty(navigator, "clipboard", {
+    configurable: true,
+    value: {
+      read: async () => [
+        {
+          types: ["text/plain"],
+          getType: async () => new Blob([clip.text]),
+        },
+      ],
+    },
+  });
+  assertEqual(canMenuPaste(), true, "localhost · https — 메뉴로 읽음");
+  class FakeData {
+    data: Record<string, string> = {};
+    setData(k: string, s: string) {
+      this.data[k] = s;
+    }
+  }
+  class FakePaste {
+    constructor(
+      public type: string,
+      public init: { clipboardData: FakeData },
+    ) {}
+  }
+  g.DataTransfer = FakeData;
+  g.ClipboardEvent = FakePaste;
+  const ctx = realCtx({});
+  const events: FakePaste[] = [];
+  ctx.root = { dispatchEvent: (e: FakePaste) => events.push(e) } as unknown as HTMLElement;
+  await menuPaste(ctx);
+  assertEqual(
+    [events[0]?.type, events[0]?.init.clipboardData.data["text/plain"]],
+    ["paste", "7\t8"],
+    "보통 붙여넣기 = 부품 paste 길로",
+  );
+  ctx.selection = {
+    시트: "s1",
+    범위: [{ r0: 2, c0: 0, r1: 2, c1: 0 }],
+    활성: { r: 2, c: 0 },
+    기준: { r: 2, c: 0 },
+  };
+  await menuPaste(ctx, "값");
+  assertEqual([val(ctx, 2, 0), val(ctx, 2, 1)], [7, 8], "값만 붙여넣기 — 활성 칸부터");
+  assertEqual(labels(pasteItems(ctx)), ["붙여넣기", "선택하여 붙여넣기 ▸"], "붙여넣기 항목");
+}
+// ── 읽기 전용 — 복사 한 줄 ─────────────────────────────────────────────────
+{
+  const ctx = realCtx({});
+  assertEqual(labels(copyOnlyItems(ctx)), ["복사"], "읽기 전용 · 미리보기 = 복사 한 줄");
+}
+console.log("spreadsheet_menu_items 시험 끝");

From 71d15bf10ba2582c3fe3145c6dcb13c65b282d78 Mon Sep 17 00:00:00 2001
From: umsangdon <umsangdon@gmail.com>
Date: Thu, 8 Oct 2026 12:37:46 +0900
Subject: [PATCH 3/3] =?UTF-8?q?chore(plan):=20=EB=B6=84=EC=84=9D=5F?=
 =?UTF-8?q?=EC=A0=95=ED=95=A8=2091-1=20=ED=8C=90=EC=A0=95=20=EC=A4=84=20?=
 =?UTF-8?q?=E2=80=94=20=EB=A9=94=EC=9D=B8=20=ED=8C=90=EA=B3=BC=20=EA=B0=99?=
 =?UTF-8?q?=EC=9D=80=20=EB=82=B4=EC=9A=A9=20=EB=B0=9B=EC=95=84=20=EB=91=A0?=
 =?UTF-8?q?(91-1)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013rJwJMVL4EE31y77TB11AP
---
 docs/raw/요구_1008/분석_정함.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/docs/raw/요구_1008/분석_정함.md b/docs/raw/요구_1008/분석_정함.md
index a8e8395cc..2fca9cb8a 100644
--- a/docs/raw/요구_1008/분석_정함.md
+++ b/docs/raw/요구_1008/분석_정함.md
@@ -56,6 +56,7 @@
 - **유출 단 수(90-1)** — 관보호공 「추가 흙막이(단)」 스테퍼를 공용으로 세월교 · 박스 유출에 · 「+ 흙막이」 단추 없앰 · 단 수 → 상자 수(관보호공과 같은 방향) · 집계표도 단 수로 상자 자름 · 유출이 날개벽 · 없음인데 상자가 있던 자료 = 숨기고 집계에서 뺌(값은 파일에 남음).
 - **도수로 · 돌붙임(90-2)** — 두께 칸(cm · 기본 30 · 사용자 확정) · 유출 성토사면 선을 사면 안쪽으로 두께만큼 오프셋한 띠(윗면 = 사면선 · 근거 교본 「지반선보다 낮게 원지반에 설치」) · 유출 끝 ~ 성토사면이 원지반 만나는 곳(흙막이 단 사이 성토 조각 포함) · 안에 돌 무늬(흙막이 돌 그리기 재사용) · 도수로 · 돌붙임 형상 같음 · 배관 · 박스 · 세월교 · 물넘이포장(`ford_chute`) · 면적 · 터파기 영향 없음.
 - **제약 삭제(91)** — 형상 자체(벽 외곽)는 원지반 · 암 참조 없음(조사_G 1). 「해당」 = 세월교 바닥 · 흙막이 기본 높이(하상) · 다단 자동 자리(원지반에 앉는 x) · I형 집수정 하단. 더 = 설계선 끝 2 px 판정(줌마다 끝점 변동) · 전면 기울기 지형 자동판정. 91-1 에서 재현 목록 → 브레인 판정 → 91-3. 끝 연결선(성토부선 · 절토선이 원지반에서 끝남)은 형상 아님 → 남김.
+- **91-1 판정(브레인 · 10-8)** — ① 세월교 바닥 = 끊음(91-2 손 칸) ② 다단 자동 자리 = 끊음(지형 무관 등간격 · 앞 단 바닥 + 1:1.2 사면 일정 길이) ③ I형 집수정 근입 = 남김(집수정 형상 규칙 · 흙막이 아님) ④ 설계선 끝 2 px 판정 = 끊음(수치 교점 0.01 m) ⑤ 전면 기울기 지형 자동판정 = 끊음(관보호공 · 세월교 · 박스 흙막이 = 성토부 표값 고정 · 사면안정 흙막이 · 옹벽 = 설치 측 칸 값 · B08 도 같은 함수) ⑥ 끝 연결선 = 남김(잔재 문구만 지움).
 - **세월교 바닥(91-2)** — 처음 놓을 때 하상값 · 손 조정 칸(박스 `riseM` 꼴) · 원지반이 바뀌어도 안 따라감 · 흙막이 기본 높이도 이 값 기준.
 - **복합경사(91-4)** — 공용 도우미 하나(`common_util_cross_berm.ts cutProfilePoints` · 경계 = 원지반 + `rock_boundary_offset_m` · 켬 = 암 프리셋 + `two_stage_slope` · 소단 = `design.berm`) · 쓰는 곳 = 흙막이 수평공간 뒤 · 박스 끝 · 세월교 측벽 끝 · ㄴ·ㄷ 집수정 끝 · 절토 쪽 배관 유출 벽 뒤(지금 절토사면이 사라짐) · 소단 셈은 구조물 끝에서 새로 · `cutLine` 두 점 → 점열(횡단 셋 · 3D).