diff --git a/common_util/common_util_cross_design.ts b/common_util/common_util_cross_design.ts
index 730670a5..3aaeebee 100644
--- a/common_util/common_util_cross_design.ts
+++ b/common_util/common_util_cross_design.ts
@@ -24,6 +24,8 @@
  * ========================================================================== */
 
 import { splitCutAreas, trapezoidAreas } from "./common_util_cross_design_areas";
+// 단면 기하(노면·측구·사면 설계고)는 파일이 700줄을 넘어 떼어냈다(2026-09-04).
+import { SectionGeometry, type ResolvedGroup } from "./common_util_cross_design_geometry";
 
 /** 지반유형 → 표준단면 프리셋 키. 짝: config `SECTION_GROUND_TYPE_PRESET`. */
 const GROUND_TYPE_PRESET: Record<string, string> = {
@@ -39,10 +41,6 @@ const DITCH_TYPES = ["standard", "l_type"];
 
 /** 사면이 원지반과 만났다고 볼 높이차(m). 짝: `_SLOPE_CLOSE_TOLERANCE_M`. */
 const SLOPE_CLOSE_TOLERANCE_M = 0.01;
-/** 사면·경계 교차 탐색 행진 간격(m)과 최대 거리. 짝: 파이썬 `step`/`max_dist`. */
-const MARCH_STEP_M = 0.05;
-const KNEE_MAX_M = 200;
-const CROSS_MAX_M = 500;
 
 export interface CrossGroundSample {
   offset_m?: number | null;
@@ -131,21 +129,6 @@ function asFloat(value: unknown, fallback: number): number {
   return parsed >= 0 ? parsed : fallback;
 }
 
-interface ResolvedGroup {
-  road_width_m: number;
-  shoulder_left_m: number;
-  shoulder_right_m: number;
-  ditch_top_width_m: number;
-  ditch_bottom_width_m: number;
-  ditch_depth_m: number;
-  l_ditch_width_m: number;
-  l_ditch_depth_m: number;
-  cross_slope_pct: number;
-  fill_slope_ratio: number;
-  cut_slope_ratio: number;
-  pavement_thickness_m: number;
-}
-
 /**
  * 짝: `_resolve_group`. 파이썬은 config 위에 패널 편집값을 덮지만, 여기서는 이미 그렇게
  * 합쳐진 한 벌(`standard`)을 받는다 — config 수치를 프론트에 복제하지 않기 위함이다.
@@ -176,15 +159,6 @@ function resolveGroup(presetKey: string, standard: StandardCrossSectionSpec): Re
   };
 }
 
-/** 짝: `_side_role`. 단면유형 → [좌측 역할, 우측 역할]. */
-function sideRole(sectionMode: string): [string, string] {
-  if (sectionMode === "left_cut") return ["cut", "fill"];
-  if (sectionMode === "right_cut") return ["fill", "cut"];
-  if (sectionMode === "both_cut") return ["cut", "cut"];
-  if (sectionMode === "both_fill") return ["fill", "fill"];
-  throw new Error(`지원하지 않는 단면유형입니다: ${sectionMode}`);
-}
-
 /** 짝: `_resolve_ditch_side`. */
 function resolveDitchSide(sectionMode: string, ditchSide: string | null | undefined): string {
   if (sectionMode === "left_cut") return "left";
@@ -220,303 +194,6 @@ function groundInterpolator(valid: Array<[number, number]>): (offsetM: number) =
   };
 }
 
-/** 짝: `_SectionGeometry`. 노면 → 측구 → 사면 순으로 offset 의 설계고를 계산한다. */
-class SectionGeometry {
-  halfRoad: number;
-  leftExtent: number;
-  rightExtent: number;
-  zCenter: number;
-  cutRatio: number;
-  fillRatio: number;
-  leftRole: string;
-  rightRole: string;
-  ditchSide: string;
-  soilCutRatio: number;
-  twoStage: boolean;
-  ditchType: string;
-  slopePerOffset: number;
-  hasDitch: boolean;
-  ditchPoints: Array<[number, number]> = [];
-  private groundAt: ((offsetM: number) => number) | null;
-  private rockOffset: number;
-  private rockKnee = new Map<string, [number, number] | null>();
-  private cutCross = new Map<string, number | null>();
-  private fillCross = new Map<string, number | null>();
-
-  constructor(params: {
-    designElevationM: number;
-    group: ResolvedGroup;
-    sectionMode: string;
-    ditchSide: string;
-    ditchType: string;
-    crossSlopePct: number;
-    groundAt: ((offsetM: number) => number) | null;
-    soilCutRatio: number | null;
-    rockBoundaryOffsetM: number | null;
-    twoStageSlope: boolean;
-    ditchEnabled: boolean | null;
-  }) {
-    const { group } = params;
-    const halfRoad = group.road_width_m / 2;
-    this.halfRoad = halfRoad;
-    this.leftExtent = halfRoad + group.shoulder_left_m;
-    this.rightExtent = halfRoad + group.shoulder_right_m;
-    this.zCenter = params.designElevationM;
-    this.cutRatio = Math.max(group.cut_slope_ratio, 1e-6);
-    this.fillRatio = Math.max(group.fill_slope_ratio, 1e-6);
-    [this.leftRole, this.rightRole] = sideRole(params.sectionMode);
-    this.ditchSide = params.ditchSide;
-    this.soilCutRatio = Math.max(params.soilCutRatio ?? group.cut_slope_ratio, 1e-6);
-    this.twoStage = Boolean(
-      params.twoStageSlope && params.groundAt !== null && params.rockBoundaryOffsetM !== null,
-    );
-    this.groundAt = params.groundAt;
-    this.rockOffset = params.rockBoundaryOffsetM ?? 0;
-    this.ditchType = params.ditchType;
-    // 횡단경사: 측구 방향으로 내려가는 단일 사면 (좌=+offset 규약).
-    const slope = params.crossSlopePct / 100;
-    this.slopePerOffset = params.ditchSide === "left" ? -slope : slope;
-
-    // 단면유형 자동 판정(D-2) — 노면 끝 지반이 설계면보다 높으면 절토, 낮으면 성토.
-    const groundAt = params.groundAt;
-    if (groundAt !== null) {
-      this.leftRole =
-        groundAt(this.leftExtent) > this.roadZ(this.leftExtent) + 1e-3 ? "cut" : "fill";
-      this.rightRole =
-        groundAt(-this.rightExtent) > this.roadZ(-this.rightExtent) + 1e-3 ? "cut" : "fill";
-    }
-
-    // 측구 생성 여부(D-1).
-    if (params.sectionMode === "both_fill") {
-      this.hasDitch = false;
-    } else if (params.ditchEnabled !== null && params.ditchEnabled !== undefined) {
-      this.hasDitch = params.ditchEnabled;
-    } else if (groundAt !== null) {
-      const ditchEdge = params.ditchSide === "left" ? this.leftExtent : -this.rightExtent;
-      this.hasDitch = groundAt(ditchEdge) > this.roadZ(ditchEdge) + 1e-3;
-    } else {
-      this.hasDitch = true;
-    }
-
-    // 측구 꼭짓점(측구측 노면 끝 기준, 바깥 방향 부호 적용).
-    const edgeOffset = params.ditchSide === "left" ? this.leftExtent : -this.rightExtent;
-    const outward = params.ditchSide === "left" ? 1 : -1;
-    const edgeZ = this.roadZ(edgeOffset);
-    if (this.hasDitch) {
-      if (params.ditchType === "l_type") {
-        // L형: 노면 끝에서 폭 W 동안 깊이 D로 내려가는 경사 바닥 + 바깥 수직벽.
-        const width = group.l_ditch_width_m;
-        const depth = group.l_ditch_depth_m;
-        this.ditchPoints = [
-          [edgeOffset, edgeZ],
-          [edgeOffset + outward * width, edgeZ - depth],
-          [edgeOffset + outward * width, edgeZ],
-        ];
-      } else {
-        // 일반: 상단폭/저폭/깊이 사다리꼴.
-        const top = group.ditch_top_width_m;
-        const bottom = Math.min(group.ditch_bottom_width_m, top);
-        const depth = group.ditch_depth_m;
-        const inset = (top - bottom) / 2;
-        this.ditchPoints = [
-          [edgeOffset, edgeZ],
-          [edgeOffset + outward * inset, edgeZ - depth],
-          [edgeOffset + outward * (inset + bottom), edgeZ - depth],
-          [edgeOffset + outward * top, edgeZ],
-        ];
-      }
-    }
-  }
-
-  /** 노면(노견 포함) 설계고 — 중심 계획고에서 횡단경사로 기운 단일 평면. */
-  roadZ(offsetM: number): number {
-    return this.zCenter + this.slopePerOffset * offsetM;
-  }
-
-  /** 짝: `_slope_start`. 사면 시작점 [오프셋 절대값 거리, 표고]. */
-  private slopeStart(side: string): [number, number] {
-    const edgeOffset = side === "left" ? this.leftExtent : this.rightExtent;
-    const edgeZ = side === "left" ? this.roadZ(this.leftExtent) : this.roadZ(-this.rightExtent);
-    if (side === this.ditchSide && this.ditchPoints.length) {
-      const outer = this.ditchPoints[this.ditchPoints.length - 1];
-      return [Math.abs(outer[0]), outer[1]];
-    }
-    return [edgeOffset, edgeZ];
-  }
-
-  /** 짝: `_rock_boundary_z`. 암반 경계선 표고 = 지반선 + 오프셋(음수=하향). */
-  private rockBoundaryZ(side: string, dist: number): number {
-    const signed = side === "left" ? dist : -dist;
-    return (this.groundAt as (offsetM: number) => number)(signed) + this.rockOffset;
-  }
-
-  /** 짝: `knee`. 절토 사면이 암반 경계선을 지나는 전환점(무릎). */
-  knee(side: string): [number, number] | null {
-    if (!this.twoStage) return null;
-    const cached = this.rockKnee.get(side);
-    if (cached !== undefined) return cached;
-    const [startDist, startZ] = this.slopeStart(side);
-    let diffPrev = startZ - this.rockBoundaryZ(side, startDist);
-    let result: [number, number] | null;
-    if (diffPrev >= 0) {
-      result = [startDist, startZ]; // 시작부터 토사(경계 위)
-    } else {
-      result = null;
-      let distPrev = startDist;
-      let dist = startDist + MARCH_STEP_M;
-      while (dist <= startDist + KNEE_MAX_M) {
-        const zRock = startZ + (dist - startDist) / this.cutRatio;
-        const diff = zRock - this.rockBoundaryZ(side, dist);
-        if (diff >= 0) {
-          const span = diff - diffPrev;
-          const ratio = Math.abs(span) > 1e-9 ? -diffPrev / span : 0;
-          const kneeDist = distPrev + (dist - distPrev) * ratio;
-          const kneeZ = startZ + (kneeDist - startDist) / this.cutRatio;
-          result = [kneeDist, kneeZ];
-          break;
-        }
-        distPrev = dist;
-        diffPrev = diff;
-        dist += MARCH_STEP_M;
-      }
-    }
-    this.rockKnee.set(side, result);
-    return result;
-  }
-
-  /** 짝: `_cut_slope_z`. 절토 사면선 표고(2단계 무릎 반영, 지반 클램프 없음). */
-  private cutSlopeZ(side: string, dist: number): number {
-    const [startDist, startZ] = this.slopeStart(side);
-    const knee = this.twoStage ? this.knee(side) : null;
-    if (knee !== null) {
-      const [kneeDist, kneeZ] = knee;
-      if (dist <= kneeDist) return startZ + (dist - startDist) / this.cutRatio;
-      return kneeZ + (dist - kneeDist) / this.soilCutRatio;
-    }
-    return startZ + (dist - startDist) / this.cutRatio;
-  }
-
-  /** 짝: `cut_cross_dist`. 절토 사면이 지반선과 처음 만나는 거리(N-2-4). */
-  cutCrossDist(side: string): number | null {
-    const cached = this.cutCross.get(side);
-    if (cached !== undefined) return cached;
-    let result: number | null = null;
-    if (this.groundAt !== null) {
-      const [startDist] = this.slopeStart(side);
-      let dist = startDist;
-      const maxDist = startDist + CROSS_MAX_M;
-      while (dist <= maxDist) {
-        const signed = side === "left" ? dist : -dist;
-        if (this.cutSlopeZ(side, dist) - this.groundAt(signed) >= 0) {
-          result = dist;
-          break;
-        }
-        dist += MARCH_STEP_M;
-      }
-    }
-    this.cutCross.set(side, result);
-    return result;
-  }
-
-  /** 짝: `fill_cross_dist`. 성토 사면이 지반선과 처음 만나는 거리. */
-  fillCrossDist(side: string): number | null {
-    const cached = this.fillCross.get(side);
-    if (cached !== undefined) return cached;
-    let result: number | null = null;
-    if (this.groundAt !== null) {
-      const [startDist, startZ] = this.slopeStart(side);
-      let dist = startDist;
-      const maxDist = startDist + CROSS_MAX_M;
-      while (dist <= maxDist) {
-        const signed = side === "left" ? dist : -dist;
-        const fillLine = startZ - (dist - startDist) / this.fillRatio;
-        if (fillLine - this.groundAt(signed) <= 0) {
-          result = dist;
-          break;
-        }
-        dist += MARCH_STEP_M;
-      }
-    }
-    this.fillCross.set(side, result);
-    return result;
-  }
-
-  /** 짝: `fill_ground_slope`. 성토측 자연 지반 평균 경사(rise/run). */
-  fillGroundSlope(): number | null {
-    if (this.groundAt === null) return null;
-    const slopes: number[] = [];
-    for (const side of ["left", "right"]) {
-      const role = side === "left" ? this.leftRole : this.rightRole;
-      if (role !== "fill") continue;
-      const [startDist] = this.slopeStart(side);
-      const endDist = this.fillCrossDist(side) ?? startDist + 10;
-      const run = endDist - startDist;
-      if (run <= 1e-6) continue;
-      const sign = side === "left" ? 1 : -1;
-      const rise = Math.abs(this.groundAt(sign * endDist) - this.groundAt(sign * startDist));
-      slopes.push(rise / run);
-    }
-    return slopes.length ? Math.min(...slopes) : null;
-  }
-
-  /** 짝: `design_z`. offset 하나의 설계 표고(사면은 지반 교차점 이후 지반 추종). */
-  designZ(offsetM: number, groundM: number): number {
-    const side = offsetM >= 0 ? "left" : "right";
-    const extent = side === "left" ? this.leftExtent : this.rightExtent;
-    if (Math.abs(offsetM) <= extent + 1e-9) return this.roadZ(offsetM);
-    // 측구 구간: 꼭짓점 사이 선형 보간(지반 무관 강제 굴착).
-    if (side === this.ditchSide && this.ditchPoints.length) {
-      const inner = Math.abs(this.ditchPoints[0][0]);
-      const outer = Math.abs(this.ditchPoints[this.ditchPoints.length - 1][0]);
-      if (Math.abs(offsetM) >= inner - 1e-9 && Math.abs(offsetM) <= outer + 1e-9) {
-        const points = this.ditchPoints;
-        for (let index = 1; index < points.length; index += 1) {
-          const x0 = Math.abs(points[index - 1][0]);
-          const z0 = points[index - 1][1];
-          const x1 = Math.abs(points[index][0]);
-          const z1 = points[index][1];
-          if (Math.abs(offsetM) > x1 + 1e-9) continue;
-          const span = x1 - x0;
-          if (span <= 1e-9) return z1;
-          return z0 + (z1 - z0) * ((Math.abs(offsetM) - x0) / span);
-        }
-        return points[points.length - 1][1];
-      }
-    }
-    const role = side === "left" ? this.leftRole : this.rightRole;
-    const [startDist, startZ] = this.slopeStart(side);
-    const dist = Math.abs(offsetM);
-    const run = dist - startDist;
-    if (role === "cut") {
-      const cross = this.cutCrossDist(side);
-      if (cross !== null && dist >= cross) return groundM;
-      return Math.min(this.cutSlopeZ(side, dist), groundM);
-    }
-    const cross = this.fillCrossDist(side);
-    if (cross !== null && dist >= cross) return groundM;
-    return Math.max(startZ - run / this.fillRatio, groundM);
-  }
-
-  /** 짝: `breakpoints`. 적분·설계선에 반드시 넣을 설계 꼭짓점 오프셋. */
-  breakpoints(): number[] {
-    const points = [0, this.leftExtent, -this.rightExtent];
-    for (const [offset] of this.ditchPoints) points.push(offset);
-    if (this.twoStage) {
-      for (const side of ["left", "right"]) {
-        const role = side === "left" ? this.leftRole : this.rightRole;
-        const knee = role === "cut" ? this.knee(side) : null;
-        if (knee !== null) points.push(side === "left" ? knee[0] : -knee[0]);
-      }
-    }
-    for (const side of ["left", "right"]) {
-      const role = side === "left" ? this.leftRole : this.rightRole;
-      const cross = role === "cut" ? this.cutCrossDist(side) : this.fillCrossDist(side);
-      if (cross !== null) points.push(side === "left" ? cross : -cross);
-    }
-    return points;
-  }
-}
-
 /**
  * 짝: `compute_cross_design`. 측점 하나의 표준횡단 설계선과 절·성토 단면적을 낸다.
  *
diff --git a/common_util/common_util_cross_design_geometry.ts b/common_util/common_util_cross_design_geometry.ts
new file mode 100644
index 00000000..466ead9b
--- /dev/null
+++ b/common_util/common_util_cross_design_geometry.ts
@@ -0,0 +1,333 @@
+/* =============================================================================
+ * common_util_cross_design_geometry.ts
+ * 표준횡단 단면 기하 — 노면·측구·사면 순으로 offset 의 설계고를 계산한다.
+ *
+ * ⚠ 짝 파일 `B06_Section/B06_Section_Engine_Design.py` 의 `_SectionGeometry` 와 한 벌이다.
+ * `common_util_cross_design.ts` 가 700줄을 넘어 떼어냈다(2026-09-04) — 계산은 그대로다.
+ * ========================================================================== */
+
+/** 사면·경계 교차 탐색 행진 간격(m)과 최대 거리. 짝: 파이썬 `step`/`max_dist`. */
+const MARCH_STEP_M = 0.05;
+const KNEE_MAX_M = 200;
+const CROSS_MAX_M = 500;
+
+export interface ResolvedGroup {
+  road_width_m: number;
+  shoulder_left_m: number;
+  shoulder_right_m: number;
+  ditch_top_width_m: number;
+  ditch_bottom_width_m: number;
+  ditch_depth_m: number;
+  l_ditch_width_m: number;
+  l_ditch_depth_m: number;
+  cross_slope_pct: number;
+  fill_slope_ratio: number;
+  cut_slope_ratio: number;
+  pavement_thickness_m: number;
+}
+
+/** 짝: `_side_role`. 단면유형 → [좌측 역할, 우측 역할]. */
+export function sideRole(sectionMode: string): [string, string] {
+  if (sectionMode === "left_cut") return ["cut", "fill"];
+  if (sectionMode === "right_cut") return ["fill", "cut"];
+  if (sectionMode === "both_cut") return ["cut", "cut"];
+  if (sectionMode === "both_fill") return ["fill", "fill"];
+  throw new Error(`지원하지 않는 단면유형입니다: ${sectionMode}`);
+}
+
+/** 짝: `_SectionGeometry`. 노면 → 측구 → 사면 순으로 offset 의 설계고를 계산한다. */
+export class SectionGeometry {
+  halfRoad: number;
+  leftExtent: number;
+  rightExtent: number;
+  zCenter: number;
+  cutRatio: number;
+  fillRatio: number;
+  leftRole: string;
+  rightRole: string;
+  ditchSide: string;
+  soilCutRatio: number;
+  twoStage: boolean;
+  ditchType: string;
+  slopePerOffset: number;
+  hasDitch: boolean;
+  ditchPoints: Array<[number, number]> = [];
+  private groundAt: ((offsetM: number) => number) | null;
+  private rockOffset: number;
+  private rockKnee = new Map<string, [number, number] | null>();
+  private cutCross = new Map<string, number | null>();
+  private fillCross = new Map<string, number | null>();
+
+  constructor(params: {
+    designElevationM: number;
+    group: ResolvedGroup;
+    sectionMode: string;
+    ditchSide: string;
+    ditchType: string;
+    crossSlopePct: number;
+    groundAt: ((offsetM: number) => number) | null;
+    soilCutRatio: number | null;
+    rockBoundaryOffsetM: number | null;
+    twoStageSlope: boolean;
+    ditchEnabled: boolean | null;
+  }) {
+    const { group } = params;
+    const halfRoad = group.road_width_m / 2;
+    this.halfRoad = halfRoad;
+    this.leftExtent = halfRoad + group.shoulder_left_m;
+    this.rightExtent = halfRoad + group.shoulder_right_m;
+    this.zCenter = params.designElevationM;
+    this.cutRatio = Math.max(group.cut_slope_ratio, 1e-6);
+    this.fillRatio = Math.max(group.fill_slope_ratio, 1e-6);
+    [this.leftRole, this.rightRole] = sideRole(params.sectionMode);
+    this.ditchSide = params.ditchSide;
+    this.soilCutRatio = Math.max(params.soilCutRatio ?? group.cut_slope_ratio, 1e-6);
+    this.twoStage = Boolean(
+      params.twoStageSlope && params.groundAt !== null && params.rockBoundaryOffsetM !== null,
+    );
+    this.groundAt = params.groundAt;
+    this.rockOffset = params.rockBoundaryOffsetM ?? 0;
+    this.ditchType = params.ditchType;
+    // 횡단경사: 측구 방향으로 내려가는 단일 사면 (좌=+offset 규약).
+    const slope = params.crossSlopePct / 100;
+    this.slopePerOffset = params.ditchSide === "left" ? -slope : slope;
+
+    // 단면유형 자동 판정(D-2) — 노면 끝 지반이 설계면보다 높으면 절토, 낮으면 성토.
+    const groundAt = params.groundAt;
+    if (groundAt !== null) {
+      this.leftRole =
+        groundAt(this.leftExtent) > this.roadZ(this.leftExtent) + 1e-3 ? "cut" : "fill";
+      this.rightRole =
+        groundAt(-this.rightExtent) > this.roadZ(-this.rightExtent) + 1e-3 ? "cut" : "fill";
+    }
+
+    // 측구 생성 여부(D-1).
+    if (params.sectionMode === "both_fill") {
+      this.hasDitch = false;
+    } else if (params.ditchEnabled !== null && params.ditchEnabled !== undefined) {
+      this.hasDitch = params.ditchEnabled;
+    } else if (groundAt !== null) {
+      const ditchEdge = params.ditchSide === "left" ? this.leftExtent : -this.rightExtent;
+      this.hasDitch = groundAt(ditchEdge) > this.roadZ(ditchEdge) + 1e-3;
+    } else {
+      this.hasDitch = true;
+    }
+
+    // 측구 꼭짓점(측구측 노면 끝 기준, 바깥 방향 부호 적용).
+    const edgeOffset = params.ditchSide === "left" ? this.leftExtent : -this.rightExtent;
+    const outward = params.ditchSide === "left" ? 1 : -1;
+    const edgeZ = this.roadZ(edgeOffset);
+    if (this.hasDitch) {
+      if (params.ditchType === "l_type") {
+        // L형: 노면 끝에서 폭 W 동안 깊이 D로 내려가는 경사 바닥 + 바깥 수직벽.
+        const width = group.l_ditch_width_m;
+        const depth = group.l_ditch_depth_m;
+        this.ditchPoints = [
+          [edgeOffset, edgeZ],
+          [edgeOffset + outward * width, edgeZ - depth],
+          [edgeOffset + outward * width, edgeZ],
+        ];
+      } else {
+        // 일반: 상단폭/저폭/깊이 사다리꼴.
+        const top = group.ditch_top_width_m;
+        const bottom = Math.min(group.ditch_bottom_width_m, top);
+        const depth = group.ditch_depth_m;
+        const inset = (top - bottom) / 2;
+        this.ditchPoints = [
+          [edgeOffset, edgeZ],
+          [edgeOffset + outward * inset, edgeZ - depth],
+          [edgeOffset + outward * (inset + bottom), edgeZ - depth],
+          [edgeOffset + outward * top, edgeZ],
+        ];
+      }
+    }
+  }
+
+  /** 노면(노견 포함) 설계고 — 중심 계획고에서 횡단경사로 기운 단일 평면. */
+  roadZ(offsetM: number): number {
+    return this.zCenter + this.slopePerOffset * offsetM;
+  }
+
+  /** 짝: `_slope_start`. 사면 시작점 [오프셋 절대값 거리, 표고]. */
+  private slopeStart(side: string): [number, number] {
+    const edgeOffset = side === "left" ? this.leftExtent : this.rightExtent;
+    const edgeZ = side === "left" ? this.roadZ(this.leftExtent) : this.roadZ(-this.rightExtent);
+    if (side === this.ditchSide && this.ditchPoints.length) {
+      const outer = this.ditchPoints[this.ditchPoints.length - 1];
+      return [Math.abs(outer[0]), outer[1]];
+    }
+    return [edgeOffset, edgeZ];
+  }
+
+  /** 짝: `_rock_boundary_z`. 암반 경계선 표고 = 지반선 + 오프셋(음수=하향). */
+  private rockBoundaryZ(side: string, dist: number): number {
+    const signed = side === "left" ? dist : -dist;
+    return (this.groundAt as (offsetM: number) => number)(signed) + this.rockOffset;
+  }
+
+  /** 짝: `knee`. 절토 사면이 암반 경계선을 지나는 전환점(무릎). */
+  knee(side: string): [number, number] | null {
+    if (!this.twoStage) return null;
+    const cached = this.rockKnee.get(side);
+    if (cached !== undefined) return cached;
+    const [startDist, startZ] = this.slopeStart(side);
+    let diffPrev = startZ - this.rockBoundaryZ(side, startDist);
+    let result: [number, number] | null;
+    if (diffPrev >= 0) {
+      result = [startDist, startZ]; // 시작부터 토사(경계 위)
+    } else {
+      result = null;
+      let distPrev = startDist;
+      let dist = startDist + MARCH_STEP_M;
+      while (dist <= startDist + KNEE_MAX_M) {
+        const zRock = startZ + (dist - startDist) / this.cutRatio;
+        const diff = zRock - this.rockBoundaryZ(side, dist);
+        if (diff >= 0) {
+          const span = diff - diffPrev;
+          const ratio = Math.abs(span) > 1e-9 ? -diffPrev / span : 0;
+          const kneeDist = distPrev + (dist - distPrev) * ratio;
+          const kneeZ = startZ + (kneeDist - startDist) / this.cutRatio;
+          result = [kneeDist, kneeZ];
+          break;
+        }
+        distPrev = dist;
+        diffPrev = diff;
+        dist += MARCH_STEP_M;
+      }
+    }
+    this.rockKnee.set(side, result);
+    return result;
+  }
+
+  /** 짝: `_cut_slope_z`. 절토 사면선 표고(2단계 무릎 반영, 지반 클램프 없음). */
+  private cutSlopeZ(side: string, dist: number): number {
+    const [startDist, startZ] = this.slopeStart(side);
+    const knee = this.twoStage ? this.knee(side) : null;
+    if (knee !== null) {
+      const [kneeDist, kneeZ] = knee;
+      if (dist <= kneeDist) return startZ + (dist - startDist) / this.cutRatio;
+      return kneeZ + (dist - kneeDist) / this.soilCutRatio;
+    }
+    return startZ + (dist - startDist) / this.cutRatio;
+  }
+
+  /** 짝: `cut_cross_dist`. 절토 사면이 지반선과 처음 만나는 거리(N-2-4). */
+  cutCrossDist(side: string): number | null {
+    const cached = this.cutCross.get(side);
+    if (cached !== undefined) return cached;
+    let result: number | null = null;
+    if (this.groundAt !== null) {
+      const [startDist] = this.slopeStart(side);
+      let dist = startDist;
+      const maxDist = startDist + CROSS_MAX_M;
+      while (dist <= maxDist) {
+        const signed = side === "left" ? dist : -dist;
+        if (this.cutSlopeZ(side, dist) - this.groundAt(signed) >= 0) {
+          result = dist;
+          break;
+        }
+        dist += MARCH_STEP_M;
+      }
+    }
+    this.cutCross.set(side, result);
+    return result;
+  }
+
+  /** 짝: `fill_cross_dist`. 성토 사면이 지반선과 처음 만나는 거리. */
+  fillCrossDist(side: string): number | null {
+    const cached = this.fillCross.get(side);
+    if (cached !== undefined) return cached;
+    let result: number | null = null;
+    if (this.groundAt !== null) {
+      const [startDist, startZ] = this.slopeStart(side);
+      let dist = startDist;
+      const maxDist = startDist + CROSS_MAX_M;
+      while (dist <= maxDist) {
+        const signed = side === "left" ? dist : -dist;
+        const fillLine = startZ - (dist - startDist) / this.fillRatio;
+        if (fillLine - this.groundAt(signed) <= 0) {
+          result = dist;
+          break;
+        }
+        dist += MARCH_STEP_M;
+      }
+    }
+    this.fillCross.set(side, result);
+    return result;
+  }
+
+  /** 짝: `fill_ground_slope`. 성토측 자연 지반 평균 경사(rise/run). */
+  fillGroundSlope(): number | null {
+    if (this.groundAt === null) return null;
+    const slopes: number[] = [];
+    for (const side of ["left", "right"]) {
+      const role = side === "left" ? this.leftRole : this.rightRole;
+      if (role !== "fill") continue;
+      const [startDist] = this.slopeStart(side);
+      const endDist = this.fillCrossDist(side) ?? startDist + 10;
+      const run = endDist - startDist;
+      if (run <= 1e-6) continue;
+      const sign = side === "left" ? 1 : -1;
+      const rise = Math.abs(this.groundAt(sign * endDist) - this.groundAt(sign * startDist));
+      slopes.push(rise / run);
+    }
+    return slopes.length ? Math.min(...slopes) : null;
+  }
+
+  /** 짝: `design_z`. offset 하나의 설계 표고(사면은 지반 교차점 이후 지반 추종). */
+  designZ(offsetM: number, groundM: number): number {
+    const side = offsetM >= 0 ? "left" : "right";
+    const extent = side === "left" ? this.leftExtent : this.rightExtent;
+    if (Math.abs(offsetM) <= extent + 1e-9) return this.roadZ(offsetM);
+    // 측구 구간: 꼭짓점 사이 선형 보간(지반 무관 강제 굴착).
+    if (side === this.ditchSide && this.ditchPoints.length) {
+      const inner = Math.abs(this.ditchPoints[0][0]);
+      const outer = Math.abs(this.ditchPoints[this.ditchPoints.length - 1][0]);
+      if (Math.abs(offsetM) >= inner - 1e-9 && Math.abs(offsetM) <= outer + 1e-9) {
+        const points = this.ditchPoints;
+        for (let index = 1; index < points.length; index += 1) {
+          const x0 = Math.abs(points[index - 1][0]);
+          const z0 = points[index - 1][1];
+          const x1 = Math.abs(points[index][0]);
+          const z1 = points[index][1];
+          if (Math.abs(offsetM) > x1 + 1e-9) continue;
+          const span = x1 - x0;
+          if (span <= 1e-9) return z1;
+          return z0 + (z1 - z0) * ((Math.abs(offsetM) - x0) / span);
+        }
+        return points[points.length - 1][1];
+      }
+    }
+    const role = side === "left" ? this.leftRole : this.rightRole;
+    const [startDist, startZ] = this.slopeStart(side);
+    const dist = Math.abs(offsetM);
+    const run = dist - startDist;
+    if (role === "cut") {
+      const cross = this.cutCrossDist(side);
+      if (cross !== null && dist >= cross) return groundM;
+      return Math.min(this.cutSlopeZ(side, dist), groundM);
+    }
+    const cross = this.fillCrossDist(side);
+    if (cross !== null && dist >= cross) return groundM;
+    return Math.max(startZ - run / this.fillRatio, groundM);
+  }
+
+  /** 짝: `breakpoints`. 적분·설계선에 반드시 넣을 설계 꼭짓점 오프셋. */
+  breakpoints(): number[] {
+    const points = [0, this.leftExtent, -this.rightExtent];
+    for (const [offset] of this.ditchPoints) points.push(offset);
+    if (this.twoStage) {
+      for (const side of ["left", "right"]) {
+        const role = side === "left" ? this.leftRole : this.rightRole;
+        const knee = role === "cut" ? this.knee(side) : null;
+        if (knee !== null) points.push(side === "left" ? knee[0] : -knee[0]);
+      }
+    }
+    for (const side of ["left", "right"]) {
+      const role = side === "left" ? this.leftRole : this.rightRole;
+      const cross = role === "cut" ? this.cutCrossDist(side) : this.fillCrossDist(side);
+      if (cross !== null) points.push(side === "left" ? cross : -cross);
+    }
+    return points;
+  }
+}