feat(bearing): 거더 짝 받침 · 종단경사 S · 솔플레이트 열 두께 (Q-SH1·4·8·9, 미연결)

받침방위각_솔플레이트검토.md §3 알고리즘의 순수 함수.
- 이웃 구조물 사이 짝짓기: 진행 방향, 방위각 차 ≤ 0.1°, 거더선 ≤ 0.1 m, 가장 가까운 것 (후보 2개 이상 WS04)
- 방위각 검사 10″ 초과 WS01 (입력 유지)
- S = z 차 / 수평거리, 오르막 쪽 구조물
- 열 두께 T = max(22, ceil(max T_req)), T1 오르막 쪽 / T2
A1–P1 검증: 짝 ①–⑤, S −1.908 / −1.906 / −1.904 / −1.904 / −1.902 %, T 30 · T1 38 · T2 22.

모델·화면에는 아직 연결하지 않는다. 높이 규칙(Q-SH7 블럭 상면 = z − (T − T_ref))이
2026-11-03 C안(받침높이 H 고정, h3 = H − T)과 충돌해 사용자 확인이 필요하다.

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

src/core/bearing-pair.ts

@@ -0,0 +1,115 @@
+/**
+ * 거더 짝 받침 · 종단경사 S · 솔플레이트 열 두께 (결정 2026-11-06, RAG/받침방위각_솔플레이트검토.md §3, Q-SH1·4·8·9).
+ * Pure. Not wired into the model yet: the height rule (Q-SH7, 블럭 상면 = z − (T − T_ref)) conflicts with the 2026-11-03
+ * C안 already in use (받침높이 H 고정, h3 = H − T, src/core/solplate-rule.ts), so only the parts both rules need live here.
+ *
+ * Frame: (E, N) in m as in the model (x = E, y = N). Azimuth: the model's 진북 방위각 (deg, clockwise from north), i.e. the
+ * workbook CAD angle θ_CAD converted by 90 − θ_CAD. A girder at azimuth θ runs along (sin θ, cos θ).
+ */
+
+export interface PairBearing {
+  no: number;
+  x: number;
+  y: number;
+  /** z (EL m). Q-SH5: both ends on the 받침블럭 상면 basis; the pier z definition is still spec Q16. */
+  z: number;
+  azimuthDeg: number;
+}
+
+export interface PairStructure {
+  name: string;
+  bearings: PairBearing[];
+}
+
+/** Q-SH1 tolerances and the Q-SH4 azimuth check. */
+export const PAIR_AZIMUTH_TOL_DEG = 0.1;
+export const PAIR_OFFSET_TOL_M = 0.1;
+export const AZIMUTH_CHECK_SEC = 10;
+
+export type PairWarning = 'WS01' | 'WS04';
+
+export interface BearingPair {
+  /** The bearing on structure k and its partner on structure k + 1 (structure order A1, P1 … Pn, A2). */
+  from: { structure: string; no: number };
+  to: { structure: string; no: number };
+  /** Horizontal distance (m), distance off the girder line of `from` (m), azimuth difference |θ_to − θ_from| (deg). */
+  distanceM: number;
+  offsetM: number;
+  azimuthDiffDeg: number;
+  /** Direction from → to as an azimuth (deg), and its difference from each input azimuth (arc seconds). */
+  directionDeg: number;
+  fromCheckSec: number;
+  toCheckSec: number;
+  /** S = (z_to − z_from) / distance × 100 (%), sign along the structure order (− = lower towards the later structure). */
+  slopePct: number;
+  /** The structure on the higher end: the 오르막 쪽 where T1 sits for both bearings. */
+  uphill: string;
+  warnings: PairWarning[];
+}
+
+const DEG = Math.PI / 180;
+const angleDiffDeg = (a: number, b: number) => Math.abs(((a - b + 540) % 360) - 180);
+
+/**
+ * Girder pairs between neighbouring structures (Q-SH1, Q-SH4). For each bearing b on structure k the candidates on k + 1 lie
+ * ahead along b's azimuth, within 0.1° of its azimuth and 0.1 m of its girder line; the closest to the line is the pair
+ * (WS04 when there were two or more). WS01 when either input azimuth is more than 10″ from the pair direction.
+ */
+export function girderPairs(structures: PairStructure[]): BearingPair[] {
+  const pairs: BearingPair[] = [];
+  for (let k = 0; k + 1 < structures.length; k++) {
+    const here = structures[k], next = structures[k + 1];
+    for (const b of here.bearings) {
+      const u = { e: Math.sin(b.azimuthDeg * DEG), n: Math.cos(b.azimuthDeg * DEG) };
+      const candidates = next.bearings.map((c) => {
+        const d = { e: c.x - b.x, n: c.y - b.y };
+        return { c, along: d.e * u.e + d.n * u.n, offset: Math.abs(d.e * u.n - d.n * u.e), dAz: angleDiffDeg(c.azimuthDeg, b.azimuthDeg), d };
+      }).filter((t) => t.along > 0 && t.dAz <= PAIR_AZIMUTH_TOL_DEG && t.offset <= PAIR_OFFSET_TOL_M)
+        .sort((p, q) => p.offset - q.offset);
+      if (!candidates.length) continue;
+      const best = candidates[0];
+      const distanceM = Math.hypot(best.d.e, best.d.n);
+      const directionDeg = (Math.atan2(best.d.e, best.d.n) / DEG + 360) % 360;
+      const fromCheckSec = angleDiffDeg(directionDeg, b.azimuthDeg) * 3600;
+      const toCheckSec = angleDiffDeg(directionDeg, best.c.azimuthDeg) * 3600;
+      const slopePct = ((best.c.z - b.z) / distanceM) * 100;
+      const warnings: PairWarning[] = [];
+      if (fromCheckSec > AZIMUTH_CHECK_SEC || toCheckSec > AZIMUTH_CHECK_SEC) warnings.push('WS01');
+      if (candidates.length > 1) warnings.push('WS04');
+      pairs.push({
+        from: { structure: here.name, no: b.no }, to: { structure: next.name, no: best.c.no },
+        distanceM, offsetM: best.offset, azimuthDiffDeg: best.dAz, directionDeg, fromCheckSec, toCheckSec,
+        slopePct, uphill: best.c.z > b.z ? next.name : here.name, warnings,
+      });
+    }
+  }
+  return pairs;
+}
+
+/** The pair a bearing belongs to, on either end; undefined when it has none (then WS03 with a fallback S, not done here). */
+export function pairOf(pairs: BearingPair[], structure: string, no: number): BearingPair | undefined {
+  return pairs.find((p) => (p.from.structure === structure && p.from.no === no) || (p.to.structure === structure && p.to.no === no));
+}
+
+/** Smallest allowed thin-end thickness T_min (mm, Q-SH3). */
+export const SOLE_T_MIN_MM = 22;
+
+/** Thickness one bearing needs: T_req = T_min + L·|S|/2 (L mm, S %). */
+export function soleRequiredT(lengthMm: number, slopePct: number, tMinMm: number = SOLE_T_MIN_MM): number {
+  return tMinMm + (lengthMm * Math.abs(slopePct)) / 200;
+}
+
+/**
+ * Row thickness and end thicknesses (Q-SH8·9): T_row = max(T_min, ⌈max T_req⌉) over the row; per bearing
+ * T1 = round(T_row + L·|S|/2) on the 오르막 쪽 and T2 = round(T_row − L·|S|/2) (≥ T_min by construction).
+ */
+export function soleRowThickness(items: { lengthMm: number; slopePct: number }[], tMinMm: number = SOLE_T_MIN_MM) {
+  const T = Math.max(tMinMm, Math.ceil(Math.max(...items.map((i) => soleRequiredT(i.lengthMm, i.slopePct, tMinMm))) - 1e-9));
+  return {
+    T,
+    ends: items.map((i) => {
+      const half = (i.lengthMm * Math.abs(i.slopePct)) / 200;
+      return { T1: Math.round(T + half), T2: Math.round(T - half) };
+    }),
+  };
+}