feat(view): round bar bends at the centre-line radius; bend factors as inputs on ③

Bars drawn through several points are one tube each, with every bend rounded by R·tan(φ/2) at the centre-line radius
(inner factor × d + d/2). The inside-radius factors (D16 and below, D19–D25, D29–D35, D38 and above) are inputs in 공통
설정, with KDS-based defaults 2 / 3 / 4 / 5. The size-class limits sit in one place (SIZE_CLASS), which also fixes
D25 (25.4) being read as the D29–D35 class in hookLength. The helper bendDeduction gives the centre-line deduction for
the length option, which is not yet applied to the 철근표 lengths.

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

index.html

@@ -181,6 +181,11 @@
             <label class="mat">D 규격 강도 <select id="mat-grade-d"><option value="300" selected>SD300</option><option value="400">SD400</option><option value="500">SD500</option></select></label>
             <label class="mat">H 규격 강도 <select id="mat-grade-h"><option value="300">SD300</option><option value="400" selected>SD400</option><option value="500">SD500</option></select></label>
             <label class="mat">S 규격 강도 <select id="mat-grade-s"><option value="300">SD300</option><option value="400">SD400</option><option value="500" selected>SD500</option></select></label>
+            <p class="lbl">굽힘 내면반경 (× 철근 지름)</p>
+            <label class="mat">D16 이하 <input id="bend-small16" type="number" step="0.5" min="0.5" /></label>
+            <label class="mat">D19–D25 <input id="bend-main25" type="number" step="0.5" min="0.5" /></label>
+            <label class="mat">D29–D35 <input id="bend-main35" type="number" step="0.5" min="0.5" /></label>
+            <label class="mat">D38 이상 <input id="bend-main51" type="number" step="0.5" min="0.5" /></label>
             <p id="mat-note" class="muted small"></p>
           </section>
         </aside>

src/core/rebar/common.ts

@@ -8,15 +8,50 @@ export const GRADE_CHOICES = [300, 400, 500] as const;
 /** Bar family by 규격 prefix: D · H · S. */
 export type GradeKey = 'D' | 'H' | 'S';
 
-/** Material inputs of ③ 공통 설정 (spec §6.2). fck and the grade per prefix are inputs. */
+/**
+ * Inside bend radius as a multiple of the nominal diameter (입력, 2026-10-23). Defaults follow KDS 14 20 52 as
+ * recorded in the plan; confirm against the code. small16 is for D16 and below (ties and stirrups).
+ */
+export interface BendFactors {
+  small16: number;
+  main25: number;
+  main35: number;
+  main51: number;
+}
+
+export const DEFAULT_BEND: BendFactors = { small16: 2, main25: 3, main35: 4, main51: 5 };
+
+/**
+ * Size classes by nominal diameter (mm). The limits lie between the sizes: D16 15.9, D25 25.4, D29 28.6, D35 34.9,
+ * so 26 and 36 separate D25 from D29 and D35 from D38.
+ */
+export const SIZE_CLASS = { small: 17, d25: 26, d35: 36 } as const;
+
+/** Centre-line bend radius (mm) of a bar of nominal diameter db: inner radius (factor × db) + db/2. */
+export function bendRadius(db: number, bend: BendFactors): number {
+  const factor = db <= SIZE_CLASS.small ? bend.small16 : db <= SIZE_CLASS.d25 ? bend.main25 : db <= SIZE_CLASS.d35 ? bend.main35 : bend.main51;
+  return factor * db + db / 2;
+}
+
+/**
+ * Length the centre line loses at a bend of deflection phi (rad) compared with the sharp corner of the same bar:
+ * 2R·tan(φ/2) − Rφ. For a 90° bend this is (2 − π/2)·R ≈ 0.429 R. Used by the centre-line length option.
+ */
+export function bendDeduction(phi: number, R: number): number {
+  return 2 * R * Math.tan(phi / 2) - R * phi;
+}
+
+/** Material inputs of ③ 공통 설정 (spec §6.2). fck, the grade per prefix and the bend factors are inputs. */
 export interface Material {
   /** 콘크리트 강도 fck (MPa). */
   fck: number;
   /** 규격 접두어별 철근 강도 (MPa): D = SD300, H = SD400, S = SD500 (입력). */
   grade: Record<GradeKey, number>;
+  /** 굽힘 내면반경 배수 (입력). */
+  bend: BendFactors;
 }
 
-export const DEFAULT_MATERIAL: Material = { fck: 27, grade: { D: 300, H: 400, S: 500 } };
+export const DEFAULT_MATERIAL: Material = { fck: 27, grade: { D: 300, H: 400, S: 500 }, bend: DEFAULT_BEND };
 
 /** Yield strength (MPa) of a bar from its 규격, e.g. H19 → the H grade. */
 export function fyOf(m: Material, size: string): number {
@@ -28,14 +63,21 @@ export function fyOf(m: Material, size: string): number {
  * A value outside GRADE_CHOICES falls back to the default for that prefix.
  */
 export function materialFrom(raw: unknown): Material {
-  const r = (raw ?? {}) as { fck?: unknown; grade?: Partial<Record<GradeKey, unknown>>; fyH?: unknown; fyS?: unknown };
+  const r = (raw ?? {}) as { fck?: unknown; grade?: Partial<Record<GradeKey, unknown>>; fyH?: unknown; fyS?: unknown; bend?: Partial<Record<keyof BendFactors, unknown>> };
+  const factor = (v: unknown, fallback: number) => (typeof v === 'number' && v > 0 ? v : fallback);
+  const bend: BendFactors = {
+    small16: factor(r.bend?.small16, DEFAULT_BEND.small16),
+    main25: factor(r.bend?.main25, DEFAULT_BEND.main25),
+    main35: factor(r.bend?.main35, DEFAULT_BEND.main35),
+    main51: factor(r.bend?.main51, DEFAULT_BEND.main51),
+  };
   const pick = (v: unknown, fallback: number) => ((GRADE_CHOICES as readonly number[]).includes(v as number) ? (v as number) : fallback);
   const grade = {
     D: pick(r.grade?.D, DEFAULT_MATERIAL.grade.D),
     H: pick(r.grade?.H ?? r.fyH, DEFAULT_MATERIAL.grade.H),
     S: pick(r.grade?.S ?? r.fyS, DEFAULT_MATERIAL.grade.S),
   };
-  return { fck: typeof r.fck === 'number' ? r.fck : DEFAULT_MATERIAL.fck, grade };
+  return { fck: typeof r.fck === 'number' ? r.fck : DEFAULT_MATERIAL.fck, grade, bend };
 }
 
 /** Members that can take their own fck on ② (부재 카드). Other members always use the 공통 fck. */
@@ -106,8 +148,8 @@ export type HookKind = 'main90' | 'tie90' | 'stirrup135';
  */
 export function hookLength(kind: HookKind, db: number): number {
   if (kind === 'main90') {
-    if (db <= 25) return 15.5 * db;
-    if (db <= 35) return 16.5 * db;
+    if (db <= SIZE_CLASS.d25) return 15.5 * db;
+    if (db <= SIZE_CLASS.d35) return 16.5 * db;
     throw new Error(`주철근 90° 갈고리 표에 없는 지름입니다 (D${db}).`);
   }
   if (kind === 'tie90') {

src/main.ts

@@ -13,7 +13,7 @@ import { pileGeometry } from './core/geometry';
 import { rebarSummary, type RebarRow } from './core/rebar/summary';
 import { shearSegments } from './core/rebar/coping';
 import { buildRebar3D, type RebarColorMode, type RebarScene } from './view/rebar3d';
-import { DEFAULT_MATERIAL, FCK_MEMBERS, fyOf, GRADE_CHOICES, isAssumedMaterial, materialFrom, type FckByMember, type FckMember, type GradeKey, type Material } from './core/rebar/common';
+import { DEFAULT_MATERIAL, FCK_MEMBERS, fyOf, GRADE_CHOICES, isAssumedMaterial, materialFrom, type BendFactors, type FckByMember, type FckMember, type GradeKey, type Material } from './core/rebar/common';
 import { allVisibleChecked, setVisibleChecked, type TypeFilter } from './core/selection';
 import { choose, defaultSummary, isSelectable, SHAPE_GROUPS, UNDEFINED_REASON, type MemberId } from './core/shape-options';
 import { parseProject, SCHEMA_VERSION, serializeProject, type ProjectFile, type ProjectInfo } from './core/project';
@@ -1000,6 +1000,9 @@ function renderMaterial(): void {
   for (const k of ['d', 'h', 's'] as const) {
     $<HTMLSelectElement>(`mat-grade-${k}`).value = String(m.grade[k.toUpperCase() as GradeKey]);
   }
+  for (const k of ['small16', 'main25', 'main35', 'main51'] as const) {
+    $<HTMLInputElement>(`bend-${k}`).value = String(m.bend[k]);
+  }
   $('mat-note').textContent = assumed ? 'fck 가정값 (I02): 입력을 바꾸면 정착·이음 길이가 달라집니다.' : '입력값을 사용합니다.';
 }
 
@@ -1047,6 +1050,19 @@ function renderMemberFck(box: HTMLDivElement, member: FckMember): void {
   box.appendChild(row);
 }
 
+/** Bend factor (× diameter) input on 공통 설정. Must be a positive number. */
+function setBend(key: keyof BendFactors, raw: string): void {
+  const value = Number(raw);
+  if (!Number.isFinite(value) || value <= 0) {
+    setStatus('굽힘 내면반경 배수는 0보다 큰 숫자여야 합니다.');
+    renderMaterial();
+    return;
+  }
+  state.material = { ...state.material, bend: { ...state.material.bend, [key]: value } };
+  setupScene();
+  renderAll();
+}
+
 function setMaterial(key: 'fck' | GradeKey, raw: string): void {
   const value = Number(raw);
   const valid = key === 'fck' ? Number.isFinite(value) && value > 0 : (GRADE_CHOICES as readonly number[]).includes(value);
@@ -1461,6 +1477,9 @@ $<HTMLButtonElement>('nav-shape').addEventListener('click', () => setStage('shap
 $<HTMLButtonElement>('nav-plan').addEventListener('click', () => setStage('plan'));
 $<HTMLButtonElement>('nav-rebar').addEventListener('click', () => setStage('rebar'));
 $<HTMLInputElement>('mat-fck').addEventListener('change', (ev) => setMaterial('fck', (ev.target as HTMLInputElement).value));
+for (const k of ['small16', 'main25', 'main35', 'main51'] as const) {
+  $<HTMLInputElement>(`bend-${k}`).addEventListener('change', (ev) => setBend(k, (ev.target as HTMLInputElement).value));
+}
 for (const k of ['D', 'H', 'S'] as const) {
   $<HTMLSelectElement>(`mat-grade-${k.toLowerCase()}`).addEventListener('change', (ev) => setMaterial(k, (ev.target as HTMLSelectElement).value));
 }

src/view/rebar3d.ts

@@ -5,7 +5,7 @@ import { bottomPiece, MAIN, widthLayout } from '../core/rebar/coping-main';
 import { C14_INSET, c14Bars, CAP, COPING_REBAR, SHEAR_LOOP_STEP, shearBars, shearBarsMulti, shearUHeight, copingSideBars, SIDE_HOOK_LEG, stairBars, undersideAt } from '../core/rebar/coping';
 import { columnRebar, COLUMN_P1 } from '../core/rebar/column';
 import { barsAcross, BLOCK_REBAR } from '../core/rebar/bearing-block';
-import { DEFAULT_MATERIAL, FckByMember, hookLength, Material, materialFor, NOMINAL_DIAMETER } from '../core/rebar/common';
+import { bendRadius, DEFAULT_MATERIAL, FckByMember, hookLength, Material, materialFor, NOMINAL_DIAMETER } from '../core/rebar/common';
 import { diameterGroupIndex, DIAMETER_GROUPS, memberOfBar, type RebarMemberKey } from '../core/rebar/color';
 import { stretchMatrix } from './scene';
 
@@ -62,6 +62,50 @@ export function buildRebar3D(m: PierModel, common: Material = DEFAULT_MATERIAL,
   const B = m.copingB;
   const straight = m.kink === null;
 
+  /**
+   * A bar through several points as one tube, each bend rounded to its centre-line radius (수정 2026-10-23).
+   * A bend of deflection φ is cut back by t = R·tan(φ/2) on both sides and joined by a quadratic curve through the corner.
+   */
+  const addPath = (name: string, k: number, pts: [number, number, number][], dMm: number, color: number) => {
+    if (pts.length < 2) return;
+    const R = mm(bendRadius(dMm, common.bend));
+    const pv = pts.map((p) => new THREE.Vector3(p[0], p[1], p[2]));
+    const path = new THREE.CurvePath<THREE.Vector3>();
+    let cur = pv[0].clone();
+    for (let i = 1; i < pv.length - 1; i++) {
+      const prev = pv[i - 1];
+      const corner = pv[i];
+      const next = pv[i + 1];
+      const u = corner.clone().sub(prev);
+      const v = next.clone().sub(corner);
+      const lenIn = u.length();
+      const lenOut = v.length();
+      if (lenIn < 1e-9 || lenOut < 1e-9) continue;
+      u.normalize();
+      v.normalize();
+      const phi = Math.acos(Math.min(1, Math.max(-1, u.dot(v))));
+      // Cut back by the tangent length, never more than half of either adjacent piece.
+      const t = Math.min(R * Math.tan(phi / 2), lenIn / 2, lenOut / 2);
+      const a = corner.clone().addScaledVector(u, -t);
+      const b = corner.clone().addScaledVector(v, t);
+      if (a.distanceTo(cur) > 1e-9) path.add(new THREE.LineCurve3(cur, a));
+      path.add(new THREE.QuadraticBezierCurve3(a, corner, b));
+      cur = b;
+    }
+    const last = pv[pv.length - 1];
+    if (last.distanceTo(cur) > 1e-9) path.add(new THREE.LineCurve3(cur, last));
+    const segments = Math.min(400, Math.max(12, Math.round(path.getLength() * 100)));
+    const geo = new THREE.TubeGeometry(path, segments, mm(dMm) / 2, 6, false);
+    geo.applyMatrix4(Ms[k]);
+    const mat = new THREE.MeshStandardMaterial({ color: rebarColor(color), roughness: 0.45, metalness: 0.1 });
+    const mesh = new THREE.Mesh(geo, mat);
+    mesh.userData = { name, roleColor: color, dMm, member: memberOfBar(name) };
+    group.add(mesh);
+    const list = byName.get(name) ?? [];
+    list.push(mesh);
+    byName.set(name, list);
+  };
+
   const addBar = (name: string, k: number, a: [number, number, number], b: [number, number, number], dMm: number, color: number) => {
     const dir = new THREE.Vector3(b[0] - a[0], b[1] - a[1], b[2] - a[2]);
     const len = dir.length();
@@ -100,7 +144,7 @@ export function buildRebar3D(m: PierModel, common: Material = DEFAULT_MATERIAL,
           [L - xk, z, n],
           [L - xk, z - hookTop, n],
         ];
-        for (let s = 0; s + 1 < pts.length; s++) addBar(name, 0, pts[s], pts[s + 1], NOMINAL_DIAMETER.H29, COLOR.coping);
+        addPath(name, 0, pts, NOMINAL_DIAMETER.H29, COLOR.coping);
       });
     }
     // Bottom bars C7 / C8 (코핑철근.md §5.2–5.3): they follow the sloped underside, 127 above it, with a vertical leg up
@@ -119,7 +163,7 @@ export function buildRebar3D(m: PierModel, common: Material = DEFAULT_MATERIAL,
       const right = left.map(([x, y, zz]): [number, number, number] => [L - x, y, zz]);
       const name = j % 2 === 1 ? 'C7' : 'C8';
       for (const pts of [left, right]) {
-        for (let k = 0; k + 1 < pts.length; k++) addBar(name, 0, pts[k], pts[k + 1], NOMINAL_DIAMETER.H29, COLOR.coping);
+        addPath(name, 0, pts, NOMINAL_DIAMETER.H29, COLOR.coping);
       }
     });
     // Shear loops C9 / C10 / C11 and the gaps between columns: a closed U at each position.
@@ -323,7 +367,7 @@ export function buildRebar3D(m: PierModel, common: Material = DEFAULT_MATERIAL,
     const off = legOffsets();
     // One name, several cylinders: each segment of the path is one bar piece.
     const path = (name: string, pts: [number, number, number][], dMm: number) => {
-      for (let k = 0; k + 1 < pts.length; k++) addBar(name, 0, pts[k], pts[k + 1], dMm, COLOR.footing);
+      addPath(name, 0, pts, dMm, COLOR.footing);
     };
     // B1–B4: along s, at W position n. legTo (absolute EL, m) is where both ends turn up or down (§5.1); undefined = straight.
     const along = (name: string, n: number, y: number, legTo: number | undefined, dMm: number) => {
@@ -375,7 +419,7 @@ export function buildRebar3D(m: PierModel, common: Material = DEFAULT_MATERIAL,
 
     // B10-1 / B10-2 (§7) at each B10 level, B11 / B12 (§8) between them. Ends turn 90° inward (B10) or down (B11, B12).
     const polyline = (name: string, pts: [number, number, number][], dMm: number) => {
-      for (let k = 0; k + 1 < pts.length; k++) addBar(name, 0, pts[k], pts[k + 1], dMm, COLOR.footing);
+      addPath(name, 0, pts, dMm, COLOR.footing);
     };
     const hookB10 = mm(hookLength('main90', NOMINAL_DIAMETER.S19)); // 296
     const hookAsm = mm(Math.round(hookLength('main90', NOMINAL_DIAMETER.S16))); // 246

tests/project.test.ts

@@ -68,8 +68,8 @@ describe('project file round trip (spec §8, plan B3)', () => {
 describe('③ 공통 설정 in the project file', () => {
   it('fck and fy are kept through save and open; older files get the defaults through the app', () => {
     const p = sampleProject();
-    const withCommon = { ...p, common: { fck: 35, grade: { D: 300, H: 400, S: 500 } } };
-    expect(parseProject(serializeProject(withCommon)).common).toEqual({ fck: 35, grade: { D: 300, H: 400, S: 500 } });
+    const withCommon = { ...p, common: { fck: 35, grade: { D: 300, H: 400, S: 500 }, bend: { small16: 2, main25: 3, main35: 4, main51: 5 } } };
+    expect(parseProject(serializeProject(withCommon)).common).toEqual(withCommon.common);
     expect(parseProject(serializeProject(p)).common).toBeUndefined();
   });
 });

tests/rebar-grade.test.ts

@@ -1,6 +1,6 @@
 import { describe, expect, it } from 'vitest';
 import { buildPier } from '../src/core/geometry';
-import { DEFAULT_MATERIAL, fyOf, isAssumedMaterial, materialFrom } from '../src/core/rebar/common';
+import { DEFAULT_BEND, DEFAULT_MATERIAL, fyOf, isAssumedMaterial, materialFrom } from '../src/core/rebar/common';
 import { rebarSummary } from '../src/core/rebar/summary';
 import { loadP1 } from './helpers';
 
@@ -19,7 +19,7 @@ describe('③ 철근 강도: 규격 접두어별 입력 (승인 2026-10-23)', ()
   });
 
   it('an older file that stored fyH / fyS is read into the grade map', () => {
-    expect(materialFrom({ fck: 35, fyH: 400, fyS: 400 })).toEqual({ fck: 35, grade: { D: 300, H: 400, S: 400 } });
+    expect(materialFrom({ fck: 35, fyH: 400, fyS: 400 })).toEqual({ fck: 35, grade: { D: 300, H: 400, S: 400 }, bend: DEFAULT_BEND });
   });
 
   it('a value outside SD300 · SD400 · SD500 falls back to the default for its prefix', () => {
@@ -34,3 +34,18 @@ describe('③ 철근 강도: 규격 접두어별 입력 (승인 2026-10-23)', ()
     expect(same).toBe(base);
   });
 });
+
+import { bendDeduction, bendRadius } from '../src/core/rebar/common';
+
+describe('굽힘 반경 (승인 2026-10-23, 입력)', () => {
+  it('centre-line radius = inner factor × d + d/2, by size class', () => {
+    expect(bendRadius(25.4, DEFAULT_BEND)).toBeCloseTo(3 * 25.4 + 12.7, 6); // H25: main25
+    expect(bendRadius(28.6, DEFAULT_BEND)).toBeCloseTo(4 * 28.6 + 14.3, 6); // H29: main35
+    expect(bendRadius(15.9, DEFAULT_BEND)).toBeCloseTo(2 * 15.9 + 7.95, 6); // H16: small16
+  });
+
+  it('a 90° bend loses (2 − π/2)·R of centre line against the sharp corner', () => {
+    const R = 100;
+    expect(bendDeduction(Math.PI / 2, R)).toBeCloseTo((2 - Math.PI / 2) * R, 6);
+  });
+});

tests/rebar3d.test.ts

@@ -108,11 +108,11 @@ describe('확대기초 B9 · B10 · B11 · B12 in 3D (확대기초철근 (1).md
     expect(rb.byName.get('B9')!.length).toBe(306 * 3);
   });
 
-  it('B10-1 / B10-2: 18 each (9 levels × 2 faces), each three pieces; B11 60, B12 47', () => {
-    expect(rb.byName.get('B10-1')!.length).toBe(18 * 3);
-    expect(rb.byName.get('B10-2')!.length).toBe(18 * 3);
-    expect(rb.byName.get('B11')!.length).toBe(60 * 3);
-    expect(rb.byName.get('B12')!.length).toBe(47 * 3);
+  it('B10-1 / B10-2: 18 each (9 levels × 2 faces); B11 60, B12 47 — one tube per bar (bends rounded, 수정 2026-10-23)', () => {
+    expect(rb.byName.get('B10-1')!.length).toBe(18);
+    expect(rb.byName.get('B10-2')!.length).toBe(18);
+    expect(rb.byName.get('B11')!.length).toBe(60);
+    expect(rb.byName.get('B12')!.length).toBe(47);
   });
 });