feat(core,view): bent coping stage 3 — footings and piles in stretch frames

- Footings, blindings and piles on a bent axis are placed in their stretch's
  frame; 일체기초 is grouped per stretch, so a combined footing never crosses
  the kink (separate footings, each aligned with its stretch).
- Footings, blindings and piles are trimmed at the mitre plane like the coping.
- The stage-2 refusal for bent foundations is removed; the Level-half-width
  refusal for columns at the kink remains.
- Tests: T형 footing crossing the kink stays in stretch 0; 2주형 with columns
  on both sides gives one footing per stretch, with mitre clipping in the scene.

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

tests/bent-coping.test.ts

@@ -17,10 +17,10 @@ const FRONT_N = -0.7;
 const BACK_N = 0.6;
 const GS = [0.6, 1.9, 3.2];
 
-function bentInput(foundationType: PierInput['foundationType'] = '현장타설말뚝'): PierInput {
+function bentInput(foundationType: PierInput['foundationType'] = '현장타설말뚝', type: PierInput['type'] = 'T형', coping = L): PierInput {
   const base = loadP1();
   const axis = buildAxis(IP1, IP3, solveIp4(IP1, { e: 1, n: 0 }, IP3, ANGLE));
-  const sStart = copingSpan(axis, L).sStart;
+  const sStart = copingSpan(axis, coping).sStart;
   const z = base.copingTopEl + 0.15;
   const bearingsAt = (row: '전열' | '후열', n: number) =>
     GS.map((g, i) => {
@@ -29,10 +29,10 @@ function bentInput(foundationType: PierInput['foundationType'] = '현장타설
     });
   return {
     ...base,
-    type: 'T형',
-    columnCount: 1,
+    type,
+    columnCount: type === '2주형' ? 2 : 1,
     foundationType,
-    copingLengthMm: L * 1000,
+    copingLengthMm: coping * 1000,
     copingWidthMm: B * 1000,
     ips: [
       { name: 'IP1', x: IP1.e, y: IP1.n, angleDeg: 0 },
@@ -123,9 +123,29 @@ describe('bent coping model (stage 2)', () => {
     }
   });
 
-  it('bent coping with footings or piles on the axis is refused until stage 3', () => {
-    expect(() => buildPier(bentInput('말뚝기초'))).toThrow('미실시');
-    expect(() => buildPier(bentInput('직접기초'))).toThrow('미실시');
+  it('footings are aligned with their stretch: a T형 footing crossing the kink stays in stretch 0 and is trimmed there', () => {
+    const piled = buildPier(bentInput('말뚝기초'));
+    expect(piled.footings).toHaveLength(1);
+    expect(piled.footings[0].k).toBe(0);
+    expect(piled.footings[0].length).toBeCloseTo(10.4, 6);
+    expect(piled.blindings[0].k).toBe(0);
+    expect(piled.piles).toHaveLength(20);
+    expect(piled.piles.every((p) => p.k === 0)).toBe(true);
+    expect(buildPier(bentInput('직접기초')).piles).toHaveLength(0);
+  });
+
+  it('2주형 bent with columns on both sides of the kink: separate footings, one per stretch', () => {
+    const m = buildPier(bentInput('말뚝기초', '2주형', 10));
+    expect(m.footings.map((f) => f.k)).toEqual([0, 1]);
+    expect(m.footings.every((f) => Math.abs(f.length - 10.4) < 1e-9)).toBe(true);
+    expect(m.piles).toHaveLength(40);
+    expect(m.piles.filter((p) => p.k === 1)).toHaveLength(20);
+    const scene = buildPierScene(m);
+    const footings = scene.parts.footings.children as THREE.Mesh[];
+    expect(footings).toHaveLength(2);
+    for (const mesh of footings) {
+      expect(((mesh.material as THREE.MeshStandardMaterial).clippingPlanes ?? []).length).toBe(1);
+    }
   });
 
   it('a kink outside the coping is refused', () => {

tests/validate-and-foundation.test.ts

@@ -181,9 +181,9 @@ describe('꺾인 코핑 IP4 (spec §4.1)', () => {
     expect(solveIp4({ e: 0, n: 0 }, { e: 1, n: 0 }, { e: 10, n: 2 }, 0)).toBeNull();
   });
 
-  it('bent coping is still reported as 미실시 by buildPier', () => {
+  it('a bend on a straight P1 sheet (IP1, IP2, IP3 collinear) is refused: IP4 would land on IP3', () => {
     const p1 = loadP1();
     const ips = p1.ips.map((p) => (p.name === 'IP4' ? { ...p, angleDeg: 5 } : p));
-    expect(() => buildPier({ ...p1, ips })).toThrow('미실시');
+    expect(() => buildPier({ ...p1, ips })).toThrow('꺾임각과 IP 배치');
   });
 });