fix(core): clockwise-positive bend angle for IP4 (right turn when travelling IP1→IP2)

Sign convention approved: a right (clockwise) deflection is positive.
solveIp4 now rotates the IP1→IP2 direction by −θ. Test covers a +10°
right turn with IP4 at (5, 0).

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

src/core/geometry.ts

@@ -138,7 +138,7 @@ export interface PierModel {
 
 /**
  * Bend point IP4 (spec §4.1-2): the point where the IP1→IP2 line meets the line through IP3 whose
- * direction is IP1→IP2 turned by the bend angle. Positive angle = counter-clockwise [확인 필요: 부호 규약].
+ * direction is IP1→IP2 turned by the bend angle. Positive angle = right (clockwise) turn when travelling IP1→IP2.
  * Returns null for a zero angle, where IP4 is not defined.
  */
 export function solveIp4(ip1: Vec2, ip2: Vec2, ip3: Vec2, angleDeg: number): Vec2 | null {
@@ -146,7 +146,7 @@ export function solveIp4(ip1: Vec2, ip2: Vec2, ip3: Vec2, angleDeg: number): Vec
   const cross = (a: Vec2, b: Vec2) => a.e * b.n - a.n * b.e;
   const len = Math.hypot(ip2.e - ip1.e, ip2.n - ip1.n);
   const d1: Vec2 = { e: (ip2.e - ip1.e) / len, n: (ip2.n - ip1.n) / len };
-  const rad = (angleDeg * Math.PI) / 180;
+  const rad = (-angleDeg * Math.PI) / 180; // clockwise is positive, so the counter-clockwise rotation uses −θ
   const d2: Vec2 = { e: d1.e * Math.cos(rad) - d1.n * Math.sin(rad), n: d1.e * Math.sin(rad) + d1.n * Math.cos(rad) };
   const t = cross({ e: ip3.e - ip1.e, n: ip3.n - ip1.n }, d2) / cross(d1, d2);
   return { e: ip1.e + t * d1.e, n: ip1.n + t * d1.n };

tests/validate-and-foundation.test.ts

@@ -167,15 +167,14 @@ function meanN(m: ReturnType<typeof buildPier>, row: '전열' | '후열'): numbe
 describe('꺾인 코핑 IP4 (spec §4.1)', () => {
   const cross = (a: { e: number; n: number }, b: { e: number; n: number }) => a.e * b.n - a.n * b.e;
 
-  it('IP4 lies on the IP1→IP2 line and on the line through IP3 turned by the bend angle', () => {
-    const ip1 = { e: 0, n: 0 };
-    const ip2 = { e: 1, n: 0 };
-    const ip3 = { e: 10, n: 2 };
-    const ip4 = solveIp4(ip1, ip2, ip3, 10)!;
-    expect(ip4.n).toBeCloseTo(0, 9);
+  it('right (clockwise) bend of +10° puts IP4 on the IP1→IP2 line, with IP3 on the turned line', () => {
     const rad = (10 * Math.PI) / 180;
-    const d2 = { e: Math.cos(rad), n: Math.sin(rad) };
-    expect(cross({ e: ip4.e - ip3.e, n: ip4.n - ip3.n }, d2)).toBeCloseTo(0, 9);
+    const d2 = { e: Math.cos(rad), n: -Math.sin(rad) }; // heading east, turning right → south-east
+    const expectedIp4 = { e: 5, n: 0 };
+    const ip3 = { e: expectedIp4.e + 5 * d2.e, n: expectedIp4.n + 5 * d2.n };
+    const ip4 = solveIp4({ e: 0, n: 0 }, { e: 1, n: 0 }, ip3, 10)!;
+    expect(ip4.e).toBeCloseTo(5, 9);
+    expect(ip4.n).toBeCloseTo(0, 9);
   });
 
   it('zero angle has no IP4', () => {