fix(core): refuse bends that double back; use a valid synthetic bend in tests

The earlier synthetic bend (IP3 at (6, 2)) put IP4 ahead of IP3 on the turned
line, so the axis folded back on itself. buildPier now refuses a kink behind
IP1 along IP1→IP2 or an IP3 behind the kink along the turned direction. Tests
use IP3 (9, −3.464), a valid 60° right turn with kink (7, 0).

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

src/core/geometry.ts

@@ -203,6 +203,18 @@ export function buildPier(input: PierInput): PierModel {
   const ip3v: Vec2 = { e: ip3.x, n: ip3.y };
   const kink = bent ? solveIp4(ip1v, ip2v, ip3v, ip4.angleDeg) : null;
   const axis = buildAxis(ip1v, ip3v, kink);
+  if (kink) {
+    // The bend must move the axis forward: the kink ahead of IP1 along IP1→IP2, and IP3 ahead of the kink along the turned direction.
+    const d1 = { e: ip2v.e - ip1v.e, n: ip2v.n - ip1v.n };
+    const len1 = Math.hypot(d1.e, d1.n);
+    const rad = (-ip4.angleDeg * Math.PI) / 180;
+    const d2 = { e: (d1.e * Math.cos(rad) - d1.n * Math.sin(rad)) / len1, n: (d1.e * Math.sin(rad) + d1.n * Math.cos(rad)) / len1 };
+    const kinkAhead = (kink.e - ip1v.e) * d1.e + (kink.n - ip1v.n) * d1.n > 0;
+    const ip3Ahead = (ip3v.e - kink.e) * d2.e + (ip3v.n - kink.n) * d2.n > 0;
+    if (!kinkAhead || !ip3Ahead) {
+      throw new Error('꺾임각과 IP 배치가 맞지 않습니다. IP4가 축 뒤로 넘어갑니다. IP3이 꺾인 방향의 앞쪽에 있는지 확인하세요.');
+    }
+  }
   const lengthIp = axis.length;
   const sStart = copingSpan(axis, L).sStart;
   const arcA = kinkArc(axis);