fix: make circular and spiral presets truthful

tests/unit/array-builder.test.js

@@ -67,6 +67,116 @@ test("격자·선형·링·Fermat preset이 개수와 생성 경계를 지킨다
   }
 });
 
+test("원형과 Fermat preset은 비정사각 경계에서도 실제 내접원 좌표를 만든다", () => {
+  const aperture = { width: 0.5, height: 0.3 };
+  const edgeInsetM = 0.02;
+  const expectedRadius = 0.13;
+  const count = 12;
+
+  for (const type of ["ring", "spiral"]) {
+    const rectangle = generatePresetMicrophones({
+      type,
+      aperture,
+      shape: "rectangle",
+      edgeInsetM,
+      count,
+    });
+    const ellipse = generatePresetMicrophones({
+      type,
+      aperture,
+      shape: "ellipse",
+      edgeInsetM,
+      count,
+    });
+    assertEqual(
+      JSON.stringify(rectangle),
+      JSON.stringify(ellipse),
+      type + " coordinates describe the preset instead of tracing the boundary shape",
+    );
+    assert(
+      rectangle.every((microphone) =>
+        positionInsideAperture(microphone.position, aperture, "rectangle") &&
+        positionInsideAperture(microphone.position, aperture, "ellipse")),
+      type + " inscribed-circle coordinates fit either generation boundary",
+    );
+  }
+
+  const ring = generatePresetMicrophones({
+    type: "ring",
+    aperture,
+    shape: "rectangle",
+    edgeInsetM,
+    count,
+  });
+  for (const microphone of ring) {
+    assertNear(
+      Math.hypot(microphone.position[0], microphone.position[1]),
+      expectedRadius,
+      1e-8,
+      "ring radius",
+    );
+  }
+
+  const spiral = generatePresetMicrophones({
+    type: "spiral",
+    aperture,
+    shape: "rectangle",
+    edgeInsetM,
+    count,
+  });
+  spiral.forEach((microphone, index) => {
+    assertNear(
+      Math.hypot(microphone.position[0], microphone.position[1]),
+      expectedRadius * Math.sqrt((index + 0.5) / count),
+      1e-8,
+      "equal-area Fermat radius " + index,
+    );
+  });
+  assertEqual(
+    generatePresetMicrophones({ type: "spiral", aperture, count: 1 })[0].position.join(","),
+    "0,0,0",
+    "single-microphone spiral is centered",
+  );
+});
+
+test("Archimedean preset은 중심부터 내접원까지 선형 반경의 실제 나선을 만든다", () => {
+  const aperture = { width: 0.5, height: 0.3 };
+  const edgeInsetM = 0.02;
+  const maximumRadius = 0.13;
+  const turns = 2.5;
+  const count = 11;
+  const microphones = generatePresetMicrophones({
+    type: "archimedean",
+    aperture,
+    shape: "rectangle",
+    edgeInsetM,
+    turns,
+    count,
+  });
+  assertEqual(microphones.length, count, "Archimedean count");
+  microphones.forEach((microphone, index) => {
+    assertNear(
+      Math.hypot(microphone.position[0], microphone.position[1]),
+      maximumRadius * index / (count - 1),
+      1e-8,
+      "Archimedean linear radius " + index,
+    );
+  });
+  assertEqual(microphones[0].position.join(","), "0,0,0", "spiral starts at center");
+  assertNear(microphones.at(-1).position[0], -maximumRadius, 1e-8, "2.5 turns end at -x");
+  assertNear(microphones.at(-1).position[1], 0, 1e-8, "2.5 turns end on x axis");
+  assertThrows(
+    () => generatePresetMicrophones({
+      type: "archimedean",
+      aperture,
+      turns: 0,
+      count,
+    }),
+    "0.25",
+    "Archimedean turn lower bound",
+  );
+});
+
 test("타원 격자는 요청한 rows x columns 수를 유지하며 경계 안에 배치된다", () => {
   const aperture = { width: 0.45, height: 0.3 };
   const microphones = generatePresetMicrophones({