// Pure circle-circle geometry for the DEEP SCAN pulse (js/scan/ScanPulse.js).
// No Phaser — kept separately so it is unit-testable in Node
// (dev/scan.test.mjs).
//
// The wavefront is a ship-centered circle of radius r. Only the part inside
// the tether region (the UNION of tether circles) is drawn — outside the
// union the wave is absorbed, so the pulse stops at the union boundary.
// For one tether circle (center A, radius R) vs the origin circle (center
// O, radius r), both "windows" are the classic circle-circle intersection:

/**
 * The arc of a circle of radius `a` (around its center) that lies inside a
 * circle of radius `b`, the two centers `d` apart.
 *
 * Returns the half-angle (radians) of the window, centered on the
 * `a`-center → `b`-center direction:
 *   Math.PI — the whole circle `a` is inside `b`
 *   -1      — no overlap
 */
export function arcInCircle(a, b, d) {
  if (a <= 0) return -1;
  if (d === 0) return a <= b ? Math.PI : -1;
  const c = (a * a + d * d - b * b) / (2 * a * d);
  if (c <= -1) return Math.PI;
  if (c >= 1) return -1;
  return Math.acos(c);
}

/**
 * The wavefront radius at which an origin-centered front first touches a
 * tether of radius `R` whose anchor is `d` away (0 = concentric circles —
 * the front grows through the whole rim at once, at r = R).
 */
export function contactRadius(R, d) {
  if (d === 0) return R;
  return Math.abs(R - d);
}

/** The farthest point of a tether rim from the origin — the point the wave
 *  is absorbed last. The sweep runs to the max of this over all tethers. */
export function farRadius(R, d) {
  return R + d;
}