Phase 2c: eclipse/overpass calculators + live-map camera polish

Calculators (apps/live-map/src/calculators/):
- eclipse.ts: findEclipseWindows(bodies, opts) — coarse scan with
  threshold-crossing detection, bisection to refine start/end,
  ternary search to find peak. Handles eclipse already in progress
  at scan-start. Uses sun = parentId===null body.
- overpass.ts: findOverpasses(opts) — coarse scan for local distance
  minima, ternary refinement. Targets: vessel, body, ground station
  (lat/lon/alt → heliocentric).

UI:
- panels/CalculatorsPanel.tsx: collapsible bottom-center panel with
  two tabs. Eclipse form: observer, eclipser, from UT → 3 windows.
  Overpass form: observer vessel, target kind+id, max dist → 5 passes.
- timeFormat.ts: shared KSP-time formatters.

Live-map camera polish (apps/live-map/src/scene/):
- camera.ts: CameraController — log-scale distance (z→exp(z)*1e8 m,
  range -3..12), spherical orbit around target, smooth lerp to
  selected body/vessel. Mouse wheel zooms, drag rotates, click
  raycasts for track toggle. Pointer-move-distance gate to
  distinguish click from drag.
- glow.ts: additive shader-based atmospheric halo (rim-falloff
  fragment shader, BackSide) attached as child of body mesh.
- layout.ts: bodyPositionAt now returns true heliocentric (walks
  parent chain); previous version returned parent-relative for
  non-root children which broke the eclipse calculator.

Bug fix:
- packages/orbital-math/src/occultation.ts: sign of projection check
  was inverted. `proj <= 0` correctly returns 0 (occluder behind
  observer), `proj > 0` triggers eclipse computation.

Tests: 28 live-map tests (10 scene + 12 calculator + 6 camera),
45 total across the workspace, all passing.

apps/live-map/src/calculators/overpass.ts

@@ -0,0 +1,151 @@
+/**
+ * Overpass calculator — finds the next N closest approaches between
+ * a vessel and a target (vessel, body, or ground station).
+ *
+ * Approach: sample the distance at fixed steps, then refine each
+ * minimum with ternary search.
+ */
+import type { CelestialBody, Vessel, GroundStation } from '@kerbal-rt/shared-types';
+import { bodyPositionAt, vesselPositionAt } from '../scene/layout.js';
+
+export type TargetKind = 'vessel' | 'body' | 'station';
+
+export interface Target {
+  kind: TargetKind;
+  id: string;
+  name: string;
+}
+
+export interface OverpassWindow {
+  /** UT at which the closest approach occurs. */
+  utPeak: number;
+  /** Distance at closest approach (meters). */
+  minDistance: number;
+  /** The target. */
+  target: Target;
+}
+
+export interface OverpassOptions {
+  observer: Vessel;
+  target: Target;
+  bodies: CelestialBody[];
+  vessels: Vessel[];
+  groundStations: GroundStation[];
+  startUt: number;
+  count?: number;
+  maxSearchTime?: number;
+  stepSec?: number;
+  /** Distance threshold for "interesting" passes (default 1000 km). */
+  distanceThreshold?: number;
+}
+
+/**
+ * Find the next `count` closest-approach events.
+ *
+ * Coarse scan: at each step, compute distance. Track the local minima
+ * (a point lower than both neighbors). For each local min, refine
+ * with ternary search to find the true peak (min distance).
+ *
+ * Returns at most `count` events with minDistance < distanceThreshold.
+ */
+export function findOverpasses(options: OverpassOptions): OverpassWindow[] {
+  const {
+    observer,
+    target,
+    bodies,
+    vessels,
+    groundStations,
+    startUt,
+    count = 5,
+    maxSearchTime = 426 * 6 * 3600, // 1 KSP year
+    stepSec = 120, // 2 minutes
+    distanceThreshold = 1_000_000, // 1000 km
+  } = options;
+
+  const dist = (t: number) => distanceAt(bodies, vessels, groundStations, observer, target, t);
+
+  const passes: OverpassWindow[] = [];
+  const end = startUt + maxSearchTime;
+  let prev = dist(startUt);
+  let curr = prev;
+  let t = startUt + stepSec;
+
+  while (t < end && passes.length < count) {
+    const next = dist(t);
+    // Local minimum: curr < prev AND curr < next
+    if (curr < prev && curr < next && curr < distanceThreshold) {
+      // Refine
+      const utPeak = refineMinimum((a: number) => dist(a), t - stepSec, t + stepSec);
+      const minDistance = dist(utPeak);
+      passes.push({ utPeak, minDistance, target });
+      // Skip ahead past the peak so we don't double-count
+      t = utPeak + stepSec * 5;
+      prev = dist(t);
+      curr = prev;
+      t += stepSec;
+      continue;
+    }
+    prev = curr;
+    curr = next;
+    t += stepSec;
+  }
+
+  return passes;
+}
+
+function distanceAt(
+  bodies: CelestialBody[],
+  vessels: Vessel[],
+  groundStations: GroundStation[],
+  observer: Vessel,
+  target: Target,
+  ut: number,
+): number {
+  const obs = vesselPositionAt(bodies, observer, ut);
+  let tgt: { x: number; y: number; z: number };
+  if (target.kind === 'vessel') {
+    const v = vessels.find((x) => x.id === target.id);
+    if (!v) return Number.POSITIVE_INFINITY;
+    tgt = vesselPositionAt(bodies, v, ut);
+  } else if (target.kind === 'body') {
+    tgt = bodyPositionAt(bodies, target.id, ut);
+  } else {
+    // station
+    const s = groundStations.find((x) => x.id === target.id);
+    if (!s) return Number.POSITIVE_INFINITY;
+    const body = bodies.find((b) => b.id === s.bodyId);
+    if (!body) return Number.POSITIVE_INFINITY;
+    const bodyPos = bodyPositionAt(bodies, body.id, ut);
+    // Ground station sits on the body surface. Convert (lat, lon, alt)
+    // to a heliocentric offset relative to the body's center.
+    // For simplicity (no rotation) we just add a small offset along
+    // the body's orbital direction.
+    const R = body.radius + s.alt;
+    const lat = (s.lat * Math.PI) / 180;
+    const lon = (s.lon * Math.PI) / 180;
+    tgt = {
+      x: bodyPos.x + R * Math.cos(lat) * Math.cos(lon),
+      y: bodyPos.y + R * Math.cos(lat) * Math.sin(lon),
+      z: bodyPos.z + R * Math.sin(lat),
+    };
+  }
+  const dx = obs.x - tgt.x;
+  const dy = obs.y - tgt.y;
+  const dz = obs.z - tgt.z;
+  return Math.hypot(dx, dy, dz);
+}
+
+/** Ternary search to find the minimum of dist in [tLo, tHi]. */
+function refineMinimum(dist: (t: number) => number, tLo: number, tHi: number): number {
+  let lo = tLo;
+  let hi = tHi;
+  for (let i = 0; i < 40; i++) {
+    const m1 = lo + (hi - lo) / 3;
+    const m2 = hi - (hi - lo) / 3;
+    const f1 = dist(m1);
+    const f2 = dist(m2);
+    if (f1 > f2) lo = m1;
+    else hi = m2;
+  }
+  return (lo + hi) / 2;
+}