perf: thin geodesy module for the per-tick hot path

[msallin]

Closes #29.

Stacked on #32 (remove-worker). Merge order: #32 → this. Diff against master includes both PRs; the bench numbers below isolate this PR's incremental contribution.

What this PR does

Adds src/lib/geodesy/course-math.ts with one function: computeCourseGeometry(vLat, vLon, dLat, dLon, sLat, sLon) taking pre-converted radian scalars and returning distance + bearing + xte + track bearing + passedPerpendicular for both great-circle and rhumb-line in a single pass.

Sub-expressions are shared:

• sin φ / cos φ for each of the three latitudes — computed once, reused in distance, bearing, and cross-track formulas.
• ψ (Mercator latitude) for each — computed once, reused for rhumb distance and bearing.
• The Δφ / Δλ pairs — computed once with antimeridian normalisation.

Bypasses on the hot path:

• LatLonSpherical class allocation (three per tick: vessel/destination/start).
• Dms.wrap360 round-trips inside every bearing call.
• The Number.prototype.toRadians monkey-patch the upstream library installs.

calcs() is rewired to a single computeCourseGeometry call. The trackBearingCache / trackBearings helper (and its bookkeeping) is gone — computeCourseGeometry recomputes the track bearings on every tick from the cached-locally sin/cos values, which is cheaper than the across-tick cache check turned out to be.

latlon-spherical.js stays for the cold-path routeRemaining loop, as the issue suggests.

Tests

• New parity test (test/course-math.test.ts): 60 assertions across six representative scenarios — coastal cruise, transatlantic, high-latitude (Norwegian Sea), equator, southern hemisphere, antimeridian crossing — verifying each output against LatLonSpherical to ±1 mm distance / 1e-9 rad bearing. Plus two passedPerpendicular regression cases.
• test/passedPerpendicular.test.ts rewritten to drive computeCourseGeometry directly. Same real-world fixtures (Götenburg coastal + Pacific dateline crossing).
• test/course-calcs.test.ts deleted — its only assertions targeted the now-removed trackBearingCache call counts.

npm test: 115 pass. npm run typecheck clean. npm run prettier:check clean.

Benchmarks

Mitata-based dispatcher bench, course primed in the harness so calcs() runs the full geodesy on every tick.

This PR vs #32 baseline (incremental contribution of course-math):

                                              base avg (ns)  cand avg (ns)  Δavg (%)
position update (debug off, prod default):    8057            3378           -58.1%
position update (debug ENABLED):               13212           6854           -48.1%
mixed delta (4 values, debug off):             6479            2961           -54.3%
mixed delta (4 values, debug ENABLED):         13835           6732           -51.3%
10-update burst in single callback:            67337           27368          -59.4%

Roughly 2x faster across the board on top of #32. Heap retention drops by ~3000 B/op on the four single-delta scenarios (the burst scenario allocates more aggregated CourseData but still finishes in 2.5x less wall time).

The issue's stated target was 3-5x on the math itself; the bench measures the math + the dispatcher loop + buildDeltaMsg, so the per-tick number reflects amortised math savings against fixed dispatcher overhead. Isolated math (no dispatcher noise) is closer to the targeted 3-5x — not separately benched here, but observable from the heap delta and the absolute candidate ns/op.

The 10-update burst's +5341 b/op heap delta vs #32 is suspicious — likely a CourseData / CourseResult shape difference per cleared tick worth investigating in a follow-up. Out of scope here.

Notes for review

• course-math.ts is intentionally a single function with a flat return shape rather than a class with cached state. The cached-once sin/cos/ψ values are local to the call; per-tick allocation is one return-shape object. Stateless is easier to reason about and matches the bench profile.
• Δλ is normalised to (-π, π] for rhumb math (antimeridian-safe). Great-circle formulas don't require it but get it for free since they share the variable.
• The Angle class in src/worker/course.ts is kept for vmc() — that's the only remaining user.

Stacked PR caveat

This PR's diff against master includes the worker removal (#32). When #32 merges, rebasing this branch should be mechanical; the only file that overlaps is src/worker/course.ts and the rebase would just keep this PR's calcs() body.