M2 step 6: Tracks, recorded to GPX in the background

`r` in the GNSS App (or `gnss track start|stop`) records a Track to
/gnss/tracks/YYYYMMDD-HHMMSS.gpx: a point every 5 s once moved 5 m
(lib/gnss/track, 7 tests: haversine, the rule, GPX text, the file name).
It keeps recording with the App closed, shows REC in the Status Bar, and
announces start and stop with a Toast. It needs a card and the time;
switching GNSS off stops it. Tracks are written like Captures: past 90 %
card usage, until full. Storage Clean-up gets a GNSS tracks category.

A Track cut short by a reset or power loss has no GPX footer; the GNSS
Service closes such files at the next boot.

Verified on the device: a recorded Track and one interrupted by a reset
both parse as GPX 1.1 on the PC.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EhqxQ49eCju4CzKYNjZzwT

lib/gnss/src/track.cpp

@@ -0,0 +1,76 @@
+#include "track.h"
+
+#include <cmath>
+#include <cstdio>
+#include <ctime>
+
+namespace roro::gnss {
+
+namespace {
+
+constexpr double kEarthRadiusM = 6371000.0;
+
+double radians(double degrees) { return degrees * M_PI / 180.0; }
+
+// UTC fields from seconds since 1970 (gmtime_r works on the device and the PC alike).
+struct tm utc(int64_t seconds) {
+    time_t t = static_cast<time_t>(seconds);
+    struct tm out;
+    gmtime_r(&t, &out);
+    return out;
+}
+
+}  // namespace
+
+double distanceMeters(double lat1, double lon1, double lat2, double lon2) {
+    double dLat = radians(lat2 - lat1), dLon = radians(lon2 - lon1);
+    double h = std::sin(dLat / 2) * std::sin(dLat / 2) +
+               std::cos(radians(lat1)) * std::cos(radians(lat2)) * std::sin(dLon / 2) * std::sin(dLon / 2);
+    return 2 * kEarthRadiusM * std::asin(std::sqrt(h));
+}
+
+bool TrackRule::due(uint32_t nowMs, double lat, double lon) {
+    if (any_ && (nowMs - lastMs_ < kEveryMs || distanceMeters(lat_, lon_, lat, lon) < kMinMeters)) return false;
+    any_ = true;
+    lastMs_ = nowMs;
+    lat_ = lat;
+    lon_ = lon;
+    return true;
+}
+
+std::string trackPath(int64_t utcSeconds) {
+    struct tm t = utc(utcSeconds);
+    char buf[48];
+    std::snprintf(buf, sizeof buf, "/gnss/tracks/%04d%02d%02d-%02d%02d%02d.gpx", t.tm_year + 1900, t.tm_mon + 1,
+                  t.tm_mday, t.tm_hour, t.tm_min, t.tm_sec);
+    return buf;
+}
+
+namespace gpx {
+
+std::string header(const std::string& name) {
+    return "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n"
+           "<gpx version=\"1.1\" creator=\"roro9stack\" xmlns=\"http://www.topografix.com/GPX/1/1\">\n"
+           "<trk><name>" + name + "</name><trkseg>";
+}
+
+std::string point(double lat, double lon, bool hasElevation, float elevationM, int64_t utcSeconds) {
+    struct tm t = utc(utcSeconds);
+    char buf[160], ele[32] = "";
+    if (hasElevation) std::snprintf(ele, sizeof ele, "<ele>%.1f</ele>", elevationM);
+    std::snprintf(buf, sizeof buf,
+                  "<trkpt lat=\"%.7f\" lon=\"%.7f\">%s<time>%04d-%02d-%02dT%02d:%02d:%02dZ</time></trkpt>", lat, lon,
+                  ele, t.tm_year + 1900, t.tm_mon + 1, t.tm_mday, t.tm_hour, t.tm_min, t.tm_sec);
+    return buf;
+}
+
+std::string footer() { return "</trkseg></trk></gpx>"; }
+
+bool finished(const std::string& tail) {
+    size_t end = tail.find_last_not_of(" \r\n\t");
+    return end != std::string::npos && end + 1 >= 6 && tail.compare(end + 1 - 6, 6, "</gpx>") == 0;
+}
+
+}  // namespace gpx
+
+}  // namespace roro::gnss

lib/gnss/src/track.h

@@ -0,0 +1,40 @@
+#pragma once
+
+#include <cstdint>
+#include <string>
+
+namespace roro::gnss {
+
+// Great-circle distance in metres (haversine, mean Earth radius).
+double distanceMeters(double lat1, double lon1, double lat2, double lon2);
+
+// When a Track takes its next point (Q63): the first one always, then at least every 5 s and only
+// after moving at least 5 m, so standing still doesn't fill the card.
+class TrackRule {
+   public:
+    static constexpr uint32_t kEveryMs = 5000;
+    static constexpr double kMinMeters = 5.0;
+
+    // True if this position should be recorded (and is then remembered as the last point).
+    bool due(uint32_t nowMs, double lat, double lon);
+    void reset() { any_ = false; }
+
+   private:
+    bool any_ = false;
+    uint32_t lastMs_ = 0;
+    double lat_ = 0, lon_ = 0;
+};
+
+// "/gnss/tracks/YYYYMMDD-HHMMSS.gpx", from the UTC start time (Storage Clean-up reads its date).
+std::string trackPath(int64_t utcSeconds);
+
+// GPX 1.1, written a line at a time: the header when a Track starts, a point per line, the footer
+// when it stops. A file whose footer never came (power lost) is closed at the next boot.
+namespace gpx {
+std::string header(const std::string& name);
+std::string point(double lat, double lon, bool hasElevation, float elevationM, int64_t utcSeconds);
+std::string footer();
+bool finished(const std::string& tail);  // the end of a file: does it close the GPX?
+}  // namespace gpx
+
+}  // namespace roro::gnss