M2 step 5: GNSS App, with the Position and Sky views

Position: the Fix line (or how long it has been searching), latitude and
longitude in decimal degrees or degrees-minutes-seconds (Settings ->
Coordinates), the Maidenhead locator, altitude, speed and course, HDOP
and UTC. Sky: the satellites by azimuth and elevation, coloured by
constellation, filled when used in the Fix, with used/in-view counts.
Tab switches. lib/gnss/geo_format holds the formatting, the locator and
the sky projection, host-tested (6 tests; locators checked against
FN31pr and JN58td).

Verified on the device by a window: 3D Fix from GPS, GLONASS, Galileo
and BeiDou.

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

lib/gnss/src/geo_format.cpp

@@ -0,0 +1,50 @@
+#include "geo_format.h"
+
+#include <cmath>
+#include <cstdio>
+
+namespace roro::gnss {
+
+namespace {
+const char* hemisphere(double degrees, bool latitude) {
+    return latitude ? (degrees < 0 ? "S" : "N") : (degrees < 0 ? "W" : "E");
+}
+}  // namespace
+
+std::string formatDecimal(double degrees, bool latitude) {
+    char buf[32];
+    std::snprintf(buf, sizeof buf, "%.5f\xC2\xB0 %s", std::fabs(degrees), hemisphere(degrees, latitude));
+    return buf;
+}
+
+std::string formatDms(double degrees, bool latitude) {
+    // Work in tenths of a second, so rounding carries into minutes and degrees.
+    long tenths = std::lround(std::fabs(degrees) * 36000.0);
+    long d = tenths / 36000, m = tenths / 600 % 60, s10 = tenths % 600;
+    char buf[40];
+    std::snprintf(buf, sizeof buf, "%ld\xC2\xB0 %02ld' %02ld.%ld\" %s", d, m, s10 / 10, s10 % 10,
+                  hemisphere(degrees, latitude));
+    return buf;
+}
+
+std::string maidenhead(double latitude, double longitude) {
+    double lon = std::fmin(std::fmax(longitude + 180.0, 0.0), 359.999999);
+    double lat = std::fmin(std::fmax(latitude + 90.0, 0.0), 179.999999);
+    std::string out;
+    out += static_cast<char>('A' + static_cast<int>(lon / 20));
+    out += static_cast<char>('A' + static_cast<int>(lat / 10));
+    out += static_cast<char>('0' + static_cast<int>(std::fmod(lon, 20) / 2));
+    out += static_cast<char>('0' + static_cast<int>(std::fmod(lat, 10)));
+    out += static_cast<char>('a' + static_cast<int>(std::fmod(lon, 2) * 12));
+    out += static_cast<char>('a' + static_cast<int>(std::fmod(lat, 1) * 24));
+    return out;
+}
+
+SkyPoint skyPosition(int azimuthDeg, int elevationDeg, int cx, int cy, int radius) {
+    int elevation = elevationDeg < 0 ? 0 : elevationDeg > 90 ? 90 : elevationDeg;
+    double r = radius * (90 - elevation) / 90.0;
+    double az = azimuthDeg * M_PI / 180.0;
+    return {cx + static_cast<int>(std::lround(r * std::sin(az))), cy - static_cast<int>(std::lround(r * std::cos(az)))};
+}
+
+}  // namespace roro::gnss

lib/gnss/src/geo_format.h

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+#pragma once
+
+#include <string>
+
+namespace roro::gnss {
+
+// "50.86920° N": five decimals, about a metre.
+std::string formatDecimal(double degrees, bool latitude);
+// "50° 52' 09.1\" N" (Settings → Coordinates, Q64).
+std::string formatDms(double degrees, bool latitude);
+// The 6-character Maidenhead locator ("JO20ef"), as radio amateurs give their square.
+std::string maidenhead(double latitude, double longitude);
+
+// Where a satellite goes on the Sky view: the zenith in the centre, the horizon on the circle,
+// north up and east right (as seen looking at the sky from above, like a map).
+struct SkyPoint {
+    int x, y;
+};
+SkyPoint skyPosition(int azimuthDeg, int elevationDeg, int cx, int cy, int radius);
+
+}  // namespace roro::gnss