gps: replace GeoCoord::latLongToMeter's spherical trig with equirectangular approximation (#11184)

src/configuration.h

@@ -88,6 +88,12 @@ along with this program.  If not, see <http://www.gnu.org/licenses/>.
 #define MESHTASTIC_PREHOP_DROP 1
 #endif
 
+// Use polynomial approximations for trigonometric functions to save flash.
+// Override with -D MESHTASTIC_TRIG_APPROX=0 for exact trig for special use cases e.g. close to Earth's poles.
+#ifndef MESHTASTIC_TRIG_APPROX
+#define MESHTASTIC_TRIG_APPROX 1
+#endif
+
 // Debug/test only: let a wired client (serial/TCP) inject frames into the RX pipeline as if they had
 // arrived over LoRa - a SIMULATOR_APP ToRadio packet is delivered through the real receive path on real
 // hardware (see MeshService::injectAsReceived). This forges over-the-air traffic, so it MUST stay 0 in

src/gps/GeoCoord.cpp

@@ -1,4 +1,5 @@
 #include "GeoCoord.h"
+#include "configuration.h"
 #include <cmath>
 
 // Narrow a UTM meter value to its unsigned field, clamping non-finite/negative/oversized inputs: an
@@ -433,6 +434,43 @@ void GeoCoord::convertWGS84ToOSGB36(const double lat, const double lon, double &
     //(airyA*airyA/(airyA / sqrt(1 - airyEcc*sin(osgb.latitude)*sin(osgb.latitude)))); // Not used, no OSTN data
 }
 
+#if MESHTASTIC_TRIG_APPROX
+// cos(x) minimax approx for x in [-pi/2, pi/2] ("cos_52"): https://www.ganssle.com/approx.htm
+static double cosLatitudeApprox(double latRad)
+{
+    constexpr double c1 = 0.9999932946, c2 = -0.4999124376, c3 = 0.0414877472, c4 = -0.0012712095;
+    double x2 = latRad * latRad;
+    return c1 + x2 * (c2 + x2 * (c3 + c4 * x2));
+}
+
+/// Approximate distance in meters via equirectangular projection (not exact spherical trig).
+/// <1% error to ~500km, degrading near the poles at long range (see test_geocoord_distance).
+float GeoCoord::latLongToMeter(double lat_a, double lng_a, double lat_b, double lng_b)
+{
+    // Don't do math if the points are the same
+    if (lat_a == lat_b && lng_a == lng_b)
+        return 0.0;
+
+    double a1 = lat_a / DEG_CONVERT;
+    double a2 = lng_a / DEG_CONVERT;
+    double b1 = lat_b / DEG_CONVERT;
+    double b2 = lng_b / DEG_CONVERT;
+
+    double meanLat = (a1 + b1) / 2;
+    double dLng = b2 - a2;
+    // Wrap to [-PI, PI]: unlike cos()/sin(), a raw longitude difference doesn't handle points that
+    // straddle the antimeridian (e.g. 179.9 and -179.9 are ~0.2 degrees apart, not ~360).
+    if (dLng > PI)
+        dLng -= 2 * PI;
+    else if (dLng < -PI)
+        dLng += 2 * PI;
+    double x = dLng * cosLatitudeApprox(meanLat);
+    double y = b1 - a1;
+    double tt = sqrt(x * x + y * y);
+
+    return (float)(6366000 * tt);
+}
+#else
 /// Ported from my old java code, returns distance in meters along the globe
 /// surface (by Haversine formula)
 float GeoCoord::latLongToMeter(double lat_a, double lng_a, double lat_b, double lng_b)
@@ -456,6 +494,7 @@ float GeoCoord::latLongToMeter(double lat_a, double lng_a, double lat_b, double
 
     return (float)(6366000 * tt);
 }
+#endif
 
 /**
  * Computes the bearing in degrees between two points on Earth.  Ported from my