fix: proper beam heading on the map

frontend/src/components/MainMap.tsx

@@ -122,10 +122,8 @@ export function MainMap({ fromGrid, toGrid, fromLabel, toLabel, beamAzimuths, be
     if (from && beamAzimuths && beamAzimuths.length) {
       const half = (beamWidth ?? 30) / 2;
       const D = 5500; // lobe length (km)
-      // A great circle pointing poleward runs to lat ±90, where Mercator is
-      // infinite — the line then snaps across the top of the map. Generate the
-      // radial with plenty of points (smooth curve) and STOP it just before the
-      // pole, so a north/south beam draws a clean line toward the edge instead.
+      // Great-circle radial out to distance D, stopping just short of the pole so
+      // a poleward line doesn't snap across the top of the Mercator map.
       const radial = (b: number): [number, number][] => {
         const pts: [number, number][] = [];
         const N = 64;
@@ -137,26 +135,17 @@ export function MainMap({ fromGrid, toGrid, fromLabel, toLabel, beamAzimuths, be
         return pts;
       };
       for (const az of beamAzimuths) {
-        const arc: [number, number][] = [];
-        for (let b = az - half; b <= az + half + 0.001; b += 2) {
-          const d = destinationPoint(from.lat, from.lon, b, D);
-          arc.push([d.lat, d.lon]);
+        // Draw the lobe as a FAN of translucent great-circle radials, not a
+        // filled polygon: a polygon breaks badly near the poles on Mercator (its
+        // edges run off toward ±90° and the fill smears across the map), while
+        // each radial LINE stays clean. The overlapping lines read as a lobe —
+        // solid near the antenna, fanning out toward the front. Works for any
+        // azimuth, north/south included.
+        for (let b = az - half; b <= az + half + 0.001; b += 1.5) {
+          const line = unwrapLon([[from.lat, from.lon], ...radial(b)]);
+          L.polyline(line as L.LatLngExpression[], { color: '#dc2626', weight: 6, opacity: 0.07 }).addTo(wo);
         }
-        const ring = unwrapLon([
-          [from.lat, from.lon],
-          ...radial(az - half),
-          ...arc,
-          ...radial(az + half).reverse(),
-        ]);
-        // Near a pole the lobe's two edges diverge wildly (one runs NW, the
-        // other NE) and look broken on a Mercator map — so for a poleward beam
-        // show ONLY the clean boresight (below). Otherwise draw the filled lobe.
-        if (!ring.some(([la]) => Math.abs(la) > 78)) {
-          L.polygon(ring as L.LatLngExpression[], {
-            color: '#dc2626', weight: 1, opacity: 0.5, fillColor: '#dc2626', fillOpacity: 0.14,
-          }).addTo(wo);
-        }
-        // Boresight (dashed centre line) — always; great-circle polyline is safe.
+        // Boresight (dashed centre line).
         const cl = unwrapLon([[from.lat, from.lon], ...radial(az)]);
         L.polyline(cl as L.LatLngExpression[], { color: '#dc2626', weight: 1.5, opacity: 0.7, dashArray: '5 4' })
           .bindTooltip(`Beam ${Math.round(az)}°`, { permanent: false, direction: 'top' }).addTo(wo);