Hi Gerd,

> I use MapSource 6.16.3 and it doesn't show the great circle line
> when I open the attached gpx file.

I can't see your attachment.

Mapsoruce draws great circle for direct routes (select "Use Direct Routes" in Preferences). I have marked waypoints for LAX an JFK and then created a route form these points. See gpx attached to my post.

In my opinion you should go for a correct solution regardless of speed penalty. I would prefer reliable program over a fast one. Later you probably can optimize some computations, where you know for sure, that error is small.

--
Best regards,
Andrzej
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<gpx xmlns="http://www.topografix.com/GPX/1/1"; creator="MapSource 6.16.3" version="1.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"; xsi:schemaLocation="http://www.topografix.com/GPX/1/1 http://www.topografix.com/GPX/1/1/gpx.xsd";>

  <metadata>
    <link href="http://www.garmin.com";>
      <text>Garmin International</text>
    </link>
    <time>2014-08-02T12:41:33Z</time>
    <bounds maxlat="40.784420287236571" maxlon="-73.783342838287354" minlat="33.95000696182251" minlon="-118.40000152587891"/>
  </metadata>

  <wpt lat="34.500010013580322" lon="-116.50001049041748">
    <time>2014-08-02T12:41:00Z</time>
    <name>D</name>
    <cmt>Road</cmt>
    <desc>Road</desc>
    <sym>Flag, Blue</sym>
    <extensions>
      <gpxx:WaypointExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
        <gpxx:DisplayMode>SymbolAndName</gpxx:DisplayMode>
      </gpxx:WaypointExtension>
    </extensions>
  </wpt>

  <wpt lat="40.633342266082764" lon="-73.783342838287354">
    <time>2014-08-02T12:21:56Z</time>
    <name>JFK</name>
    <cmt>Droga</cmt>
    <desc>Droga</desc>
    <sym>Flag, Blue</sym>
    <extensions>
      <gpxx:WaypointExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
        <gpxx:DisplayMode>SymbolAndName</gpxx:DisplayMode>
      </gpxx:WaypointExtension>
    </extensions>
  </wpt>

  <wpt lat="33.95000696182251" lon="-118.40000152587891">
    <time>2014-08-02T12:21:33Z</time>
    <name>LAX</name>
    <cmt>Droga</cmt>
    <desc>Droga</desc>
    <sym>Flag, Blue</sym>
    <extensions>
      <gpxx:WaypointExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
        <gpxx:DisplayMode>SymbolAndName</gpxx:DisplayMode>
      </gpxx:WaypointExtension>
    </extensions>
  </wpt>

  <rte>
    <name>LAX1 to JFK</name>
    <extensions>
      <gpxx:RouteExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
        <gpxx:IsAutoNamed>true</gpxx:IsAutoNamed>
        <gpxx:DisplayColor>Magenta</gpxx:DisplayColor>
      </gpxx:RouteExtension>
    </extensions>
    <rtept lat="33.95000696182251" lon="-118.40000152587891">
      <time>2014-08-02T12:21:33Z</time>
      <name>LAX1</name>
      <cmt>Droga</cmt>
      <desc>Droga</desc>
      <sym>Flag, Blue</sym>
      <extensions>
        <gpxx:RoutePointExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
          <gpxx:Subclass>004000000000FFFFFFFFFFFFFFFFFFFFFFFF</gpxx:Subclass>
        </gpxx:RoutePointExtension>
      </extensions>
    </rtept>
    <rtept lat="40.633342266082764" lon="-73.783342838287354">
      <time>2014-08-02T12:21:56Z</time>
      <name>JFK</name>
      <cmt>Droga</cmt>
      <desc>Droga</desc>
      <sym>Flag, Blue</sym>
      <extensions>
        <gpxx:RoutePointExtension xmlns:gpxx="http://www.garmin.com/xmlschemas/GpxExtensions/v3";>
          <gpxx:Subclass>000000000000FFFFFFFFFFFFFFFFFFFFFFFF</gpxx:Subclass>
        </gpxx:RoutePointExtension>
      </extensions>
    </rtept>
  </rte>

</gpx>
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