By using the Bezier curve polyline draw function provided by nicoabie I was able to draw a curved line from one point on the map to another. The problem is that this function does not take in to account the fact that when a point is past the maximum coordinate mark it is not necessarily on the other side of the map, since it wraps around.
For example, drawing a curved line from Seattle to Tokyo. A regular polyline would go across the Pacific ocean, but the the curved line draws east across the whole globe.
geodesic: true
does not work in this case since the line must have a consistent curvature.
My question is: can a consistently curved line be drawn that takes in to account map wrapping?
Use the option third "nowrap" argument of the google.maps.LatLng class to force all the relevant points to have the same sign (set it to true, it defaults to false).
gmarkers[10].setPosition(new google.maps.LatLng(35.689488,139.69170)); // Tokyo
gmarkers[0].setPosition(new google.maps.LatLng(47.60621,(360-122.332071),true)); // Seattle
boundsCenter.setPosition(new google.maps.LatLng(36.096756,(360-178.986565),true)); // control point 1
gmarkers[6].setPosition(new google.maps.LatLng(48.511996,180)); // control point 2
var curvedLine = new GmapsCubicBezier(gmarkers[0].getPosition().lat(), gmarkers[0].getPosition().lng(), boundsCenter.getPosition().lat(), boundsCenter.getPosition().lng(), gmarkers[6].getPosition().lat(), gmarkers[6].getPosition().lng(), gmarkers[10].getPosition().lat(), gmarkers[10].getPosition().lng(), 0.01, map);
working fiddle