Is there a reason you can't draw a polyline from the origin of the globe?
Was trying to do this for each of the directions:
new Cesium.Cartesian3(10 * 1000 * 1000, 0, 0)
followSurface : false
But I got the exception: Could not project point (0, 0, 0) to 2D
This is more for curiosity than anything else, just to help get the hang of the coordinate system