Anyway we can unit test this?

What about straight lines that aren't parallel to lines of longitude or latitude, like this case

var viewer = new Cesium.Viewer('cesiumContainer', { infoBox : false });
var entities = viewer.entities;

entities.add({
    corridor : {
        positions : Cesium.Cartesian3.fromDegreesArray([
-90,30, /*45 deg 100km*/
-89.260833,30.633889, /*45.373056 deg 100km*/
-88.511944,31.263611, /*45.758056 deg 100km*/
-87.753056,31.888889, /*46.155278 deg 100km*/
-86.983889,32.509444, /*46.565 deg 100km*/
        ]),
        width : 40000,
        height : 0,
        outline : true,
        outlineColor : Cesium.Color.WHITE,
        outlineWidth : 4,
        material : Cesium.Color.fromRandom({alpha : 0.7})
    }
});

viewer.zoomTo(viewer.entities);

Change width to 400 and it's straight as an arrow, but it is crooked when it's 40000.

I generated these series of points using
http://www.movable-type.co.uk/scripts/latlong.html
Destination point given distance and bearing from start point

And converted to decimal degrees using
http://www.fcc.gov/encyclopedia/degrees-minutes-seconds-tofrom-decimal-degrees

Thanks @slysnake, I switched back to my first solution which is check the angle between the direction vectors projected onto the tangent plane. The first time I forgot to re-normalize.

@mramato I added tests. This is ready for another review.

You're welcome, I'm glad I could help. Though I haven't really studied the code much to see how it all works. It's strange that narrow widths are straight, but not wide widths. I thought widths wouldn't affect the path.

Update CHANGES.md.

Can we merge this today so it makes 1.7?

Tests pass, example code in the linked issue is clearly fixed in this branch (and broken in master). I updated CHANGES.