Description:
I created a polygon, moved the camera closer to the polygon, and the polygon was clipped.
ULR is a screen recording file。
Sandcastle code:
var viewer = new Cesium.Viewer('cesiumContainer');
var redPolygon = viewer.entities.add({
    name : 'Red polygon on surface',
    polygon : {
        hierarchy : Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0,
                                                        -115.0, 36.0,
                                                        -114.0, 36.0,
                                                        -114.0, 37.0,
                                                        -115.0, 37.0]),
        material : '../images/Cesium_Logo_Color.jpg',
        height : 0,
    }
});
viewer.zoomTo(viewer.entities);