Currently, we can do distance math for filter (geo_distance) and sort (_geo_distance) from a given [lon,lat] to a geo_point. We cannot do this currently for a [lon,lat] to the surface of a geo_shape object (distance "N"). There's a bit of a workaround for the geo_distance filter: you can create a circle of a specified radius M and check for an "intersects" relation. However, there are some cases where this does not work (e.g. if M > (N + [span of geo_shape]) it's now "within").

A few examples:

• A vehicle is supposed to follow an indexed LineString / MultiLineString path and we want to find when it has deviated from the path by more than 100 meters [filter]
• Find the nearest landmark (geo-shape) to my present location [sort]