Sequentially number features (intersecting and non-intersecting) along linear path

Question

We need to sequentially number features along a linear path.  It's easy to number features that intersect with the route, but what about those that are not intersecting?  See this graphic which illustrates how we need to number things, from west-to-east.  This is a hypothetical screenshot, so I know the parcels don't look correct.  Also we cannot assume that the route will always be in a one-way direction.  Sometimes it'll be West to East and sometimes it'll be North to South, etc.

MicZatorsky_AEC · Answer

In that case, instead of using polygon centroids, use the polygons.   LFAR will return a start and end m-value for each polygon.

Find the minimum m-value for each polygon, sort that list and then you have the new order ID.

danretired · Answer

Then you will have to find the rule that suits all situations, like left-most extent top point or something.  Feature extent can easily be obtained

mroberts_troy · Answer

Thanks for that recommendation, but centers are not always in order of feature.  See this example:

In this example, the blue shape clearly comes first, but the center is to the "right" of the red shape, and therefore it would be ordered second using your method.