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I would like some advice on setting up a workbench that could retrieve the number of interior angles in a polygon that are classed as concave (i.e. >180 degrees).

 

So far I have the following:

  1. run my polygon featureclass through the 'convexity filter' to obtain only concave polygons.
  2. I then use the 'Orientor' to assign the right hand rule before passing it through the 'VertexAngleCalculator'.
  3. I then use a tester to filter those angle that are negative (i.e. concave).
  4. Use 'statistics calculator grouped by original polygon UID to get the total count of features.
  5. merge these attributes with the original feature class.

 

This works fine as long as the first/last vertex in the polygon is not a concave angle. This is because the 'VertexAngleCalculator' returns a value of '0' for the start/end vertex - and therefore cannot be classified.

 

Unless there is a simpler way to obtain all interior angles for each polygon, my thoughts would be to re-run the process a second time, first shifting the order of vertices by 1 index place. Then removing all features from both passes with a angle attribute of 0, and removing duplicates from the first pass that have the same geometry and angle attribute as in the second pass. Unfortunately I have no idea how to do this in FME.

 

Any help would be greatly appreciated!

You can calculate the angle of the start/end vertex from all other angles, as the sum of all interior angles of the polygon is 

(NumberOfVertices − 2) × 180

Note that the VertexCounter counts both the start and the end vertex, so you will have to subtract 3 from the result of this transformer.

You can calculate the angle of the start/end vertex from all other angles, as the sum of all interior angles of the polygon is 

(NumberOfVertices − 2) × 180

Note that the VertexCounter counts both the start and the end vertex, so you will have to subtract 3 from the result of this transformer.

Thanks geomancer, a much simpler solution!

You're welcome!

Meanwhile, I have been thinking of a completely different approach.

Calculate the convex hull of the polygon, perform an AreaOnAreaOverlayer or a Clipper, and work with the polygon(s) that are not part of the original polygon. If such a polygon is convex, its number of vertices minus 2 (or 3, using the VertexCounter, see above) gives the number of concave angles in the adjacent part of the original polygon.

There is a caveat though, as the resulting polygons may be concave themselves.

This can probably be solved (by looping, I guess), but I have not gotten that far yet.

@callumt​ You have the best solution from @geomancer​ . But I was pretty sure the TopologyBuilder also returns the angles so I played around with that, and it does. Attached is an option using TopologyBuilder (FME 2021.2)

@callumt​ You have the best solution from @geomancer​ . But I was pretty sure the TopologyBuilder also returns the angles so I played around with that, and it does. Attached is an option using TopologyBuilder (FME 2021.2)

Thanks Mark, I hadn't used the Topology builder yet so its good to know of all available solutions.

You may also be interested in the PolylineAnalyzer from FME Hub (which, despite its name, also processes polygons).

It gives the inner angles over the AngleBetweenLines port (when you first set the orientation to 'Right Hand Rule' with the Orientor), and appears not to have the problem of returning a value of '0' for the start/end vertex.

Besides the plethora of other excellent answers, I've now fixed the issue in VertexAngleCalculator causing the shared start/end vertex on area features to have a zero angle.

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