Checking if vertices of polygon are in clockwise or anti-clockwise direction in QGIS?

Question

Is there a simple way to calculate a field in QGIS indicating if the vertices of each polygon feature in a layer are in clockwise or anti-clockwise direction?

For simplicity, lets assume the layer has multiple polygon features, with a single geometry per feature (no multifeatures/multipolygons), and without donuts or other complications.

I have found related questions, but none of them give an answer to my question.

These ones are ESRI specific:

• Order of polygon vertices in general GIS: clockwise or counterclockwise

• Polygon creation (Clockwise rotation or not)

This one resolves the problem from a math point of view, but not applied to QGIS

• https://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order

The same algorithm is implemented in a shapely function - see links provided by Andreas Muller:

• http://toblerity.org/shapely/shapely.algorithms.html
• https://web.archive.org/web/20080209143651/http://www.cgafaq.info/wiki/Polygon_Area

Answer 1

This solution uses the Advanced Python field calculator in QGIS 2.18 described here and the function signed_area (i copied it from shapely source code)

In the dialog we choose the Input layer first and a Result field name (somename) and *Field type' (Float). In the Global expression field we insert code of a python function called signed_area:

def signed_area(pr):
    """Return the signed area enclosed by a ring using the linear time
algorithm at http://www.cgafaq.info/wiki/Polygon_Area. A value >= 0
indicates a counter-clockwise oriented ring."""
    xs, ys = map(list, zip(*pr))
    xs.append(xs[1])
    ys.append(ys[1])
    return sum(xs[i]*(ys[i+1]-ys[i-1]) for i in range(1, len(pr)))/2.0

And in the field called Formula we write:

value = signed_area($geom.asPolygon()[0])

Because asPolygon returns a list like object, we make sure to access the outer ring by using index 0 on that list. The result can be saved to a temporary layer and shows up in QGIS after calculation. An disadvantage may be, the a totally new layer is created, instead of just a new field is created.

Answer 2

For anybody looking for the same answer, below is how I implemented the code based on Andreas Muller's answer. It delivers a text field with a "clockwise" or "anti-clockwise" label for each polygon.

• In QGIS, go the the Processing Toolbox > Advanced Python field calculator
• Select your input layer
• Field type = String
• Length = 30 (or choose whatever fits you)
• Global expression:

(paste this)

def signed_area(pr2):
     """Return the signed area enclosed by a ring using the linear time
     algorithm at http://www.cgafaq.info/wiki/Polygon_Area. A value >= 0
     indicates a counter-clockwise oriented ring."""
     xs, ys = map(list, zip(*pr2))
     xs.append(xs[1])
     ys.append(ys[1])
     return sum(xs[i]*(ys[i+1]-ys[i-1]) for i in range(1, len(pr2)))/2.0

def rotation_dir(pr):
     signedarea = signed_area(pr)
     if signedarea > 0:
         return "anti-clockwise"
     elif signedarea < 0:
         return "clockwise"
     else:
         return "UNKNOWN"

• value: rotation_dir($geom.asPolygon()[0])

I verified this works well in QGIS for a vector layer (memory provider, not a shapefile) with polygons rotating in multiple directions (clockwise and anti-clockwise).

Answer 3

If all you need is to determine whether a polygon has its points set CW or CCW, shapely objects have a property for that:

import shapely
polygon = shapely.geometry.Polygon([(0, 0), (1, 1), (1, 0)]) 
polygon.exterior.is_ccw # False
polygon = shapely.geometry.Polygon([(0, 0), (1, 0), (1, 1)])
polygon.exterior.is_ccw # True