Deleting vertices inside polygon area in QGIS

Question

I am trying to remove vertices inside a polygon area which do not form an outside boundary to the polygon. Example picture below with the vertices to be removed in red markings.

Deleting the vertices manually with the editing tool is not an option since there are 1000s of these in my dataset.

Is there an effective way to get rid of these vertices in QGIS, so only the polygon boundary is left?

Answer 1

If the vertices immediately before and after the ones that are within the polygon are coincident, the solution could be running the Processing > Vector geometry > Fix geometries tool from the Processing Toolbox (Ctrl+Alt+T).

Answer 2

To identify the vertices to delete, check the interior angle at each vertex and where this angle is very high (near to 360 degrees), you can delete the vertex.

To measure the interior anlge, I use this solution. You can now use QGIS expressions with the expression below an re-draw the polygon, but exluding the vertices with interior angle larger than let's say 350 degrees (you can change this value on line 3 of the expression to fit your needs).

I would advice to first use the expression with Geometry Generator to see the result and when satisfied, create the output as actual geometry (new layer) with Geomtry by Expression - see here for the differences between both options. The expression remains the same.

Blue: initial polygon, four vertices deleted, resulting in the new polygon with red outline - visualized here with Geometry generator:

Changing the angle to 180, you get another result that deletes all "bays" of the polygon:

Use this expression:

with_variable(
    'angle',
    350,  -- change this value to fit your needs
    make_polygon(
        make_line(
            point_n($geometry,1),
            array_filter(
                array_foreach(
                    generate_series (2,  num_points( $geometry)-1),
                    if (
                        with_variable (
                            'vertex',
                            @element,
                            with_variable (
                                'azimuth1',
                                degrees (
                                    azimuth(
                                        point_n($geometry,@vertex-1),
                                        point_n($geometry,@vertex)
                                    )
                                ),
                                with_variable (
                                    'azimuth2',
                                    degrees (
                                        azimuth(
                                            point_n($geometry,@vertex),
                                            point_n($geometry,@vertex+1)
                                        )
                                    ),
                                    case
                                    when (@azimuth1 > @azimuth2) and (@azimuth1 > @azimuth2+180) then 540-@azimuth1+@azimuth2
                                    when (@azimuth1 > @azimuth2) then 180-@azimuth1+@azimuth2
                                    when (@azimuth1 < @azimuth2) and (@azimuth1+180>@azimuth2) then 180 + @azimuth2-@azimuth1
                                    when (@azimuth1 < @azimuth2) then @azimuth2-@azimuth1-180 
                                end
                                )
                            )
                        ) < @angle,
                        point_n($geometry,@element),
                        'delete'
                    )
                ),
                @element is not 'delete'
            )
        )
    )
)

Answer 3

Try these geoprocessing tools:

• Snap geometries to layer and snap the layer to itself
• Buffer with 0 distance
• Snap points to grid