Calculating dominant angle of a polygon in QGIS without main_angle function

Question

How can I calculate dominant angle of a polygon in QGIS without main_angle function?

I have a shapefile of Oriented Minimum Bounding Box rectangles (accessible from the following link: https://drive.google.com/drive/folders/1Xr_0Apg9s7s0daevIUctWTr0-WCABC83?usp=sharing) produced by using as Input Layer a shapefile of irregular polygons (accessible from the following link: https://drive.google.com/drive/folders/1BKp5VbR1aMAzCObGprvqeL0WSMqpTX32?usp=sharing)

Figure 1: Shapefile of Oriented Minimum Bounding Box

Figure 2: Shapefile of Irregular Polygons

I need to find the main_angle of every polygon in the Oriented Minimum Bounding Box layer.

I used the main_angle function available in QGIS 3.16 onwards.

main_angle function returns the main angle of a geometry.

However, when I constructed centerlines using the centroid of the polygons (in this case rectangles) and main_angle values computed using the main_angle function in QGIS with the following expression:

intersection (
extend (
    make_line (
        centroid ($geometry), 
        project (
            centroid ($geometry), 
            25000, 
            radians("main_angle")
        )
    ),
    25000,
    0
),
$geometry

)

Main_angle of the polygons computed with main_angle function is not at all times

the angle of longest collection of segments as in the image below encircled below:

What expression can be used such that main_angle is always the angle of longest segment of the Oriented Minimum Bounding Box in a project whereby main angle of every Oriented Minimum Bounding Box is the determining factor of accuracy of end results.

I found this comment from the following link: https://georezo.net/forum/viewtopic.php?id=119435

You need an expression dependent on the height and width data:

The end result I am seeking is the overall orientation of all ploygons collectively as illustrated in the image below from the Line Direction Tool QGIS plugin. By unfortunately provides no values.

I used XLSTAT to use Principal Component Analysis but did not achieve conculsive results. Computed results and report is accessible from following link: https://drive.google.com/drive/folders/1CHDfJ9poD8tk-KQLmRV8NbilZCyGtTs5?usp=sharing

Answer 1

I inspected your data, the solution is based on that. First, create a new field longest that evaluates which side of your rectangle is the longest, width or height. Use this expression in the field calculator: if ( "width" > "height" , 'width', 'height').

Than you can create the centerline using this expression with Geometry generator or Geometry by expression as you already have a field angle in your data that, depending on which one is the longest side, can be used to create what you want:

intersection (
    $geometry, 
    extend (
        make_line (
            centroid ($geometry), 
            project ( 
                centroid ( $geometry ), 
                20,  
                if  (
                    "longest" =  'width' , 
                    radians ("angle"-90 ), 
                    radians ("angle" )
                )
            )
        ), 
    20,
    0
    )
)

If you want to get the mean value for the angle (azimuth) of all these lines, create a new layer centerline using Geometry by expression with the expression from above. On this line layer, create a new field azimuth using field calculator that calculates the angle of each line with this expression:

degrees (
    azimuth (
        start_point ($geometry), 
        end_point ($geometry)
    )
)

Now, you can use Menu Vector / Analysis tools / Basic statistics for fields on the centerline layer and setting the field azimuth as input (see screenshot below). The mean value for all centerlines, calculated with your data and according to this tool is 39.470817687074835.