Identifying polygons with arcs using QGIS

Question

I have a polygon layer where there may be polygons and circular arcs as in the image.

How can I identify the polygons which have those arcs parts?

Answer 1

Working on the assumption that in an arc like in the posted screenshot, the distance between vertices will be very similar and the azimuth from one vertex to the next will change at a fairly constant rate, I cobbled together this messy code in the Python Console to test the idea:

lyr = iface.activeLayer()

for f in lyr.selectedFeatures():
    geom = f.geometry()

    for p in geom.parts():
        verts = p.vertices()
        p0 = verts.next()
        p1 = verts.next()
        dist = p0.distance(p1)
        az = p0.azimuth(p1)
        dev = 0
        tol = 0.1
        angular_tol_max = 10
        angular_tol_min = 0.01
        in_arc = False
        
        for v in verts:
            d = p1.distance(v)
            a = p1.azimuth(v)
            if((abs(d-dist)/dist) > tol):
                dist = d
                in_arc = False
            else:
                if (angular_tol_min < abs(az-a) < angular_tol_max) and dev != 0:
                    #print ("this might be an arc",((az-a)/dev))
                    if( (-tol) < ((az-a)/dev) > (tol)):     
                        #print ("this realy might be an arc")
                        if in_arc == False:
                            rb = QgsRubberBand(iface.mapCanvas())
                            rb.setColor(QColor(255, 0, 0))
                            rb.setWidth(3)
                            rb.addPoint(QgsPointXY(p0.x(), p0.y()))
                            rb.addPoint(QgsPointXY(p1.x(), p1.y()))
                        rb.addPoint(QgsPointXY(v.x(), v.y()))
                        in_arc = True
                    else:
                        in_arc = False
                else:
                    in_arc = False
            p0 = p1
            p1 = v
            dev = az - a
            az = a

It iterates through the vertices comparing the distance and azimuth to the previous vertex, when it detects a segment with a similar length and change in direction as the previous segment it assumes they are part of the arc. The tolerance can be changed by the value of the tol variable (current value of 0.1 means up to 10% difference in segment length) and the angular_tol_max and angular_tol_min currently 10 and 0.01 meaning the azimuth change must be at less than 10 degrees and at at least 0.01 degrees.

It seems to work OK, I expect it would fail where the azimuth of adjacent segments changes from slightly less than 360 to slightly more than zero.