How to get rotation angle of a rectangular polygon with PyQGIS

Question

I have an unreferenced point layer that is rectangular in shape. It is made out of rows of unequally spaced points, with spacing between the rows of either 1 or 3 meters.

I also have a multipolygon layer that corresponds with the mentioned point layer in size, but the multipolygon layer is georeferenced (the four corner coordinates are known). I also have a column that indicates where is the Zero/Start corner, with the following values: East, West, North, or South.

Is there a way in pyqgis to obtain the Zero/Start coordinate of the corner vertex from the polygon layer based on the value in the Zero/Start column? In the example shown, the value of the Zero/Start column is South. I would also like to know if there is a way to get the angle of rotation between two layers. My idea is to first rotate the point layer with the following code:

vector_layer_edit_utils = QgsVectorLayerEditUtils(lyr)
rotation_angle = 0 # angle that is needed
zero_start = QgsPointXY(0, 0) # start coordinate of the unreferenced point layer
lyr = QgsProject.instance().mapLayersByName("point_layer")[0]
feats = lyr.getFeatures()
lyr.startEditing()
for feat in feats:
    geom = feat.geometry()
    geom.rotate(rotation_angle, zero_start)
    lyr.changeGeometry(feat.id(), geom)
lyr.commitChanges()

It's not clear to me what is the direction of the rotation, clockwise or counterclockwise. I would then translate the rotated layer to the coordinate obtained from the polygon vertex with the following code:

feats = lyr.getFeatures()
zero_coordinate = QgsPointXY(0, 0) # replace with the coordinate from the polygon layer
lyr.startEditing()
for feat in feats:
    vector_layer_edit_utils.translateFeature(feat.id(), zero_coordinate.x(), zero_coordinate.y())
lyr.commitChanges()

Answer 1

You can get the angle you need from the points of the rectangle using arctangent (Numpy arctan2)

import numpy
layer = iface.activeLayer()
features = layer.getFeatures()
top_left = [999999,9999999]
bot_left = [999999,9999999]
bot_right = [0,0]
rot_point = QgsPoint(0,0)
for feature in features:
    print("Type",feature.geometry().type(), QgsWkbTypes.PolygonGeometry)
    #these will be 2 if polygon.
    geom = feature.geometry()
    if geom.isMultipart():
        print("This is a multi polygon")
        multipolygon = geom.asMultiPolygon()
        polygon = multipolygon[0] #only get the first polygon in the list
    else:
        print("This is a single polygon")
        polygon = geom.asPolygon()
        
    n = len(polygon[0])
    for i in range(n-1): #first and last point the same
        this_x = polygon[0][i].x()
        this_y = polygon[0][i].y()
        print( this_x , this_y)
        if this_x < top_left[0]:
            top_left = [this_x , this_y]
        if this_x > bot_right[0]:
            bot_right = [this_x , this_y]
        if this_y < bot_left[1]:
            bot_left = [this_x , this_y]
            rot_point = polygon[0][i]
            
            
    #vertices = multipolygon[0].asPolygon()

# Get the vertices of the first polygon
    print(f"Top Left point {top_left}")
    print(f"Bottom Right point {bot_right}")
    print(f"Bottom Left point {bot_left} = Zero Start")
    delta_x = bot_right[0] - bot_left[0]
    delta_y = bot_right[1] - bot_left[1]
    tilt_ang = numpy.arctan2(delta_y, delta_x)
    print(f"Radians {tilt_ang}")
    print(f"Degrees {numpy.degrees(tilt_ang)}")
    print(f"Rotation Point = {rot_point}")

rotation_angle = numpy.degrees(tilt_ang) * -1
#rot_point =QgsPointXY(78009.613,2945880.6889)
plyr = QgsProject.instance().mapLayersByName("point_layer")[0]
feats = plyr.getFeatures()
plyr.startEditing()
for feat in feats:
    geom = feat.geometry()
    geom.rotate(rotation_angle, rot_point)
    plyr.changeGeometry(feat.id(), geom)
plyr.commitChanges()