Finding which side of closest polyline point lies on in QGIS?

Not a single query but the following code can be executed in the Python Console. The code essentially does the following:

• Iterates each line feature and calculates the distance from this to a selected point feature;
• Stores these in a dictionary;
• A proximity is used to limit iterating through each line feature (i.e. a value of 100 means only lines within 100m of the point will be included);
• Sorts the dictionary and selects the line feature with the minimum distance from the point;
• Gets the coordinates of the start and end vertices;
• Determines if the point lies on the left- or right-hand side of the line (assuming the line is a single straight line).

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pointLayer = QgsProject.instance().mapLayersByName('point')[0]
lineLayer = QgsProject.instance().mapLayersByName('line')[0]

# Set proximity limit
proximity = 1
distance_dict = {}

for point in pointLayer.selectedFeatures():
    start_point = point.geometry().asPoint().x()
    end_point = point.geometry().asPoint().y()
    for line in lineLayer.getFeatures():
        distance = point.geometry().distance(line.geometry())
        if distance < proximity:
            distance_dict[line.id()] = distance
    closestFeature = sorted(distance_dict.keys(), key=(lambda key:  distance_dict[key]))
    lineLayer.selectByIds([closestFeature[0]])
    for line in lineLayer.selectedFeatures():
        start_geom = line.geometry().asPolyline()[0]
        end_geom = line.geometry().asPolyline()[1]
    d = ((start_point - start_geom.x()) * (end_geom.y() - start_geom.y())) - (((end_point - start_geom.y()) * (end_geom.x() - start_geom.x())))
    if d < 0: 
        print('Left')
    elif d > 0:
        print('Right')
    else:
        print('On line')

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Example of selected points (highlighted in yellow):

• Right of line -

  

• Left of line -