PyQGIS – How to Create Arc with Start, End, Centre, and Radius

polygonpyqgis

I am trying to create some polygons where some of the sections correspond to curves/arcs. I have been provided with start point, end point, centre point, radius and direction (clockwise/ anti-clockwise) to create these curved sections. See below for reference:

enter image description here

I have seen this post that has helped massively but unfortunately I do not know how to derive my arc midpoint from the values I have been given (centre point and radius).
I would like to do this programmatically using Python/PyQGIS but somehow, I am unable to find a solution. So far, I have managed to manually trace the midpoint section for the curve and used it to create my lineString layer.

Is there a pythonic way to achieve this and convert to polygon?

This is my code so far:

# Import modules
from qgis.core import *
from qgis.utils import *

# coord for curved section
start_lat, start_lon = 39.08626748, -2.66563606
end_lat, end_lon = 39.20366816, -2.51489454
# This mid point has been traced manually to recreate the curve
mid_curv_lat, mid_curv_lon = 39.20366816, -2.65091330

# coord for squared section
point3_lat, point3_lon = 39.11293834, -2.41907255
point4_lat, point4_lon = 38.98554723, -2.55822285

# coord and radius
centre_lat, centre_lon = 39.13921171, -2.58290392
radius_km = 9.26

    # Begin a new project
    iface.newProject()
    
    # Create a QgsCircularString
    circularRing = QgsCircularString()
    # Set first point, intermediate point for curvature and end point
    circularRing.setPoints([
        QgsPoint(start_lon, start_lat),
        QgsPoint(mid_curv_lon, mid_curv_lat),
        QgsPoint(end_lon, end_lat)]
    )
    
    # Create geometry using the instance of QgsCircularString
    curve = QgsGeometry(circularRing)
    
    # Create a QgsLineString
    lineString = QgsGeometry.fromPolyline([QgsPoint(end_lon, end_lat), 
                 QgsPoint(point3_lon, point3_lat),
                 QgsPoint(point4_lon, point4_lat),
                 QgsPoint(start_lon, start_lat)]
    )
    
    # Create curve and line features
    fet_curve = QgsFeature()
    fet_curve.setGeometry(curve)
    
    fet_line = QgsFeature()
    fet_line.setGeometry(lineString)
    
    # Create a memory layer
    layer = QgsVectorLayer(
        "LineString?crs=epsg:4326&field=id:integer&field=name:string(20)&index=yes",
        "temporary_points",
        "memory"
    )
    # Add the layer
    QgsProject.instance().addMapLayer(layer)
    # Add the feature to the layer provider
    pr = layer.dataProvider()
    pr.addFeatures([fet_curve, fet_line])
    
    # Update extent
    layer.updateExtents()
    
    # Zoom to extent
    iface.mapCanvas().setExtent(layer.extent())
    iface.mapCanvas().refresh()

EDIT: data sample

|Label|Position|Order|CoordPair         |Orientation|Radius_Km|
|-----|--------|-----|------------------|-----------|---------|
|C    |        |1    |39.08627, -2.66564|           |         |
|C    |        |2    |39.20367, -2.51489|           |         |
|C    |        |3    |39.11294, -2.41907|           |         |
|C    |        |4    |38.98555, -2.55822|           |         |
|C    |Centre  |     |39.13921, -2.5829 |1          |9.26     |
|A    |        |5    |38.91119, -2.25953|           |         |
|A    |        |1    |38.99365, -2.21096|           |         |
|A    |        |2    |38.94734, -2.09687|           |         |
|A    |        |3    |38.89763, -2.10139|           |         |
|A    |        |4    |38.86149, -2.18385|           |         |
|A    |Centre  |     |38.927, -2.11607  |1          |9.26     |
|B    |        |2    |38.74627, -2.41767|           |         |
|B    |        |3    |38.74062, -2.26179|           |         |
|B    |        |4    |38.68866, -2.25953|           |         |
|B    |        |1    |38.69769, -2.42445|           |         |
|B    |Centre1 |     |38.72367, -2.44253|1          |9.26     |
|B    |Centre2 |     |38.71464, -2.25388|1          |9.26     |

Best Answer

I believe QgsCircularString.fromTwoPointsAndCenter() is a method that could help you construct those arcs. It creates a circular string consisting of a single arc which represents the curve from one point to another with a specified center point.

I've updated your example using the mentioned method and also addressed your problem of converting the exterior line to a polygon.

# coord for curved section
start_lat, start_lon = 39.08626748, -2.66563606
end_lat, end_lon = 39.20366816, -2.51489454

# coord for squared section
point3_lat, point3_lon = 39.11293834, -2.41907255
point4_lat, point4_lon = 38.98554723, -2.55822285

# center coord
centre_lat, centre_lon = 39.13921171, -2.58290392

# Create the arc segment
arc = QgsCircularString.fromTwoPointsAndCenter(
    QgsPoint(start_lon, start_lat),
    QgsPoint(end_lon, end_lat),
    QgsPoint(centre_lon, centre_lat)
)

# Creates the polygon segment
line = QgsLineString(
    [QgsPoint(end_lon, end_lat), QgsPoint(point3_lon, point3_lat),
    QgsPoint(point4_lon, point4_lat), QgsPoint(start_lon, start_lat)]
)

# join both segments together
curve = line.toCurveType()
curve.addCurve(arc)

# create polygon geometry from exterior line
polygon = QgsPolygon()
polygon.setExteriorRing(curve)
geom = QgsGeometry(polygon)

# Create polygon feature
poly_feat = QgsFeature()
poly_feat.setGeometry(polygon)

# Create a memory layer
layer = QgsVectorLayer(
    "Polygon?crs=epsg:4326&field=id:integer&field=name:string(20)&index=yes",
    "temporary_points",
    "memory"
)
# Add the layer
QgsProject.instance().addMapLayer(layer)
# Add the feature to the layer provider
pr = layer.dataProvider()
pr.addFeatures([poly_feat])

# Update extent
layer.updateExtents()

# Zoom to extent
iface.mapCanvas().setExtent(layer.extent())
iface.mapCanvas().refresh()

arcs

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