Align country name at the polygon’s centroid

qsomap.py

@@ -103,6 +103,36 @@ def is_point_in_polygon(point, polygon):
         return True  # odd number of intersects -> inside polygon
 
 
+def polygon_centroid(polygon):
+    """ Calculate the centroid (center of mass) of the given 2D polygon.
+
+    See https://en.wikipedia.org/wiki/Centroid#Of_a_polygon for the source
+    formulae.
+
+    Args:
+        polygon: 2xN numpy array with x and y coordinates of N points.
+
+    Returns:
+        (x, y): The coordinates of the center of mass.
+
+    """
+    # Separate the coordinates
+    x = polygon[0, :]
+    y = polygon[1, :]
+
+    # First, calculate the area of the polygon
+    A = 0.5 * np.sum(x[:-1] * y[1:] - x[1:] * y[:-1])
+
+    # Calculate x and y of the centroid
+    C_x = np.sum((x[:-1] + x[1:])
+                 * (x[:-1] * y[1:] - x[1:] * y[:-1])) / (6 * A)
+
+    C_y = np.sum((y[:-1] + y[1:])
+                 * (x[:-1] * y[1:] - x[1:] * y[:-1])) / (6 * A)
+
+    return C_x, C_y
+
+
 def svg_make_inverse_country_path(doc, map_radius, polygon, **kwargs):
     # build a closed circle path covering the whole map
     commands = [f"M 0, {map_radius}",
@@ -257,7 +287,8 @@ def svg_add_maidenhead_grid(doc, ref_lat, ref_lon, map_radius):
         lon = x * 2 * np.pi / N
         lat = np.linspace(-np.pi/2, np.pi/2, resolution)
 
-        x, y = map_azimuthal_equidistant(lat, lon, ref_lat, ref_lon, map_radius)
+        x, y = map_azimuthal_equidistant(lat, lon,
+                                         ref_lat, ref_lon, map_radius)
         points = np.array([x, y]).T + map_radius
 
         group.add(doc.polyline(points, **{'class': 'maidenhead_line'}))
@@ -306,9 +337,10 @@ def svg_add_country_names(doc, simplegeodata, map_radius):
             w = np.max(x) - np.min(x)
             h = np.max(y) - np.min(y)
 
-            # FIXME: calculate center of mass
+            # align text at the center of mass
-            center_x = np.median(x) + map_radius
+            center_x, center_y = polygon_centroid(poly)
-            center_y = np.median(y) + map_radius
+            center_x += map_radius
+            center_y += map_radius
 
             kwargs = {
                     'class': 'country_label',