How to calculate lat and lon of a rectangle from a center point - dictionary

Question

I would like to draw a rectangle based on a center point lat and lon assuming a given length and width, let's say 4.5m and 1.5m, respectively. I guess, we need the bearing too. I've made a simulation by drawing a rectangle on Google Earth, getting the positions and putting them on my code. However, I need something automatic. My question is how can I link the Cartesian coordinates to those four points (rectangle) in meters.
Here is my code:
import geopandas as gpd
from shapely.geometry import Polygon
lat_point_list = [41.404928, 41.404936, 41.404951, 41.404943]
lon_point_list = [2.177339, 2.177331, 2.177353, 2.177365]
polygon_geom = Polygon(zip(lon_point_list, lat_point_list))
import folium
m = folium.Map([41.4049364, 2.1773560], zoom_start=20)
folium.GeoJson(polygon_geom).add_to(m)
folium.LatLngPopup().add_to(m)
m
I would like this:
Update:
I know this is basic trigonometry. If I split the rectsngle into triangles, we can find the different points. I know it is basic for simple exercises, however, I don't know of it changes when using Cartesian coordinates. Then, my goal is to get the points A, B, C and D, knowing the center of the rectangle in latitude and longitude, length and width.

Answer 1

Get the rectangular (NE, SW) bounds of your point and use that as bounds to folium.Rectangle.
Example, using your data. 4.5m and 1.5m are a bit small to see the rectangle:
import geopy
import geopy.distance
import math
import folium
def get_rectangle_bounds(coordinates, width, length):
start = geopy.Point(coordinates)
hypotenuse = math.hypot(width/1000, length/1000)
# Edit used wrong formula to convert radians to degrees, use math builtin function
northeast_angle = 0 - math.degrees(math.atan(width/length))
southwest_angle = 180 - math.degrees(math.atan(width/length))
d = geopy.distance.distance(kilometers=hypotenuse/2)
northeast = d.destination(point=start, bearing=northeast_angle)
southwest = d.destination(point=start, bearing=southwest_angle)
bounds = []
for point in [northeast, southwest]:
coords = (point.latitude, point.longitude)
bounds.append(coords)
return bounds
# To get a rotated rectangle at a bearing, you need to get the points of the the recatangle at that bearing
def get_rotated_points(coordinates, bearing, width, length):
start = geopy.Point(coordinates)
width = width/1000
length = length/1000
rectlength = geopy.distance.distance(kilometers=length)
rectwidth = geopy.distance.distance(kilometers=width)
halfwidth = geopy.distance.distance(kilometers=width/2)
halflength = geopy.distance.distance(kilometers=length/2)
pointAB = halflength.destination(point=start, bearing=bearing)
pointA = halfwidth.destination(point=pointAB, bearing=0-bearing)
pointB = rectwidth.destination(point=pointA, bearing=180-bearing)
pointC = rectlength.destination(point=pointB, bearing=bearing-180)
pointD = rectwidth.destination(point=pointC, bearing=0-bearing)
points = []
for point in [pointA, pointB, pointC, pointD]:
coords = (point.latitude, point.longitude)
points.append(coords)
return points
start_coords = [41.4049364, 2.1773560]
length = 4.50 #in meters
width = 1.50
bearing = 45 #degrees
m = folium.Map(start_coords, zoom_start=20)
bounds = get_rectangle_bounds(tuple(start_coords),width, length )
points = get_rotated_points(tuple(start_coords), bearing, width, length)
folium.Rectangle(bounds=bounds,
fill=True,
color='orange',
tooltip='this is Rectangle'
).add_to(m)
# To draw a rotated rectangle, use folium.Polygon
folium.Polygon(points).add_to(m)