Calculate vertices' coordinates of a rectangle, given midline and broadth of rectangle?

Question

I have latitude and longitude of two points making the midline of a rectangle. Now I want to determine coordinates of 4 vertices of that rectangle. I know how to calculate on plane geometry by using line equation. But on geographic geometry, I'm new. I already read how to calculate one unit of latitude and longitude decimal degree but I'm still confused how to add them to a given point to calculate wanted points. My problem is like this: Given: - Broadth of rectangle - Coordinates of two points making the midline, distance between these two points are equal to the width Result: Coordinates of 4 vertices of rectangle For example: The given midline has two points: A (10.767008,106.665884) B (10.767715,106.667151) Broadth is 4-metre long All I could do now is to calculate the width of rectangle from those two points. How can I use width and height to calculate 4 vertices of this rectangle? All of my calculated cases are on small scale (part of one street of a city) so I think altitude can be excluded

Answer 1

#python file for given problem Date: 20th May 2025

#Author : rahul sehrawat

import math

def rectangle_vertices(latA, lonA, latB, lonB, breadth_m):

# Constants

meters_per_deg_lat = 111320

# Use average latitude for longitude meter conversion

avg_lat = (latA + latB) / 2

meters_per_deg_lon = 111320 * math.cos(math.radians(avg_lat))

# Step 2: Vector AB in meters

dx = (lonB - lonA) * meters_per_deg_lon

dy = (latB - latA) * meters_per_deg_lat

# Step 3: Length and unit vectors

length = math.sqrt(dx**2 + dy**2)

ux = dx / length

uy = dy / length

# Perpendicular unit vector (rotated +90 degrees)

px = -uy

py = ux

# Step 4: Half breadth offset

half_b = breadth_m / 2

offset_x = px * half_b

offset_y = py * half_b

# Step 5 & 6: Calculate vertices

# V1 = A + offset

v1_lon = lonA + offset_x / meters_per_deg_lon

v1_lat = latA + offset_y / meters_per_deg_lat

# V2 = A - offset

v2_lon = lonA - offset_x / meters_per_deg_lon

v2_lat = latA - offset_y / meters_per_deg_lat

# V3 = B - offset

v3_lon = lonB - offset_x / meters_per_deg_lon

v3_lat = latB - offset_y / meters_per_deg_lat

# V4 = B + offset

v4_lon = lonB + offset_x / meters_per_deg_lon

v4_lat = latB + offset_y / meters_per_deg_lat

return [(v1_lat, v1_lon), (v2_lat, v2_lon), (v3_lat, v3_lon), (v4_lat, v4_lon)]

# Example inputs

A = (10.767008, 106.665884)

B = (10.767715, 106.667151)

breadth = 4 # meters

vertices = rectangle_vertices(A[0], A[1], B[0], B[1], breadth)

for i, (lat, lon) in enumerate(vertices, 1):

print(f"Vertex {i}: Latitude = {lat}, Longitude = {lon}")