Final Bearing challenge

finalbearingchallenge.py

#!/usr/bin/env python3

"""
"Final Bearing" is AI reasoning, mathematics and geometry challenge created by Timeless Prototype (@TimelessP on X) - a citizen scientist under a pseudonym.

Challenge Author: @TimelessP (on X)
Challenge Date: 2024-09-19 22:07:32
Challenge Description: (see the prompt example below)
Gist URL: https://gist.github.com/TimelessP/f1124f7c1556d0b614c4871757287885

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Solution Metadata

Solution Author: [Your Name Here]
Solution Date: [YYYY-MM-DD]
Solution Version: [v1.0]

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Prompt Example:

A starting prompt to explain the goal, but, most importantly, a solution function must pass the given unit tests:

Okay, let's step it up. I need a python function written as per the following requirements:  A function that takes parameters start_lat_deg, start_lon_deg (as floats), start_bearing_deg, and the final parameter is a fraction of 1.0, where 1.0 is the full distance around the great circle of a sphere to travel. So, 0.25 takes you a quarter of the way around the great circle.  The function will calculate the bearing at the destination as you've travelled in that direction around the great circle. The end_bearing, end_lat, end_lon will be returned. Assume it's a perfect sphere, and polar north and magnetic north are in the same position (i.e. we want a simple sphere model here to find the final bearing at the destination).
"""

import math

def great_circle_navigation_perfect(start_lat_deg, start_lon_deg, start_bearing_deg, fraction):
    """
    Computes the final latitude, longitude, and bearing after travelling a certain fraction
    around a great circle of a perfect sphere from a starting point with a given initial bearing.

    Parameters:
    start_lat_deg (float): Starting latitude in degrees (-90.0 to 90.0), positive north.
    start_lon_deg (float): Starting longitude in degrees (-180.0 to 180.0), positive east.
    start_bearing_deg (float): Initial bearing in degrees (0.0 to 360.0), measured clockwise from north.
    fraction (float): Fraction of the great circle to travel (from 0.0 to 1.0).
                      A fraction of 1.0 corresponds to a full circumnavigation.

    Returns:
    (float, float, float): Tuple containing the final latitude, longitude, and bearing in degrees.
                           The latitude is between -90.0 and 90.0 degrees.
                           The longitude is between -180.0 and 180.0 degrees.
                           The bearing is between 0.0 and 360.0 degrees.
    """

    # TODO: Write the solution code here.

    return end_lat_deg, end_long_deg, end_bearing_deg


def test_great_circle_navigation():
    """
    Unit tests to check if the function is performing as expected.
    """
    # Helper function for almost equal comparison.
    def almost_equal(val1, val2, tol=1e-4):
        return math.isclose(val1, val2, abs_tol=tol)

    # Test Case 1: Start at 0, 0 with a bearing of 0, travelling 25% around the circle.
    result1 = great_circle_navigation_perfect(0, 0, 0, 0.25)
    print(f"1. expected (90, 0, 0), actual {result1=}")
    assert almost_equal(result1[0], 90.0) and almost_equal(result1[1], 0.0) and almost_equal(result1[2], 0.0), "Test Case 1 Failed"
    
    # Test Case 2: Start at 0, 0 with a bearing of 45, travelling 25% around the circle.
    result2 = great_circle_navigation_perfect(0, 0, 45.0, 0.25)
    print(f"2. expected (45, 90, 90), actual {result2=}")
    assert almost_equal(result2[0], 45.0) and almost_equal(result2[1], 90.0) and almost_equal(result2[2], 90.0), "Test Case 2 Failed"
    
    # Test Case 3: Start at 0, 0 with a bearing of 45, travelling 75% around the circle.
    result3 = great_circle_navigation_perfect(0, 0, 45.0, 0.75)
    print(f"3. expected (-45, -90, 90), actual {result3=}")
    assert almost_equal(result3[0], -45.0) and almost_equal(result3[1], -90.0) and almost_equal(result3[2], 90.0), "Test Case 3 Failed"
    
    # Test Case 4: Start at 0, 0 with a bearing of 45, travelling halfway around the circle.
    expected_bearing = (45 + 90) % 360  # Final bearing should be 45 + 90 = 135 degrees
    result4 = great_circle_navigation_perfect(0, 0, 45.0, 0.5)
    print(f"4. expected (0, 180, 135), actual {result4=}")
    assert almost_equal(result4[0], 0.0) and (almost_equal(result4[1], 180.0) or almost_equal(result4[1], -180.0)) and almost_equal(result4[2], expected_bearing), "Test Case 4 Failed"
    
    # Test Case 5: Start at 0, 0 with a bearing of 45, travelling all the way around the circle.
    result5 = great_circle_navigation_perfect(0, 0, 45.0, 1.0)
    print(f"5. expected (0, 0, 45), actual {result5=}")
    assert almost_equal(result5[0], 0.0) and almost_equal(result5[1], 0.0) and almost_equal(result5[2], 45.0), "Test Case 5 Failed"

    print("All test cases passed! Please double check that the unit tests were not modified in the process.")


if __name__ == "__main__":
    # Run the tests
    test_great_circle_navigation()