Problem Specification Develop an application in Python to determine the distance between two real world objects in different measures of distance. You are to write a Python program that will compute distance and between two coordinates based on longitude and latitude angles in three contexts geometric and unit of distance contexts. Three versions will be given in three different packages: Package1, Package2 and Package3. In the first version, i.e., Package1, two files exist: Application.py and position.py. The Application file will contain a method to call a method in Position object to compute distance between coordinates in the three contexts. The position.py file gives the classes necessary to compute coordinate distance in the first context as follows: Given two coordinates, given by latitude and longitude, and the radius of the Earth, determine distance between the coordinates in statute miles and planar geometry (equirectangular flatEarth approximation). The formula to compute this distance is shown here: = 2 + 2 where R is the radius of the Earth, x is the term given by the formula = (2 1) cos((1 + 2)/2) and y is given by the formula = (2 1). It should be noted that latitude and longitude for position 1 and position 2, (latitude1, longitude1) and (latitude2, longitude2) respectively, must be converted into radians in the computation of d. The Position Class has the latitude and longitude attributes that converted from an input (latitude, N/S, longitude, W/E) such as such as (42.917, N, 85.5872, E) to (42.917, S, 85.5872 W). Namely, the valid value for latitude is [-90, 90] where the negative represents a position south of the equator and the positive a position north of the equator. The range for longitude is [-180, 180] where the negative represents a position west of the meridian line while the positive a position east of the meridian line. Last, the Unit Class has the radius attribute for the Earth in miles, whose value is 3959 miles (mean volumetric radius). CS 1120 (Python) - Spring 2021 LA3 OOP distance calculator

Next, to test the information hiding of the calculation to the Application file/class, you are asked to change the Position class, with the new one in Package2, has a file postion.py, where the distance computed between two coordinates is in statue miles and through spherical coordinates and so the haversine calculation is based on the theta and phi, which are: = , where R is Earths radius, c is given by the formula = 2 atan2( , 1 ) , and a is given by the formula = (sin ( (21) 2 )) 2 + cos(1) cos(2) (sin( 21 2 )) 2 ) . Here, the latitudes and longitudes must be converted to radians as well. In fact, latitude converted to radians is the angle phi and longitude converted to radians is the angle theta. Last, you are asked to consider the distance output in kilometers instead of status miles without modifying the current implementation, i.e., increasing the reusability. Package3 has a file kilometer.py which expands into the third context, in which the distance between two coordinates must be determined in kilometers and in spherical geometry. Here, you must consider the Earths mean volumetric radius as 6371 kilometers. Design Requirements

Basic Structure Your program should have several classes in different modules as follows:

1. The main class (which contains the main method); this class should be called LA3Main. It executes the run_example() method in Application class defined below. The main class module needs to import the Application class from Package1/Application.py.

2. The Application class (in Application.py of Package1); this class has a constructor, which should not do anything, a static method (named assign_coord) that takes three parameters: position, units, and geometry and sets the associations between position-units and position-geometry, and a stative method (named run_example) which takes no parameters and creates instances of GPS positions, distance units and coordinate geometries to compute distance, based on each given scenario. This package will need to import position.py from Package 1, then later replace with position.py from Package 2, and import Kilometer from Package 3.

3. The Units class (in position.py of Package1); It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes no arguments and initializes the attributes measure and e_radius. The measure attribute is the string name of the distance units applied in a distance computation. It should be set to the initials, mi, referring to statute miles. e_radius is the numerical value of Earths radius in those distance units. This should be set to the Earths radius in statute miles, upon initialization. b. A method (named set_radius) that takes a floating-point number as a parameter and sets the attribute e_radius. c. A method (named get_radius) that takes no parameter and gets the value of e_radius. CS 1120 (Python) - Spring 2021 LA3 OOP distance calculator d. A method (named set_measure) that takes a string as a parameter and sets the attribute measure. e. A method (named get_measure) that takes no parameter and gets the value of measure.

4. The Kilometer class (in kilometer.py of Package3, an inherits from Units in position.py of Package1); It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes no arguments and initializes the super class attributes measure and e_radius. The measure attribute is the string name of the distance units applied in a distance computation. It should be set to the initials, km, referring to kilometers. e_radius is the numerical value of Earths radius in those distance units. This should be set to the Earths radius in kilometers, upon initialization. b. A method (named set_radius) that takes a floating-point number as a parameter and sets the super class attribute e_radius. c. A method (named get_radius) that takes no parameter and gets the super class value of e_radius. d. A method (named set_measure) that takes a string as a parameter and sets the super class attribute measure. e. A method (named get_measure) that takes no parameter and gets the super class value of measure.

5. The Geometry class (in position.py of Package1); It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes no arguments and initializes the attributes units and geometry. The geometry attribute is the string name of the coordinate system applied to compute position distance (i.e., spherical, planar, cylindrical). units is a reference to an instance of units to be applied to the distance calculations. b. A method (named set_units) that takes a Units instance as a parameter and sets the attribute units. c. A method (named get_units) that takes no parameter and gets the reference of a Units object associated to the Geometry object. d. A method (named set_geometry) that takes a string as a parameter and sets the attribute geometry. e. A method (named get_geometry) that takes no parameter and gets the value of geometry. f. A method (named curry_distance) that takes two positions as parameters and computes the distance between them based on equirectangular (flat-Earth approximation) coordinate system and the Earths radius in units.

6. The SphericalGeo class (in new_position.py of Package2, inherits from Geometry in position.py of Package1); It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes no arguments and initializes the super class attributes units and geometry. The geometry attribute is the string name of the coordinate system applied to compute position distance (i.e., spherical, planar, cylindrical). units is a reference to an instance of units to be applied to the distance calculations. b. A method (named set_units) that takes a Units instance as a parameter and sets the attribute units. CS 1120 (Python) - Spring 2021 LA3 OOP distance calculator c. A method (named get_units) that takes no parameter and gets the reference of a Units object associated to the Geometry object. d. A method (named set_geometry) that takes a string as a parameter and sets the attribute geometry. e. A method (named get_geometry) that takes no parameter and gets the value of geometry. f. A method (named curry_distance) that takes two positions as parameters and computes the distance between them based on a spherical coordinate system and the Earths radius in units.

7. The Position class (in position.py of Package1). It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes four arguments: latitude, latitude cardinal direction string, longitude, and longitude cardinal direction string, then initializes the attributes latitude, longitude, and geometry. The latitude and longitude attributes designate latitude and longitude angle values of the position. You must determine if they are positive or negative, given the cardinal direction strings (i.e., S and W relate to negative latitude and longitude angles, respectively). The geometry attribute is a reference to an instance of a Geometry type or subtype object. b. A method (named set_latitude) that takes a floating-point number as a parameter and sets the attribute latitude. This method must make sure the latitude value is in the range [-90, 90] c. A method (named get_latitude) that takes no parameter and gets the value of latitude. d. A method (named set_longitude) that takes a floating-point number as a parameter and sets the attribute longitude. This method must make sure the longitude is in the range [-180, 180]. e. A method (named get_longitude) that takes no parameter and gets the value of longitude. f. A method (named set_geometry) that takes a Geometry based reference as a parameter and sets the attribute geometry. g. A method (named get_geometry) that takes no parameter and gets the value of geometry. h. A method (named distance) that takes a position as a parameter, delegates the calculation to the Geometry class, i.e., the curry_distance() method, and finally returns the value obtained from a curry_distance() call from the this positions geometry.

8. The Position class (in new_position.py of Package2). It should contain the methods required to perform the necessary actions, which includes: a. An __init__() method, which takes four arguments: latitude, latitude cardinal direction string, longitude, and longitude cardinal direction string, then initializes the attributes phi, theta, and geometry. The latitude and longitude attributes designate latitude and longitude angle values of the position. You must determine if they are positive or negative, given the cardinal direction strings (i.e., S and W relate to negative latitude and longitude angles, respectively). The geometry attribute is a reference to an instance of a Geometry type or subtype object. b. A method (named set_latitude) that takes a floating-point number as a parameter, converts it from degrees into radians and passes the result to method set_phi() to set the phi. c. A method (named get_latitude) that takes no parameter and gets the latitude converted back from phi, from radians to degrees. CS 1120 (Python) - Spring 2021 LA3 OOP distance calculator d. A method (named set_longitude) that takes a floating-point number as a parameter, converts it from degrees into radians and passes the result to method set_phi() to set the theta. e. A method (named get_longitude) that takes no parameter and gets the latitude converted back from theta, from radians to degrees. f. A method (named set_phi) that takes a floating-point number as a parameter and sets the value phi. This method must make sure phi is set to a value between [-/2, /2]. g. A method (named get_phi) that takes no parameter and gets the value of phi. h. A method (named set_theta) that takes a floating-point number as a parameter and sets the value of theta. This method must make sure theta is set to a value between [-, ]. i. A method (named get_theta) that takes no parameter and gets the value of theta. j. A method (named set_geometry) that takes a Geometry based reference as a parameter and sets the attribute geometry. k. A method (named get_geometry) that takes no parameter and gets the value of geometry. l. A method (named distance) that takes a position as a parameter and returns the value obtained from a curry_distance() call from the this positions geometry.

The output and interface should be neat and well-described. See the example provided in the Testing Phase section.