Shortest-Path-And-Rhumb-Line

This project simulates the generation of shortest paths and rhumb lines between coordinates. It displays the final generated paths on a 2D plane and a 3D sphere. The project is created using Unity3d and provides the following features:

Setting the start and end coordinates	Displaying the paths on a 2D plane and a 3D sphere
Tutorial on how to compute the shortest path	Traversing the paths

Demo

We created a WebGL application that demonstrates different features provided by our simulation. A complete demo can be found on https://omaddam.github.io/Shortest-Path-And-Rhumb-Line/.

Getting Started

These instructions will get you a copy of the project on your local machine for development and testing purposes.

Prerequisites

The things you need to install before you proceed with development:

1. Unity3d (2020.2.0f1) [required].

Installing

A step by step guide to get you started with development.

Download, clone, and setup the repository

git clone https://github.com/omaddam/Shortest-Path-And-Rhumb-Line.git

Initialize git flow

git flow init

Standards

General Standards

• Line ending: CRLF
• Case styles: Camel, Pascal, and Snake case
  • Arguments, paramters, and local variables: camel case (e.g. shortestPath)
  • Global variables: pascal case (e.g. StartCoordinates)
  • Constants and static variables: snake case (ALL CAPS) (e.g. DEFAULT_COLOR)
• Methods naming convention:
  • Pascal case (e.g. GeneratePath)
  • Verbs

Commenting Standards

• /// Summaries: Full-usage of English grammar and punctuation. (e.g. Add periods to the end of your summaries, as if you were writing a phrase or sentence.)
• // In-line comments: quick, point-form. Grammar and punctuation not needed

Assets / App

• Contains all scripts and resources used in the demo.
• Scripts are created under Assets/App/Scripts folder.

Third Party Packages

• All packages should be included under Assets/ThirdParty folder.
• Contains all packages downloaded from the Unity3d store.

Assets / Others

• All components should be included under Assets/<Name> folder. (e.g. Assets/SphericalPaths)
• Each component should be isolated and under NO CIRCUMSTANCES referencing or using another component's scripts.
• Components are NOT allowed to reference or call application/demo scripts.

Code Based Documentation

Assets / SphericalPaths

This folder contains the implementation of the algorithms that compute the shortest path and the constant path (rhumb line). The algorithms' implementation can be found in the DataStructure folder while the rest of the components are for visualization purposes.

DataStructure

The data structure contains 3 classes.

• Coordinates: represents a single point on a map.

  • Properties
    • CartesianCoordinates: the latitude and longitude coordinates of the point.
    • Width: the width of the 2D plane this point will be presented on. The width is double the height.
    • PlaneCoordinates: x and y coordinates normalized and scaled to be displayed on the 2D plane.
    • Radius: the radius of the 3D sphere this point will be presented on.
    • SphericalCoordinates: x, y, and z coordinates normalized and scaled to be displayed on the 3D sphere.

• Path: represents a path on a map.

  • Properties
    • Coordinates: list of coordinates sorted in the order that defines the path.
    • Start: references the first coordinates in the path.
    • Last: references the last coordinates in the path.

• PathComputationMethods: a static class that provides extensions and methods to compute paths and bearing angles. We only list some of the methods below.

  • Methods
    • GetRhumbPath: generates the path between the two coordinates using rhumb line.
    • GetShortestPath: generates the path between the two coordinates using shortest path.
    • ComputeRhumbPathBearingAngle: computes the bearing angle at a provided coordinates while facing a target in a direction that follows the rhumb line path.
    • ComputeShortestPathBearingAngle: computes the bearing angle at a provided coordinates while facing a target in a direction that follows the shortest path.

Point

A Point represents coordinates on a map in the form of a pin. It is used as a template by the plane and sphere components when displaying the coordinates.

• Prefab: Assets/SphericalPaths/Prefabs/Point.prefab
• Script: Assets/SphericalPaths/Scripts/Point.cs
  • Initialize: sets the color, location, and rotation of the pin.

Path

A Path uses line renderers to represent paths, trails, and projections on a map. It is mainly used as a template by the plane and sphere components when displaying the paths.

• Prefab: Assets/SphericalPaths/Prefabs/Path.prefab
• Script: Assets/SphericalPaths/Scripts/Path.cs
  • Initialize: sets the color and displays lines to connect all the coordinates.

Plane / Sphere

A 2D plane / 3D spherical map that uses the two prefabs; Point and Path; to visualize the shortest path and rhumb line between two coordinates.

• Prefabs:
  • Assets/SphericalPaths/Prefabs/Plane.prefab
  • Assets/SphericalPaths/Prefabs/Sphere.prefab
• Scripts:
  • Assets/SphericalPaths/Scripts/Plane.cs
  • Assets/SphericalPaths/Scripts/Sphere.cs
    • ClearPoints: deletes all points on the map.
    • DisplayPoints: appends and displays points on the map.
    • ClearPaths: deletes all paths on the map.
    • DisplayPaths: appends and displays paths on the graph.

The sphere prefab also includes another script that allows the user to drag and rotate the map.

• Script: Assets/SphericalPaths/Scripts/SphereRotation.cs