PROJECTS
Intelligent Navigation
Mapping and routing application written to automatically redirect a user towards the most favourable and highly-rated establishment of their choice (gas station, grocery store, restaurant, hotel, etc.).
Google Cloud APIs integrated with software application, to connect it with online world spatial analysis and routing services; geometric algorithms and basic computer intelligence pipelines written to automate the process with minimal user-input.
Written over the course of 24 straight hours of granola bars and caffeine chocolates at a Hackathon, it has as much personality as it does functionality. The "Navigate!" button should have been labeled "Navigate..." as it takes three clicks to initialize, and sometimes it looks for restaurants in the ocean... nevertheless, it will always be sure to find the best place in town!
For more information, please see the following link: https://devpost.com/software/ez-nav . If it is no longer working, that means my API key has expired.
Spherical Harmonics
Defined as a set of polynomial functions which obey Laplace's equation, rendering them harmonic.
More generally, they can be used to represent potential fields occuring in space.
For this example below, they are used to approximate the individual components of Earth's gravitational field, called the "geoid".
These equations more precisely represent the anomalies in Earth's gravity, which are caused by a variety of complex processes resulting from the gravitational pull of other celestial bodies and even the forces inside the Earth. Due to the ordered nature of the universe, these processes can be modeled accurately with a relatively simple series of recursive equations.
Fun fact: If you want to lose weight, walk towards the equator!
HOW IT WORKS
The "Spherical Harmonic 2D Calculator" is a simple application that makes use of HTML code with embedded CSS for style and Javascript for computation.
Computation is done by running basic linear arrays through a variety of formulas which find the value of each Legendre Polynomial throughout the circumference of a 2D circle.
Representing Spherical Harmonics when viewed as a 2D cross-section of the Earth, these Legendre Polynomials are then triple-integrated over the radius, latitude, and longitute of the Earth.
The below calculator allows for the generation of 2D Legendre polynomial functions, which is the first step in generating 3D spherical harmonics. "m" and "n" are entered, and the appropriate polynomials are generated. Toggles allow for the generation of one or five in sequence, and normalization brings all into a common scale for comparison.
Each incrementation of "n" increases the angular momentum of the corresponding spherical harmonic, while "m" increases the principal quantum number. For each energy level n there are just as many quantum states m, while higher energy levels correspond to a more diminished effect on the Earth's gravity yet a greater amount of positive and negative zones of influence. Some 3D examples are shown below the calculator.
3D spherical harmonics
Generated within MATLAB using the Polynomial equations found with the above calculator, the effects of each Legendre Polynomial and its corresponding spherical harmonic representation on the Earth can be simply visualized.
Red zones correspond to zones of positive gravity influence, while blue zones are negative. After taking a triple integral of the polynomial equations to form a square-shaped mesh, a sphere was generated and the resulting mesh wrapped around it to produce a simulation of said harmonic's influence around the Earth. Again generating these effects using cartesian coordinates, a more precise look at the forces within each harmonic can be obtained.
Aerial Photography Footprints
Aerial photography is a field of surveying that deals primarily with photogrammetry and remote sensing, in order to make measurements on the Earth's surface utilizing small aircraft and high-performance sensors such as camera and LIDAR.
A "footprint" is used to refer to the area of ground underneath an aircraft that is in frame at the time a photo is taken.
Camera mounting equipment will typically be used to accomodate for the movement of an aircraft, acting as a gymbal to ensure that photo footprints are kept pointing straight down. Under certain circumstances however, a mount may be unavailable or malfunctioning, meaning that these parameters must be accounted for in post-processing.
The smallest deviations of an aircraft in flight have the potential to introduce errors in the range of tens of meters, rendering error mitigation especially critical when determining the comprehensiveness of data coverage.
HOW IT WORKS
Aircraft sensor systems consist of a camera, a GNSS (multi-satellite GPS) sensor, an IMU (inertial measurement unit), and an internal clock. Each time a photo is taken, the exact time, location, and orientation of the sensor are recorded.
When an unstabilized mount is being used, the measurements from the IMU (roll, pitch, yaw) result in a distortion of the photo footprint. Not only is the footprint no longer rectangular, but it is no longer centered directly below the aircraft.
An equation to find this difference in footprint location and shape was derived mathematically; a visual basic executable program was made which reads in provided spreadsheets containing the IMU and GNSS data, and outputs georeferenced vector representations of each photo footprint.
PROCESS FLOWCHART
OUTPUTS, SHOWING POTENTIAL COVERAGE GAPS
