Logan Brown
Visualizing Complex, Time Dependent, Fourier Transform Functions In Three-Dimensions
In this project, I created a new application for teaching the Complex Fourier Series. After researching the Fourier transform and Fourier series, an initial prototype of this project was created using the Javascript programming language, that could draw a mathematically defined path using Fourier Series. Scalable Vector Graphics (“SVG”) file support was implemented.
The prototype was tested by drawing my robotics team’s logo, as a closed path. This initial prototype allowed for exploration of how the Fourier Transform works, and it inspired the creation of a new prototype in a three dimensional space.
After the initial prototype, I wrote a custom 3D renderer in Javascript to support expanding the time axis into the z-direction. The ability to display custom paths was added to my 3D rendering system.
Finally, the ability to animate, or visualize complex summed helices was added showing the helices being untwisted to form a line of a shifted helix. This demonstration is more complete, allowing viewers to intuitively understanding how the Fourier transform works because it shows the entirety of the Fourier transform operation at the same time. As nothing is hidden, the learner is not left to assume information, making concepts easier to comprehend.