We were intrigued that dumplings appear across the world and wanted our project to cover various different types, which is why we chose to model pierogi, gyoza, and xiaolongbao. Each of these dumplings had different basic shapes, so we were able to use an array of functions to model them, and each presented unique challenges. For example, the xiaolongbao was difficult to incorporate a sine wave with an increasing amplitude on a spherical radius rather than dependent on simply the x, y, or z axis. On the other hand, the gyoza’s base function had a very different slope than the pleats at its top, so we had to try many different types of functions, eventually finding two saddle functions to merge the pleated dumpling shape with the reverse side of the gyoza’s body to match the traditional gyoza’s shape.
Almost all of the functions are graphed with parameterized curves, and we used polar coordinates to simplify graphing since most of them are spherical. We graphed many different functions that we had learned about throughout the course, from simple planes, saddles and ellipsoids to asymmetric sine functions, logarithmic cones, and modified tangent functions.
