Week 0 Blog - Introduction

Hello everyone!

I’m Samuel Yang, and welcome to my first senior project blog! I’ll be updating this blog weekly with progress on my Senior Project, as I tackle the challenge of developing a tool for teaching 4D Visualization.

Higher-dimensional space is one of the topics that most fascinates me in my study of math, especially because of its relevance to the Physics of spacetime. But despite finding many online resources to help me learn just the most basic of 4D behaviors, I often found myself facing mind-twistingly complex and indistinct animations. The visual resources available make learning 4D much harder than it needs to be, often serving only as supplements to textbook-level explanations, and often requiring readers to put in great effort and precision to build mental models that may not be accurate.

But why is this even important? In addition to being a stepping stone for learning the physics of spacetime, 4D visualization also offers a way to understand variables in 3D space, things like temperature or pressure, potentially opening the door for applying mathematical and geometrical identities for efficient calculations. That’s why I’ll be focusing my project on making 4D more approachable to students by making stand-alone animations and interactive software for improved learning and accuracy.

To start my project off, I’ll jump right in by bringing my unique approach to 4D visualization, color, and transparency variation based on the fourth-dimension coordinate and using it to recreate existing wireframe animations. Through the next five weeks, I’ll create animations for other existing models and expand my own method to use full cross-sectional slices in addition to wireframes. By the end of those five weeks, I’ll have a set of animations and a quiz to test the effectiveness of each visualization model in teaching 4D.

After sending that quiz to gather results, I’ll spend the remaining 5 weeks turning my non-interactive animations into an interactive space for users to explore 4D shapes and operations, and if I have time, I’ll add graphical inputs and possibly contact physics.

With this plan set, I look forward to seeing you all next week, where I’ll hopefully have some animations to show. For now, here’s a graph for any curious minds among you to explore, featuring a wireframe and cross-section: https://www.desmos.com/3d/bnp8l5lbic.