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Geometry Processing from a Mathematics Education Major’s Eyes- The First Three Weeks

Hi! I am Brittney Fahnestock, and I am a rising senior at the State University of New York at Oswego. This is one of the smaller, less STEM-based state schools in New York. That being said, I am a mathematics education and mathematics double major. Most of my curriculum has been pedagogy-based, teaching mathematics and pure mathematics topics like algebraic topology. 

So, as you might have read, that does not seem to have applied mathematics, coding, or geometry processing experience. If you are thinking that, you are right! I have minimal experience with Python, PyTorch, and Java. All of my experience is either based on statistical data modeling or drawing cute pictures in Java. So again, my experience has not been much help with what was about to take place!

The introduction week was amazing, but hard. It helped me catch up information-wise since I had minimal experience with geometry processing. However, the exercises were time-consuming and challenging. While I felt like I understood the math during the lectures, coding up that math was another challenge. The exercise helped to make all of the concepts that were lectured about more concrete. While I did not get them all working perfectly, the reward was in trying and thinking about how I could get them to work or how to improve my code. 

Now, onto what my experience was like during the research! In the first week, we worked with Python. I did a lot more of the coding than expected. I felt lost many times with what to do, but in our group, we were trying to get out of our comfort zones. Getting out of our comfort zones allows us to grow as researchers and as humans. As a way to make sure we were productive, we did partner coding. My partner knew a lot more about coding than I did. This was a great way to learn more about the topic with guidance! 

We worked with splines, which of course was new for me, but they were interesting. Splines not only taught me about coding and geometry but also the continuity of curves and surfaces. The continuity was my favorite part. We watched a video explaining how important it is for there to be strong levels of continuity for video games, especially when the surfaces are reflective. 

Week two was a complete change of pace. The language used was C++, but no one in the group had any experience with C++. Our mentor decided that we would guide him with the math and coding, but he would worry about the syntax specifics of C++. I guess this was another form of partner/group coding. While it exposed us to C++, our week was aimed at helping us understand the topics and allowing us to explore what we found interesting.

We worked with triangle marching and extracting iso-values with iso-segmentation and simplices. I had worked with simplicies in an algebraic topology context and found it super interesting to see the overlap in the two fields.

I have an interest in photography, so the whole week I saw strong connections to a passion of mine. This helped me to think of new questions and research ideas. While a week was not quite long enough to accomplish our goal, we plan on meeting after SGI to continue our work!

I can not wait for the last three weeks of SGI so I can continue to learn new ideas about geometry processing and research!