Here's a journal of my experiences at the DREU program this summer
I have just arrived and I am getting settled in! Had a crash course on differential geometry in the morning, and I'm trying to figure out some basic functions this afternoon. My plan is to adventure to a coffee shop for a second home.
Everyone in Oregon is so nice! My roommates and colleagues have been super cool and have been showing me around town. I have been slowing refreshing my MATLAB skills and I hope to be able to contribute something valuable! I have the first meetinging with Dr. Grimm this week and I hope to learn more in depth about the projects I will be working on.
Happy 4th of July!! Corvallis is fairly small but we kept plenty busy :) I went to the farmer's market on Wednesday and Saturday; there are SO many berries!
This week I was able to get all of the curve fitting algorithms working (at least I think!). More importantly, I am becoming more familiar with MATLAB and coming up with effective strategies to combat errors. Next week I will be trudging through the code that will animate the expansion and contraction of the chick hearts. I will post it up on the Research page as soon as I get it working!
I was able to get several of the animations working!!
I had to rerun several of the data sets because we weren't seeing as much movement as we had hoped in the contours. I was able to get a loop going for the sets to run all night to avoid wasting the day time. There are 8 chicks and 3 contours per chick, and for each contour there are 196 time steps. After all that data has been read, there were 9 different fits to apply to the data! I'm so glad I didn't have to do anything by hand :)
The time is flying by so quickly!! I can hardly believe I'm half way done. I feel established and yet as though I have just arrived. I worked on making an animation of the contours and curvature separated by chicken and by contour. Additionally, I plot the curvature approximation data on top of the original. It provides a much cleaner viewing space. This will also help my foundational understanding of how the data moves and hopefully make 3D curve animations easier to conceive. I also experimented with plotting the way the weights of the basis functions change over time. The only multi-basis curve analysis I was familiar with before this summer was the Fourier Series (sinosodial fit). It has been interesting to see how accurately the different types of fits reconstruct the data. Since the chicken heart is essentially a tube at this point, a relatively simple curvature analysis works best. The more complex types of analysis do not make as precise reconstructions, and have been prone to create endpoint matching issues. Dr. Grimm added a section of code to fix the end points, but the piecewise linear and quadratic fits do the best job. This is somewhat surprising, especially when the original curvature data is compare to the fitting data. Some of the more complex fits are almost exactly the same as the original data, but the simpler fits still return the best approximations.
This week I worked to write a code that will take in 3D data points. If the basis and coefficients are known, I want to be able to construct the curvature. The basis and coefficients were derived from the original data, so I do not directly read in any points. I want to be able to use the information from the basis to find the curvature at specific times. Since everything is in 3D, I needed to make modifications to my existing 2D curvature code. The contour points are run through ode45 and the solution parameters are used to evaluate the curvature at specified time steps. It took me awhile and lots of questions to get it running but it works now. Woo!
I continued to clean up my code for reading 3D point bases with coefficients. Dr. Grimm and Dr. Ross Hatton are still not sure how the 3D points will be generated, so I have to make the code very flexible. I began working on an alternative way to map the curvature without using the basis. The points will be read in directly and the in-plane and out-of-plane angles will be used to approximate the curvature.
We have decided to use a torsion free model for the 3D code. I am still adjusting to this type of model. I had never really though about curvature in this way before. I have come to realize that research involves a lot of trial and error and takes a lot of patience.
This week I began to work on the rotation code. I want the fitted points to be centered around the origin during the reconstruction. This way, I will be able to compare the original data to the fitted data visually. I am having a lot of scaling issues and my out of plane curvature isn't mapping back correctly. Good thing I still have another week!
For my final journal entry, check out my Final Paper on the Research page! :) It's been a fabulous summer. I hope I can return to Oregon again soon!