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## Last Day of SGI 2023 Tutorial Week

After many exercises, lectures, presentations, and MATLABs abruptly closing, we reached the end of the first week of SGI 2023. It was a wild and incredible ride. And we reach the end with a course by Nicholas Sharp on Robustness in Geometry Processing. We also had a guest lecture by Teseo Schneider and, finally, our release of the projects for the next week. Having this experience while in my home city of Recife, Brazil is incredible.

In Sharp’s presentation, we learned that meshes extracted from real data are much less clean than ideal meshes. So, we must create techniques and methods to perform robust geometry processing. In the first part, we learned about floating point arithmetic. We learned that contrary to what we programmers want to think, floating point numbers are NOT real numbers and can introduce many errors during arithmetic. For example, we learned that there are better ideas than performing a strict equality comparison and that we should add a tolerance factor to account for errors.

We also got an introduction to different numerical solvers and how meshes with some properties can break numerical solvers. Although these properties can result from error, sometimes they are intentional. As an example of such properties that can break processing, meshes can have:

• Duplicate Vertices
• Faces of wrong orientation
• Can be nonmanifolds
• And many more

To get a feeling of how to perform different processing methods, we did some activities on how to do processing with “bad meshes” Those activities are available here. One such example was an activity on bad meshes. For example, we were given a “bad_armadillo”, a variation of the traditional armadillo mesh that, when loaded, looked odd:

To correct this issue, we used Meshlab. When we loaded it into Meshlab, it became clear that some normals were inverted:

So, after orienting the meshes to the right side, we “fixed the mesh”:

And now MATLAB can load it the proper way.

We also got a presentation by Professor Teseo Schneider of the University of Victoria on their work on collision detection. Their technique could simulate different structures such as chains, arches, dimensional card houses, and even a cube rotating in a turntable with varying friction parameters. To end the lecture, he showed a really satisfying simulation of a stack of bricks being hit by a wrecking ball (Figure taken from his paper, available here):

Finally, at the end of the day, we got the list of the projects we will work on next week. I was paired with many amazingly talented fellow students (one of them is also Brazilian like me!) to work on a project on Hybrid Neural and Grid Representations, mentored by Peter Chen. I can’t wait for what SGI 2023 has in store!

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## First Day of Summer Geometry Initiative 2023

The opening day of the MIT Summer Geometry Initiative 2023 was filled with engagement as the students dived into the world of geometry.

The program kicked off with Dr. Solomon welcoming the 2023 SGI Fellows and provided basic information on how the week will go.

It was followed by Dr. Oded Stein’s course introducing the basic techniques in geometry processing using the gptoolbox library. His talk started with a review of the basic concepts of geometry from the perspectives of different people who might use it. Dr. Stein also introduced the students to some advanced topics, such as how to store surfaces on a computer and how to define the boundary of a surface. The students were given various MATLAB exercises to experiment with the ideas he talked about.

In the afternoon, we had a guest lecture from Dr. Vladmir (Vova) Kim at Adobe, who spoke on the applications of geometry processing. He explained how geometry processing can be used to manipulate shapes in different ways, such as deformation, using neural progressive meshes and parameterization. The methods he introduced can be applied to computer graphics and computer vision. The lecture provided us with a glimpse into state-of-the-art in this cutting-edge field.

Overall, the first day of the MIT Summer Geometry Initiative 2023 was a resounding success. The students left with a solid foundation in geometry processing, ready to tackle more advanced topics in the days ahead.