{"id":119,"date":"2023-07-15T12:05:52","date_gmt":"2023-07-15T12:05:52","guid":{"rendered":"https:\/\/summergeometry.org\/sgi2023\/?p=119"},"modified":"2023-07-15T23:02:53","modified_gmt":"2023-07-15T23:02:53","slug":"last-day-of-sgi-2023-tutorial-week","status":"publish","type":"post","link":"https:\/\/summergeometry.org\/sgi2023\/last-day-of-sgi-2023-tutorial-week\/","title":{"rendered":"Last Day of SGI 2023 Tutorial Week"},"content":{"rendered":"\n

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<\/a> on\u00a0Robustness in Geometry Processing<\/strong>. We also had a guest lecture by Teseo Schneider<\/a> and, finally, our release of the projects for the next week.\u00a0<\/em>Having this experience while in my home city of\u00a0Recife<\/a>, Brazil is incredible.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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:<\/p>\n\n\n\n