Abstract:
We propose a novel approach, called Progressive Parameterizations, to compute foldover-free parameterizations with low isometric distortion on disk topology meshes. Instead of using the input mesh as a reference to define the objective function, we introduce a progressive reference that contains bounded distortion to the parameterized mesh and is as close as possible to the input mesh. After optimizing the bounded distortion energy between the progressive reference and the parameterized mesh, the parameterized mesh easily approaches the progressive reference, thereby also coming close to the input. By iteratively generating the progressive reference and optimizing the bounded distortion energy to update the parameterized mesh, our algorithm achieves high-quality parameterizations with strong practical reliability and high efficiency. We demonstrate that our algorithm succeeds using a massive test data set containing over 20712 complex disk topology meshes. Compared to the state-of-the-art methods, our method possesses higher computational efficiency and practical reliability.

Short Bio:
Ligang Liu is a professor at the School of Mathematical Sciences, University of Science and Technology of China. He received his B.Sc. (1996) and his Ph.D. (2001) from Zhejiang University, China. Between 2001 and 2004, he worked at Microsoft Research Asia. He paid an academic visit to Harvard University during 2009 and 2011. His research interests include digital geometric processing, computer graphics, and image processing. He serves as the associated editors for journals of IEEE Transactions on Visualization and Computer Graphics, IEEE Computer Graphics and Applications, Computer Graphics Forum, Computer Aided Geometric Design, and Computer&Graphics. He served as the conference co-chair of GMP 2017 and the program co-chairs of GMP 2018, CAD/Graphics 2017, CVM 2016, SGP 2015, and SPM 2014. His research works could be found at his research website: http://staff.ustc.edu.cn/~lgliu