Dmitry Sokolov
Université de Lorraine and Inria
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Talk title
Variational Approaches to Locally Injective Deformations and Distortion Control?
Abstract
Constructing mappings that are both locally injective and low-distortion is a fundamental problem in geometry processing, mesh generation, and numerical simulation. This talk presents a variational perspective that spans the spectrum from eliminating fold-overs to optimizing distortion. We will start with mesh untangling and then turn to distortion control, discussing bounded-distortion formulations, quasi-isometric stiffening as a way of approaching the smallest achievable distortion, and how these ideas can be extended from piecewise-linear to curved, high-order meshes.
We will then explore a different class of representations in which the optimization variables are not mesh vertices, but coefficients of a Laplace–Beltrami operator. This raises the question of how local injectivity and distortion can be controlled when the degrees of freedom describe an underlying operator rather than the deformation directly.
Together, these examples illustrate how variational formulations can provide a unified framework for enforcing geometric validity and controlling distortion across different representations of a mapping.
Biography
Dmitry Sokolov is a Professor of Computer Science at the University of Lorraine. His research focuses on computer graphics, geometric modeling, and geometry processing, with particular emphasis on geometric data structures, mesh generation and processing, parametrization, and 3D modeling. He received his M.S. degree from Saint Petersburg State University in 2003 and his Ph.D. in Computer Graphics from the University of Limoges in 2006. He joined the University of Lorraine in 2008 and obtained his Habilitation à diriger des recherches in 2016. Since 2026, he is on secondment from the University of Lorraine to Inria, where he leads TEXEL, a joint Inria–CEA research team.