In this special issue of Computer Aided Geometric Design, we are pleased to present the proceedings of the fourteenth International Conference on Geometric Modeling and Processing (GMP), scheduled for 2020. Even if the global Covid-19 pandemic prevented us from holding in-person academic conferences as normal, we hosted a lively GMP 2020 online event on September 23, 2020. The program included short talks summarizing several papers accepted to this special issue, together with live discussions.
The GMP 2020 call for papers attracted a total of 74 full paper submissions. After a two-cycle double-blind review process conducted by members of the GMP International Program Committee, 20 papers were accepted for this special issue, and 9 fast-track papers were referred to Computer Aided Geometric Design (CAGD), pending major revision. The work presented in this special issue reflects the breadth of research related to the theory and practice of processing geometric data. As with past offerings at GMP, many papers here report on state-of-the-art algorithms and models for classical problems at the intersection of computation and geometry, from quad-dominant meshing to spline fitting to atlas generation and parameterization. Other works in this issue apply geometric problem-solving to applications as diverse as bas-relief portrait modeling and 3D tiling, presented alongside papers with theoretical developments needed to understand algebraic curves and surfaces.
As with many venues in applied science and engineering, several works presented this year at GMP are driven by advances in machine learning. This year's GMP papers include learning techniques for ill-posed problems in geometry, including 3D model generation from a single image, point cloud recognition, and even predicting medial axis transforms. Conversely, geometric modeling and processing also can bring new perspectives to abstract learning problems, as reflected in a paper in this issue on abstract semi-supervised learning.
As trends and methodologies in geometry continue to evolve, GMP continues to provide a premier venue for sharing work that advances cutting-edge, creative, and rigorous techniques for understanding shape. Special thanks go to Rida T. Farouki and Konrad Polthier, the Editors-in-Chief of Computer Aided Geometric Design, and to the entire Elsevier support team for the production of this special issue.