# Three months at Inria Sophia-Antipolis

As an ITN Marie Skłodowska-Curie Action, ARCADES had planned two secondments for each of the Early Stage Researchers under its umbrella. The first of my two secondments was for three months―March to May 2018―at Inria Sophia-Antipolis, and specifically at the AROMATH team under the guidance of Bernard Mourrain.

AROMATH is involved with problems and questions that arise in shape representation, property analysis and model computation. From the team’s website:

AROMATH is a project in Computational Algebraic Geometry, investigating algebraic approaches to address these geometric problems. It aims at developing new methods for high quality and efficient modeling and processing in geometry, based on algebraic representations and tools.

Apart from Bernard Mourrain, I also worked closely with Ahmed Blidia, an ESR in ARCADES as well. Their recent work was on $G^1$-continuity of surface patches, that follow a quad-mesh configuration of arbitrary topology, effectively constructing basis functions that satisfy the $G^1$-continuity property along the edges and vertices. They achieve this by computing transition maps across shared edges that lead to the computation of the new $G^1$ basis [1]. My contribution was on implementing a numerical optimization approach to the same problem and methodology that adequately “increases” the $G^1$-continuity along shared edges of the patches. In practice, we define a least-squares problem with an objective function $F$ to be minimized based on the transition maps of their previous approach. We take advantage of the bilinear partial derivatives of the objective function $F$ by solving two separate sets of linear systems of equations and taking two separate steps towards the minimizer.

I also had the joy of presenting an overview of my PhD work so far and the target scope of my completed thesis during the PhD Seminars of Inria Sophia-Antipolis, after the kind invitation of Evgenia Kartsaki, co-organiser of the seminars. There was significant diversity in the backgrounds of the audience, which is expected for such a large institution as Inria, so the focus of the initial part of the talk was heavily focused on recent related advances in the field of architectural geometry, through examples of Evolute’s portfolio. This is always pleasant to me―giving a high-level introduction to my field―because it reminds me of what ignited my interest for this field in the first place.

Overall, it was an extremely pleasant and rewarding experience. Inria is a leading French research institution and Nice is a lovely city and an ideal starting point to explore the entire French Riviera. Popular destinations like Cannes, Antibes, Èze and Monaco are all less than a half-hour drive away. I direct any interested students that study in my previous department, the Department of Informatics & Telecommunications of the National & Kapodistrian University of Athens, to this link.

1. Ahmed Blidia, Bernard Mourrain, Nelly Villamizar. $G^1$-smooth splines on quad meshes with 4-split macro-patch elements. Computer Aided Geometric Design 52: 106-125 (2017). [link