Carles Checa (ESR1)

2014-18: Bachelor in Mathematics by Universitat Politècnica de Catalunya
2018 – 2015: Joint Master’s degree in Mathematics given by the ALGANT consistorium with 1st year Universittà degli Studi di Padova and 2nd year Leiden University.
Master’s thesis in UNIPD repository:  Torsor dual pairs

Research activities: Algebraic systems, polyhedral geometry, tropical geometry, toric geometry, matrix representations, point clouds.

Research Project: Optimised predicate toolbox for geometric design and processing.
Advisors: Ioannis Emiris, Elias Tsigaridas
Institution: ATHENA Research and Innovation Center, Greece

Efficient geometric processing for Design and Manufacturing relies on a number of fundamental primitives or predicates that must be executed extremely fast and very accurately. Such predicates are critical for several algorithms developed within GRAPES, regardless of the underlying representation. We develop components of a toolbox for ray-shooting, surface-surface intersection, computing distances and tangents, and detecting self-intersection. Our methods handle objects given by powerful and novel representations: point clouds, simplicial/curved meshes, and matrix representation, using advanced algebraic techniques like syzygies, fitting and interpolation. We target problems from our industrial partners e.g. swept volume computation, computation with offsets, and self-intersection.

Expected Results: We exploit various algebraic formulations to optimise our approach, with respect to the degree of involved polynomials and the complexity of the geometric object. We develop a prototype implementation of the toolbox to use for validation and experimentation, leading up to a high-performance implementation, based on the generic programming paradigm that exploits multi-core architectures.

The project will take place at ATHENA RC at the ErGA Lab. The PhD will be awarded by the Dept. of Informatics and Telecommunications of the National Kapodistrian University of Athens.

Secondments are planned at INRIA (Sophia-Antipolis, France) by September 2021 and at industrial partner RISC-SW (Linz, Austria) by August 2022.


  • Under preparation