Andrea Raffo (ESR9)

2016-cur: Doctorate Degree in Mathematics (SINTEF and University of Oslo, Norway).
2014-2016: Master’s degree in Mathematics (University of Genova, Italy).
2016: Erasmus + programme (University of Bergen, Norway).
2011-2014: Bachelor’s degree in Mathematics (University of Genova, Italy).

Research activities:
2016-cur: subreviewer for CAGD
2016: Report at National Research Council (Italy) in computation of hybrid color-geometry descriptors for 3D model retrieval (only italian version available)

2015: Tutorials in Linear Algebra and Geometry for students in chemical and electrical engineering (University of Genova, Italy)

Project: Locally refined approximate implicitisation for design and manufacturing

Supervisor: Tor Dokken

Institution: Dept of Applied Mathematics, SINTEF, Oslo, Norway

Approximate implicitisation of curves and surfaces has until now focused on approximation by a single polynomial. However, when addressing composite shapes composed of multiple curves or surfaces, implicitisation by a single polynomial is inadequate, because it inevitably requires a high polynomial degree. To avoid this, one resorts to a piecewise algebraic representation. The simplest such representation, tensor product B-splines, defines piecewise polynomials over a regular grid. The main challenge for this representation comes from the required regularity of the grid: any refinements to increase the level of local detail will span the whole width of the grid. In contrast, the refinements of locally refined LR-splines are truly local, thus facilitating the approximation of local detail and the introduction of additional degrees of freedom only where needed. LR piecewise algebraic surfaces provide a watertight representation, and offer an alternative to the boundary representations of traditional CAD systems. The representation is also highly suitable for layered manufacturing, since plane sections can be extracted as algebraic curves. The project will, among others: study of the approximation properties of locally refined algebraic representations, address the question of how to implement an inside/outside notion across a complex volume, and look at the challenges of representing boundary representation CAD models in this new format.

The project will take place at the Dept of Applied Mathematics, SINTEF. The PhD will be awarded by the University of Oslo.

Secondments are planned at ATHENA (Athens, Greece) (3 Months: Investigate the application of sparse elimination theory to implicitisation of LR-Splines) and at industrial partner RISC-Software (Linz, Austria).