**Education:**

2015–2016,Master 2: Algebra and geometry, University Sophia Antipolis, Nice,

Included courses:

Trimester 1: algebraic geometry, algebraic topology, stochastic calculus.

Trimester 2: algebraic curves, effective methods in real algebraic geometry.

2014–2015,Master 1 Geometry, University of sciences and technology Houary Boumedienne, Algiers.

2013–2014 License 3: algebra and cryptography, University of sciences and technology Houary Boumedienne,Algiers

2012–2013,License 2: algebra and cryptography, University of sciences and technology Houary Boumedienne,Algiers

2011–2012,License 1: mathematics and computer sciences,University Saad Dahleb of Blida,Blida

**Research activities: **

Master thesis: Free projective plan curves. Supervisor: Alexandru Dimca

#### Project: New geometric models for the design and computation of complex shapes

**Supervisor:** Bernard Mourrain

**Institution:** Inria Sophia Antipolis, France

The representation of complex shapes is a major bottleneck in geometric modelling. Classical representations are based on bspline surfaces, which are trimmed and assembled to describe shapes. But these models have several drawbacks: weak connection between topology and geometry, inaccuracies along trimmed curves, obstacles in their local refinement. They induce a high computational cost in many geometric operations and in the use and transformation of these models.The objective of the Ph.D. project is to investigate new geometric representations, based on new types of spline functions, which extend the standard bspline representation used in CAD. We will study the space of piecewise polynomial functions of bounded degree on domains with arbitrary topology. We will analyze their dimension and determine bases with good geometric properties. These functional spaces will be used to construct families of models with a prescribed topology, which automatically satisfy regularity constraints along edges or across surfaces. We will also investigate local refinement properties for adaptive methods in geometric representation problems.

We aim to demonstrate the impact of the approach in specific modelling problems. Several applications are foreseen: fitting and reconstruction of structured shapes from point clouds, description of computational domains for isogeometric analysis and numerical simulations, deformation of models for shape optimization, shape design from sketchs and curve networks. Some of these applications such as modelling problems for ship hull, bulb, propellers and for architecture will be investigated in collaboration with industrial partners of the network.

The project will take place at Inria Sophia Antipolis, in the team GALAAD. The PhD will be awarded by the University of Nice.

**Secondments** are planned at the industrial partners Evolute (Vienna, Austria) and HRS (Athens, Greece).

#### Publications

- Ahmed Blidia, Bernard Mourrain and Nelly Villamizar. G1-smooth splines on quad meshes with 4-split macro-patch elements, Computer Aided Geometric Design, 52-53, 106 – 125, 2017, (Preprint)