Publications

Intersection of conic sections using geometric algebra

authors	Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick.
title	Intersection of conic sections using geometric algebra.
conference	CGI ENGAGE 2023, Aug 2023, Shanghai, China. pp.175-187
DOI	https://dx.doi.org/10.1007/978-3-031-50078-7_14
HAL ID	⟨hal-04210085⟩

Comments

One of the goals of my thesis was to find a nice method to extract points from conics intersections objects, in a 2D version of QCGA that we called QC2GA. It is when working on that specific problem that I realized that considering these objects as pencils of conics helped to understand and manipulate them. This paper received the best presentation award of ENGAGE, and a extension will be published in the journal AACA very soon.

Pencils of CGA for Voronoi and Power Diagrams

authors	Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick.
title	Pencils of CGA for Voronoi and Power Diagrams.
conference	CGI ENGAGE 2024, Jul 2024, Geneva, Switzerland.
DOI	incomming
HAL ID	⟨hal-04636752⟩

Comments

We realized that pencils of circles are very convenient to compute the interface of two Voronoi Diagram cells. This also generalizes to any Power diagram with or without multiplicative weight.* Pencils and set operators in 3D CGA The paper have been accepted and presented at the conference, but we are waiting for it to be published.

Pencils and set operators in 3D CGA

authors	Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick.
title	PENCILS AND SET OPERATORS IN 3D CGA.
conference	AGACSE 2024, Aug 2024, Amsterdam, Netherlands.
DOI	incomming
HAL ID	⟨hal-04569529⟩

We applied the pencils frameworks to circles of 3D CGA, who are \(2\)-pencils of spheres. All these results probably generalize to pencils of higher order, but this has not been tested yet.

The paper have been accepted and presented at the conference, but we are waiting for it to be published.