Publications

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 an extension has been published in the journal AACA.

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.

Geometric algebra is an elegant tool for dealing with geometric problems and takes a place of increasing importance in many domains. Among many algebras, GAC (Geometric Algebra for Conics) and QC2GA (Quadric Conformal Two-Dimensional Algebra) allow to represent conics and their intersections. This thesis is then about trying to extract the points of conic-conic intersection objects of QC2GA.This task is achieved successfully in this thesis, and is the precursor for the making of framework based on pencils of shapes for the conception and consideration of geometric algebra based on blades of points. The resulting framework is then applied first to 3D CGA (conformal geometric algebra) for developing some set operators for pencils of spheres and applying them for finding the smallest tangent sphere of two skew lines, and lastly to 2D CGA for constructing Voronoi and power diagram as well as their multiplicatively weighted version with pencils of circles