Linear Algebra in Curves and Surfaces Modeling

Geometric modeling is the branch of applied mathematics devoted to methods and algorithms for mathematical description of shapes. Two-dimensional models are of crucial interest in design, technical drawing and computer typography, while three-dimensional models are central to computer-aided-geometric-design (CAGD) and computer-aided-manufacturing (CAM), and widely used in many applied technical fields such as civil and mechanical engineering, architecture, geology, medical image processing, scientific visualization, entertainment. Moreover, since CAGD methods are main ingredients in Isogeometric analysis – an emergent new paradigm for numerical treatment of PDEs which can be seen as a superset of FEMs – it turns out that geometric modeling acquires some relevance also in this area. The main goal of geometric modeling is to create and improve methods, and algorithms for curve and surface representations which is mainly achieved by means of suitable class of functions like splines, or refinable functions to which linear subdivision schemes are associated. For both, the manipulation and the analysis of such a class of functions, several tools of linear algebra play a crucial role like those suited for structured matrices, totally positive matrices, polynomial equations or computation of joint spectral radius. Therefore, aim of this mini-symposium is to gather scientists that, working on different aspects of curves ad surface modeling, face classical and new linear algebra problems and use linear algebra tools to move a step forward in their respective fields.