Pascal Romon – författare

L'ouvrage s'adresse aux etudiants et etudiantes de master, eleves-ingenieurs, ingenieurs et chercheurs ou chercheuses souhaitant comprendre les developpements recents en geometrie differentielle discrete.Cette discipline en plein essor fait la synthese entre l'approche continue classique des courbes et surfaces et celle, discontinue, des polyedres et triangulations, qui est utilisee quotidiennement en informatique ou en architecture. Ce croisement est a la source de problemes mathematiques non triviaux et de developpements theoriques profonds.En partant des fondements de la geometrie (seules des connaissances basiques sur la geometrie du plan et de l'espace sont requises), le livre developpe les outils et notions necessaires a la comprehension des concepts les plus recents de courbure discrete, de flot, de calcul differentiel discret et d'offset. Ces idees sont illustrees et motivees par des applications comme le lissage, le remaillage ou la construction architecturale de surfaces libres.

This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.