New techniques for subdivision modelling

Abstract

In this dissertation, several tools and techniques for modelling with subdivision surfaces are presented. Based on the huge amount of theoretical knowledge about subdivision surfaces, we present techniques to facilitate practical 3D modelling which make subdivision surfaces even more useful. Subdivision surfaces have reclaimed attention several years ago after their application in full-featured 3D animation movies, such as Toy Story. Since then and due to their attractive properties an ever increasing amount of research papers emerged, both in theoretical as well as in practical fields. The main contributions of this work are: • a subdivision scheme, which locally minimizes curvature variation, to obtain surfaces which are locally as spherelike as possible; this surface scheme is based on a tensor product of circular splines; • a combined quadrilateral-hexagonal surface scheme which generates optimal surfaces for initial meshes which contain both quadrilateral as well as triangular regions; • adding support for borders, sharp edges, and adaptivity to a hexagonal subdivision scheme, to make this scheme more suitable for modelling in practice; • a construction algorithm for meshes optimized for Stam and Loop’s Quad/Triangle scheme; to our knowledge it is the first such algorithm in literature; • a 3D sketching system with 2D input which uses a mass-spring system to preserve surface quantities.