Free-form surface representation and approximation using T-splines

Abstract

The problem of describing the surface information of a complex shaped object with a computer is often encountered in the fields of computer aided design and computer graphics. The surface of such an object could have arbitrary shape and is usually called the free-form surface. T-splines are a recently developed generalization of non-uniform rational B-splines (NURBS) technology enabling local refinement, which can overcome many drawbacks of NURBS and offer a more flexible representation for free-form surfaces. T-splines have a potential of becoming the next industry standard for free-form surfaces in high end animation and computer aided design industry. It is apparent that to permit this potential to be fully realized, there must be developed solid mathematical theory and a comprehensive set of supporting algorithms. The research of this thesis therefore aims to investigate some fundamental algorithms of T-splines and to explore their use in surface approximation.