| This thesis consists of two parts. In Part I, we present the construction of multivariate Hermite subdivision schemes. An extensive use of the theory multiresolution analysis and, more specifically, the so-called strong convergence theory of two-scale refinement equation are used to construct and analyze multivariate Hermite subdivision schemes.; In Part II, we show how to apply Hermite subdivision schemes to construct free-form subdivision surfaces. Since the concept of what differential geometers call jets is essential in bringing Hermite subdivision schemes to the free-form surface setting; we term the resulted subdivision surfaces jet subdivision surfaces. We address the design of curvature continuous extraordinary vertex rules. |
