Application of subdivision surfaces in ship hull form modeling

Abstract

The restriction of tensor-product B-splines to regular control meshes and thus four-sided surfaces is the reason that hull form modeling is still a challenge. This limitation is addressed by subdivision surfaces as they originate from the idea to define B-spline surfaces on irregular control meshes. Often subdivision is considered as a method to refine polygon meshes, but the linear nature of polygon meshes is generally not qualified for hull form representation. Therefore an introduction to the theory of generalized B-splines is given which employs the notion of subdivision to define smooth B-spline surfaces on irregular control meshes.This article covers the application of generalized B-splines for the representation of hull forms. It is possible to represent hull forms with a single B-spline surface. The main advantage is, however, the ability to use the control mesh for modeling. It is shown that the structure of a control mesh and the principles to define a control mesh are essentially the same as for curve networks which are mostly used to define hull surfaces. In contrast to the common belief in the industry, it is analyzed that the approximation-based definition of a hull surface in terms of a control mesh simplifies modeling and improves the robustness compared to interpolation-based methods such as the commonly found interpolation of curve networks.