Reparameterization of B-spline surface and its application in ship hull modeling

Abstract

NURBS are widely used in the design of free curves and surfaces and have been the industrial standard for product design in CAD/CAM. Ship hull surfaces are complex doubly-curved surfaces and usually decomposed into patches based on feature curves. Due to the topologically rectangular limitations of tensor-product NURBS surfaces and the inevitable problem of surface merging caused by decomposition, the reconstruction of ship hull still remains a complicated problem. The theoretical research of merging NURBS surfaces is relatively comprehensive, but the difficulty lies in how to merge surfaces defined in different knot vectors at the common boundary curve since control meshes form T-junctions. This paper proposes a methodology of reparameterizing B-spline surfaces, using a fast progressive-iterative approximation (FPIA) method to refit section curves or isoparametric curves with constraints, thus making the topological structure of control meshes regular, uniform and orthogonal. Subsequently, a KCS container ship with bulbous bow and stern is utilized as an illustration for reconstructing with B-splines. The lighting effects and lines plan derived from the hull surface demonstrate that this approach can achieve fair, smooth and watertight surfaces. The approach exhibits strong robustness, versatility and generalization ability, and provides theoretical innovation and practical design methods for representing and reconstructing complex ship hull.