Interactive modelling of fair ship hulls with B-spline surfaces avoiding gaps and discontinuities

ABSTRACT

Ship hull surfaces are commonly represented as parametric B-spline or NURBS¹ surfaces. The shape of a surface is controlled by a regular mesh of vertices with constant numbers of vertices in each parametric direction. This restriction complicates the modelling of complex features like bulbous bows, stern bulbs, transoms. Multiple surface patches may be used to overcome the limitations of a regular control mesh, but it is challenging to keep the patches properly aligned at the seams. This paper presents a systematic methodology to design fully featured ship hulls without any gaps, overlaps or tangent and curvature discontinuities. With proper layout of the control vertex mesh and exploitation of the geometrical properties inherent to the B-spline/NURBS definition, the resulting three-dimensional hull models are readily transferred to analysis and manufacturing systems.

KEYWORDS:

• Computer aided design
• ship design
• hull modelling
• B-splines

Acknowledgments

The author would like to thank the reviewers for their thoughtful comments and suggestions to improve the paper. A special thank you goes to Professor Horst Nowacki for his life-long dedication to education and the advancement of computer aided ship design.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 NURBS stands for Non-Uniform Rational B-Spline

2 Underlining is used to mark vectors, e.g. ${\underset{\_}{V}}_i=(x_i,y_i,z_i{)}^T$. The superscript ${}^T$ indicates a transposed vector.

3 Normally three colinear vertices at the end are sufficient, but here vertices ${\underset{\_}{V}}_0$ and ${\underset{\_}{V}}_1$ will be identical