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difficult tasks. EzHULL solves this problem simply by using topological information stored in the non-
manifold data structure. Using topological information, EzHULL can determine the partial order of
intersection points on each surface patch, and then generate a new wireframe line by rearranging the
segments of the partially ordered intersection points into a globally ordered points list (Fig. 6).
(3) Wireframe shading: The X-edges are converted into polylines for visualization and shaded using
a technique which we call 'wireframe shading', which is a technique that shades the wireframe curves
with a luminance calculated using a normal vector at each vertex of the polylines. The normal vector
of a vertex is calculated by interpolating the outer normal vectors of section 4.1. If the wireframe
model shaded using this technique, the lines with normal vectors directed towards the observer are
bright, and the others are shaded. Therefore, the wireframe shading can give the pseudo 3D-effect and
help to improve the presentation of the wireframe fairing, even for a complex hull form (Fig. 7).

Figure 6: The buttock lines of a goose neck Figure 7: A twin skeg hull without wireframe
hull, which are generated using points ordering shading (left) and with wireframe shading
5 CONCLUSIONS

EzHULL system developed in this research, provides an association based cross fairing and generates
a surface from a wireframe model using X-topology and non-manifold data structure. The association
based cross fairing offers designers an effective wireframe fairing, by monitoring how adjacent lines
are affected when a particular line is changed. Direct conversion from a wireframe model to a surface
model enables 3-D surface hull form to be visualized even at the earliest design stages. The topological
information of the converted surface model helps to resolve the points ordering problem in the
wireframe model and the geometric information is used to shade the wireframe model with a cubic
effect. In addition to these features, EzHULL also provides convenient and intuitive wireframe editing
system for planar and spatial curves, hull form variations and various facilities for hull form design.
EzHULL' is now available as a commercial system, and it is our hope that the EzHULL system will
give new vision to hull form designers.
References

1. Soon-Hung Han and Soon-Sub Lee. (1994). A Reference Model for the Computer-Aided Design of
Hull Forms. Transaction of the Society of Naval Architects of Korea 31:4, 15-22. written in Korean
2. Sang-Hun Lee and Kun-Woo Lee. (1996). Compact Boundary Representation and Generalized Euler
Operators for Non-manifold Geometric Modeling. Transactions of the Society of CAD/CAM
Engineers 1 : 1, 1 - 19. written in Korean
3. Young-Bok Choi and Kyu-Yeul Lee. (1999). A Study on the Hull Form Design System on the Basis
of the Associative Geometry Objects. Transaction of the Society ofNaval Architects of Korea 36:4,
105-1 15. written in Korean
4. Gerald Farin. (1 999). NURBS from Projective Geometry to Practical Use 2nd Ed, AK Peters
5. Gerald Farin. (1997). Curves and Surfaces For CAGD 4th Ed, Academic Press

' Contact information: http://www. ezgraph.co.kr