Cross Sectional Design

Lines Plans: Three Dimensional Design in Two Dimensions

Before computer aided design hull design had long been executed on paper or film using ships curves, spline battens and ducks. Later, during production design, the lines would be laid out in full scale on the loft floor providing the opportunity to fair the shape of the hull to a higher degree of refinement. In all cases, it was down to the designer or loftsman to ensure the shape truly represented a 3D representation by checking the correspondence of measurements in the different views, the profile buttocks, plan waterlines and body plan sections. In addition, because the curves representing the hull form are unique slices or cross-sections through surface there is always a need for the loftsman to mentally visualise the full shape. This was the skill and art of this vocation.

The introduction of computers and electronically controlled systems created the possibility of representing shapes using numbers and with this the opportunity to use electronically controlled tooling to cut and manufacture parts to a higher degree of accuracy and repeatability. Follow the process back from the computer manufactured parts to their definition it is logical that for a ship it is beneficial if the shape of the hull form can be represented electronically. During the 1960s, parametric representation of geometry with techniques such as B-Splines [] and Coons Patches [] were applied to capture form and shape electronically and then used to control machines to produce physical objects. Pierre Bezier used the curves which bear his name to design the shape of Renault Cars []. Ship’s hull forms were also captured using Bezier surfaces [fog].

The rise of NURBS

While the capture of surface shape allowed great improvements in accuracy and repeatability not everyone could access this technology because the cost and size of the computer systems that could support this functionality could only be supported by large organisations. In the 1980s, computer technology began shrunk in size, increased in power and become affordable. This allowed more people access to this technology and the opportunity for innovation. Software development tools improved and software experiments with shape representation matured into effective design and manufacturing applications, CAD-CAM. Techniques such as B-Splines and NURBS became natural solutions to the design of shape and representation of form because the parametric values used to generate shape are spatial coordinates which may be drawn with the surface. Using a pointer or mouse the coordinates can be manipulated and the resulting shape interactively updated. Effectively, computer software could replace the physically splines and weight that designers were using on their desk and provide the means to drive detailed shape in 3D. The designer no longer needs to ensure correspondence between 2D views, its 3D object and with the surface being a continuous geometric representation it’s not necessary to mentally visualise the shape. Furthermore, the ability to capture surface shape electronically using a relatively small amount of parametric information provides a very efficient method of exchanging shape between different software systems.

However, NURBS control polygons aren’t always a perfect design interface. As surface shape become more complex, with different magnitudes of curvature and different sized shape features, the number of control points significantly increases. The small movements of control points can significantly affect fairness and managing the whole definition becomes a challenge. Ship hull forms contain a great variety of shapes. Planar regions and linear extrusions are found around the middle and sharp curved features at the ends. Trying to represent this using a single rectangular NURBS surface is possible but it’s a very time consuming process to design and capture the shape of a ship with a single patch. Efficiencies can be achieved by using a number of patches to represent the shape and adjusting the size of the patch to the scale of the features. But it remains a challenge to manage the surface continuity between patches if the surfaces are positioned by using the control polygon points. They need to be precisely positioned which is hard to achieve with a mouse and the process becomes slow and tedious for the user. It is, however, much easier to design the surface by using curves to represent the boundaries of the surface, the features and cross-sections through the shape – Cross Sectional Design. In effect, the definition produced is similar to a lines plan but in 3D. Computer software generates a continuous surface based on the network of curves defined by the designer. The surface itself may still be represented using NURBS but the designer is no longer interacting with the control polygon directly and the software takes care of precisely positioning points that these multiple patch surface representations required.

Design Tool Opportunities

Interacting indirectly with the hull surface representation provides an opportunity for the software assist the designer create shape. Design curves may be dynamically snapped together to create the curve network. Attributes may be assigned to points and curves to control shape, introducing features such as knuckles, tangents, blends and straight curve segments. These features capture Design Intent in a way that is a much more obvious and precise way of controlling shape than the positioning of control points, which may be accidentally repositioned.

Powerful Surface Design But Not Without Challenge

Although Cross Sectional Design provides a powerful way of designing complex surface shapes use of the technique is not without challenge. The surface representation is generated by aligning the edge of surface patches with curves segments between the network junctions or vertices and constraining the tangents at the edge of these surface patches to correspond to ribbon-like tangents interpolated along each curve with direction controlled by the crossing curves at each junction. This arrangement creates two challenges in the software.

  1. The quality of the tangent is controlled by the angle between curves at vertices. Quality is best when curves cross perpendicularly but as the crossings at a vertex become parallel the tangent becomes undefined. In this situation it’s necessary for the software to avoid mathematical errors by estimating an appropriate tangent direction.
  2. Mathematical surfaces used in CAD software are rectangular four-sided patches but curve network often feature a number of faces that may not be four sided. If a face has less than four sides a degenerate patch may be used by reducing a side to a point. If a face has more than four sides its necessary to decompose the shape into a number of faces that can be represented using four sided patches. Again, this is a case where software has to estimate shape when decomposing a multi-sided face.

When designing a curve network it is of course best to avoid these cases that could be problematic to interpret but it’s fairly impossible to design a realistic hull surface without encountering these situation. Minimising the impact comes with skill and experience. Cross Sectional Design is a very effective rapid design approach but if the designer is unsure of the correct shape or how features blend together it is easy to get stuck. Often this happens when trying to introduce a shape that is not completely defined or incorrect for that part of the surface, i.e, an impossible shape. The worst thing to do is to keep on adding more points and more definition. Take the opportunity to have a time out and review whether shape being defined is perceived correctly.

X-Topology Lofting – Another Opinion

One of the challenges with using Cross-Sectional Design to generate a surface is that it’s necessary to maintain valid topological connections in the curve network in addition to designing the surface. Sometimes you just want to throw some curves into a design to see what shape appears without worrying about being concerned about topology. X-Topology Lofting generates an implied surface by intersecting several sequences of cubic spline curves through the curve network. The shape produced is not affected by the angle of curves at network vertices or the number of edges in a network face. It also generates hull shape around 10 times faster than the process required to generate a complete mathematical surface from the curve network. Another advantage is that the curve intersection and fitting technique highlights inconsistencies in the quality of the curve network far better than the surface representation because the blending of the patches has a tendency to diminish and minimise poor curvature. Therefore, the recommended approach is to use X-Topology Lofting to design hull shape and build up curve network introducing the X-Topology surface as the design becomes mature. Subsequently, the contours generated by both techniques can be compared directly and areas for improvement identified where the shape of the two methods diverges.


The X-Topology Surface and Lofting tools in PolyCAD when used in combination provide an accelerated process for designing or replicated a hull surface and implicitly identify areas of poor surface definition. This makes for a productive and rewarding hull design experience which may be enjoyed by the user.