Boat hulls with smoothly curve stems - how to model

Round bottom boat hulls frequently have stems which curve smoothly into the keel. A NURBS surface with four sides is not a simple fit to such a shape.
Curved Stem Lines 1
I know of three methods to model such a hull side using a single NURBS surface on each side. Each has advantages and disadvantages. A Rhino .3dm file with an example of each method is attached. BowCurve11.3dm (350.3 KB) The surfaces are very close to each other in shape. Note that the orange curves are isolines but do not indicate the number of control points used for each surface.

Perhaps the most obvious method is to use a three sided surface (actually a four sided surface but on side has zero length). This allows direct control over the shape of the stem. The shape near the upper corner where the isocurves converge can be difficult to adjust and maintain fairness. The surface cannot be simply extended at the upper corner. This method can be a quick way to create a surface for hydrostatic calculations and similar.

A second method is to split the stem curve to create an additional side. This also allows direct control of the shape of the stem but care is needed to ensure the stem curve has the desired continuity across the split. This method eliminates the converging isolines in the upper corner. The tradeoff is near the stem curve split the u and v isocurves become almost parallel, and are parallel at the split. This make adjustment and fairing of the surface shape in this area difficult. The surface may have problems extending at the split in the stem. This method can work well for creating a surface from a set of lines which will not be modified.

B Singularity
The third method is to extend the surface past the stem and maintain the four sides. then trim the surface to the stem. This trimming can frequently be done with a plane on or parallel to the centerline of of the boat. This method does not provide direct control over the stem shape like the previous two methods. The stem shape is determined by the shape of the untrimmed surface. The resulting surface can be easier to adjust and fair than surfaces using the other two methods. Also while the trimmed surface usually can be extended without any problems and then trimmed as desired.

(This will also be posted in


Another method is to split the sheer to create four sides for the surface. This allows direct control of the shape of the stem. I do not have any experience with this method. File updated to include an example of this method: BowCurve21.3dm (399.0 KB)

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Hi David,

Good initiative with this thread!

In general I avoid the “split” approach because Rhino is having problems with NURBS corners where u- and v-directions are parallel or tangential. You’ll notice when you for example offset these surfaces:

I think Rhino should handle these cases better in the future because when you convert a SubD-Ngon ToNurbs then you’ll also get exactly such a corner.

Anyways I’ll avoid it because other NURBS applications downstream in the marine industry also fail to handle these cases.