Constrained design of simple ship hulls with B B -spline surfaces
This paper presents a mathematical method to define a ship hull based on numerical constraints directly related to geometric features of the hull surface and on naval architecture parameters that uniquely define a hull form. These geometric parameters have physical, hydrodynamic or stability implications from the design point of view. B B -spline curves and surface representations were combined with a constrained approach to produce the final hull display. The presented method follows the traditional design principles of naval architecture, starting with a Sectional Area Curve (SAC) that controls buoyancy and a waterplane curve that ensures stability. A B B -spline outline of these two curves is adopted and a nonlinear problem is solved to obtain their constrained definition that agrees with the geometric design parameters. Two boundaries are also introduced into the constrained definition that control the limits of the hull, the centre and deck lines, which are complemented with tangent values at these edges to gain local control of the hull. A net of curves or hull stations is created that matches the previously defined constraints. These curves follow an analytic expression that ensures that a given area, waterline breadth and initial tangent angle are obtained. This is an important advantage of the method because a hull form library or template is not necessary, but limit the type of ship hulls that can be attained. The method continues with a constrained B B -spline fitting of points on the analytical curves that ensures the tangent angles and checks the distance from the points to the B B -spline. A final lofting surface of the previous B B -spline curves produces the hull surface.
b b -splines b b b b b constrained shape generation ship surface design