Nurbs modeling for design waterline based on the variation of sectional area curve

Hull form design from parent ships transforms the ship's parameters based on the variation of theoretical sectional area curve of the Lackenby method. The correction and modification of the theoretical sectional area curve is essentially the change of ship displacement, hull form coefficients, and the longitudinal center of buoyancy from the parent ships. In the preliminary design stage, the hull form design approach from parent ships minimizes the risks compared to the new design while still retaining hydrostatic and hydrodynamics' advantages. However, the Lackenby method of ship hull form variation uses a linear or quadratic function to shift the sectional area curves, regardless of the ship's hull form faring, especially the curvature's discontinuity the bow, stern, and midship. Therefore, the computer graphic algorithm based on the B-spline function is studied and applied; simultaneously, the mathematical model for the designed waterline is built in the form of a continuous curve instead of the B-spline segments. In this study, the mathematical model for the coastal container ship's design water line is constructed, ensuring continuity and fairing throughout the continuous B-spline curve. The geometry continuity evaluation results are expressed through the parameter curve's curvature and resistance component calculations' performance by computational analysis.