## 5 Conclusions  
This paper presents a parametric design approach for monohull unstepped planing hulls. In the design process, longitudinal functions and shape coefficients are used for the design of the shapes of key areas. The curve and surface equations of the ship are  
Figure 24: A radiused chine hull form. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Unit** & **Deep-V** & **Radiused Chine** \\ \hline \(h_{t}\) & m & 0 & 0.16 \\ \(L_{0}\) & m & 9.96 & 6.64 \\ \(L_{c}\) & m & 20.16 & 13.44 \\ \(H_{c}\) & m & 1.56 & 1.02 \\ \(L\) & m & 21 & 14 \\ \(H_{f}\) & m & 2.76 & 1.84 \\ \(B_{t}\) & m & 2.2 & 1.3 \\ \(H_{t}\) & m & 2.3 & 1.42 \\ \(L_{sm}\) & m & 6.78 & 4.52 \\ \(B_{sm}\) & m & 2.5 & 1.7 \\ \(B_{cm}\) & m & 1.86 & 1.24 \\ \(B_{c0}\) & m & 1.78 & 1.19 \\ \(\alpha_{k}\) & \(\circ\) & 35 & 35 \\ \(\beta_{s}\) & \(\circ\) & 30 & 30 \\ \(\beta_{c}\) & \(\circ\) & 25 & 25 \\ \(A\) & m\({}^{2}\) & 31.32 & 13.92 \\ \(x_{Ac}\) & m & 8.784 & 5.856 \\ \(\lambda_{k1}\) & & \(-\)0.37 & \(-\)0.36 \\ \(\lambda_{k2}\) & & \(-\)0.06 & \(-\)0.05 \\ \(\lambda_{s1}\) & & 0.87 & 0.85 \\ \(\lambda_{s2}\) & & 0.13 & 0.13 \\ \(\lambda_{e}\) & & 0 & 0.1 \\ \(\lambda_{f}\) & & 0.07 & 0.06 \\ \(\theta a\) & \(\circ\) & 7 & 12.5 \\ \(\theta b\) & \(\circ\) & 17 & 17 \\ \(\theta c\) & \(\circ\) & 45 & 45 \\ \((m\),\(n)\) & & \((2,3.2)\) & \((2,3.2)\) \\ \(\gamma_{\mathrm{k}}(x)\), & \(\circ\) & 10 & \(8+3\)\((1-x/L)\) \\ \(\gamma_{c}(x)\), & \(\circ\) & 10 & \(8+3\)\((1-x/L)\) \\ \(k_{s}\) & & 0 & 0.12 \\ \(k_{m}\) & & 0 & \(-\)0.06 \\ \(W_{\mathrm{RM}}\) & m & 0.09 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the examples. appropriately evaluated and analyzed based on B-spline theory, resulting in a smoothly continuous surface for the hull. The key findings of the present investigation are summarized as follows:  
1. When conducting multi-parameter optimization of the hydrodynamic performance of planing hulls, increasing the independence of design parameters can reduce the complexity of the problem. In this study, a detailed analysis and formal transformation of the design parameters have been carried out. A series of non-dimensional shape coefficients are derived, which can independently control the geometric characteristics of the hull. These design parameters represent well-defined physical interpretations and hydrodynamic concepts, specifically targeting geometric characteristics that exhibit a significant impact on the performance of planing hulls. The design of shape coefficients takes advantage of the decimation characteristics of Bezier curves and provides flexibility in the selection of shape coefficients. 2. A bottom-up approach to hull frame design is developed. To this end, a system of equations is established based on the design parameters to solve the control points of the curves. Appropriate curve node vectors and curve discretization methods are set, which enhance the efficiency and quality of surface production. The resulting hull surface is of high accuracy and smoothness, which indicates the suitability of the B-spline approach for the parametric modeling of planing hulls. 3. An appropriate design program has been developed based on the parametric design method proposed in this article, which allows the rapid production of smooth and complete hull surfaces. By modifying the design parameters, the dimensions of the hull can be appropriately adjusted, or different shapes of the hull can be produced. The generation of different hull forms and the analysis of design parameters indicate that this design method provides ample design space and high degrees of freedom for the forms of monohull unstepped planing hulls. 4. In this study, all the curves and surfaces used can be expressed in the form of NURBS, which indicates their high universality.